HUNGARIAN JOURNAL OF INDUSTRY AND CHEMISTRY Vol. 46(2) pp. 1-100 (2018) hjic.mk.uni-pannon.hu Contents Tribological Behaviour of Polymers in Terms of Plasma Treatment: A Brief Review HAYDER AL-MALIKI AND GÁBOR KALÁCSKA 1-11 Application of 2N Design of Experiment Method for the Evaluation of the Efficiency and Cross-Effects of Oilfield Chemicals ZOLTÁN LUKÁCS AND TAMÁS KRISTÓF 13–17 Strong Reachability of Reactions with Reversible Steps ESZTER VIRÁGH AND BÁLINT KISS 19–25 Production of a Biolubricant by Enzymatic Esterification: Possible Synergism between Ionic Liquid and Enzyme ZSÓFIA BEDŐ, KATALIN BÉLAFI-BAKÓ, NÁNDOR NEMESTÓTHY, AND LÁSZLÓ GUBICZA 27–31 Comparison Between Static and Dynamic Analyses of the Solid Fat Content of Coconut Oil VINOD DHAYGUDE, ANITA SOÓS, ILDIKÓ ZEKE, AND LÁSZLÓ SOMOGYI 33–36 Monitoring of Chemical Changes in Red Lentil Seeds During the Germination Process ILDIKÓ SZEDLJAK, ANIKÓ KOVÁCS, GABRIELLA KUN-FARKAS, BOTOND BERNHARDT, SZABINA KRÁLIK, AND KATALIN SZÁNTAI-KŐHEGYI 37–42 Recovery of Itaconic Acid by Electrodialysis VERONIKA VARGA, KATALIN BÉLAFI-BAKÓ, DÁVID VOZIK, AND NÁNDOR NEMESTÓTHY 43–46 The Initial Magnetic Susceptibility of Dense Aggregated Dipolar Fluids SÁNDOR NAGY 47–54 Worker Movement Diagram Based Stochastic Model of Open Paced Conveyors TAMÁS RUPPERT AND JÁNOS ABONYI 55–62 Investigations into Flour Mixes of Triticum Monococcum and Triticum Spelta KATALIN KÓCZÁN-MANNINGER AND KATALIN BADAK-KERTI 63–66 Formation of Glycidyl Esters During the Deodorization of Vegetable Oils ERZSÉBET BOGNÁR, GABRIELLA HELLNER, ANDREA RADNÓTI, LÁSZLÓ SOMOGYI, AND ZSOLT KEMÉNY 67–71 Effect of Algae Treatment on Stevia Rebaudiana Growth RÉKA CZINKÓCZKY AND ÁRON NÉMETH 73–77 Comparison of Particle Size Distribution Models for Polymer Swelling ÁDÁM WIRNHARDT AND TAMÁS VARGA 79–84 Effects of Different Heat Treatments on the Chemical and Microbiological Characteristics of Egg-Free and Quail Egg Dried Pasta ILDIKÓ SZEDLJAK, VIKTÓRIA TÓTH, JUDIT TORMÁSI, ANIKÓ KOVÁCS, LÁSZLÓ SOMOGYI, LÁSZLÓ SIPOS, AND GABRIELLA KISKÓ 85–90 Optimal Design and Operation of Buffer Tanks Under Stochastic Conditions BÁLINT LEVENTE TARCSAY, ÉVA MIHÁLYKÓ-ORBÁN, AND CSABA MIHÁLYKÓ 91–100 HUNGARIAN JOURNAL OF INDUSTRY AND CHEMISTRY Vol. 46(2) pp. 1-11 (2018) hjic.mk.uni-pannon.hu DOI: 10.1515/hjic-2018-0011 TRIBOLOGICAL BEHAVIOUR OF POLYMERS IN TERMS OF PLASMA TREATMENT: A BRIEF REVIEW HAYDER AL-MALIKI ∗1 AND GÁBOR KALÁCSKA1 1Faculty of Mechanical Engineering, Mechanical Engineering PhD School, Szent István University, Páter Károly utca 1, H-2100 Gödöllő, HUNGARY A review to enrich the literature concerning the effect of various plasmas on the tribological behaviour of polymers and monitor the developments of plasma for the modification of polymer surfaces over recent decades using up-to-date data. A comparative study of plasmas was conducted to identify the most useful and efficient ones which facilitate optimal improvements with regard to the characterizations of polymer surfaces and tribological properties. The studies included in this review strongly suggest that (besides Plasma-Immersion Ion Implantation, PIII) atmospheric plasmas (dielectric barrier discharges, DBD) are an effective technique in terms of modifying the characterizations of polymer surfaces thereby enhancing the tribological behaviour of polymers under different operating conditions that extends the operating life of elements within the machine. Keywords: polymer, plasma treatment, surface characterization, tribology 1. Introduction The term tribology originates from two Greek words, namely τριβω (tribo), a verb which means “I rub”; and the suffix -logy which is derived from λωγια (logia) which can be translated as “study of” or “knowledge of”. This word was introduced by the British scientists Bow- den, Tabor [1] and Jost in 1964 [2]. Luke Mitchell, a professor of lubrication, observed the problems caused by increasing the level of friction exerted on machines [3]. Tribology is the science which studies the princi- ples and applications of friction, wear and lubrication [4]. Friction and wear are widespread phenomena in our daily lives. Processes that result in friction occur when moving surfaces are in contact with each other [5]. Fric- tion is a consequence of two main non-interacting com- ponents (adhesion and deformation) and can be consid- ered as an approach for all materials including polymers. Polymers are nonpolar materials that exhibit unique tri- bological behaviour, and some of them possess good self- lubrication characteristics, examples of which are stated in [6, 7]. The rapid development of industry was accom- panied by the urgent need to decrease the size of equip- ment which in turn leads to a higher degree of friction and enhanced rates of wear to be exerted on the elements of machines. This prompted the evolution of several surface- modification techniques, in particular for polymers, to di- minish the disadvantages of friction and wear. The alter- ation of surface properties such as hydrophilicity, chemi- cal composition and roughness lead to inevitable changes ∗Correspondence: haidrlatif@gmail.com in tribological behaviour which provided an opportunity for researchers to govern such behaviour with regard to polymers. Therefore, specific techniques have been de- veloped over the last few years to modify the surfaces of polymers to improve frictional behaviour and adhe- sive bonding performance. A lot of chemical and physical techniques have been developed to treat the surfaces of polymers. Chemical techniques are the processes which deal with wet or chemical reactions on surfaces, for in- stance, wet etching, grafting, acid-induced oxidation and plasma polymerization. Physical techniques deal with the modification of physical surfaces such as corona dis- charge, ion or electron beams, photon beams, plasma dis- charge and oxidizing flames [8]. Experimentally, the chemical treatments of polymer surfaces exhibit some disadvantages such as localized corrosion and environmental pollution. In contrast, phys- ical treatments have been adapted recently to modify the surface of polymers [9]. One of the most effective tech- niques to modify the surfaces of polymers are plasmas which facilitate changes in the properties of polymer sur- faces by several processes, for instance, cleaning, abla- tion, crosslinking and surface chemical functionalization [10]. Recently, plasma surface treatment was referred to as the most accepted method of modifying the surface of polymeric materials due to its remarkable stability con- cerning the enhancement of surface properties compared to conventional techniques, in particular, atmospheric plasma treatment which has the ability to operate under ambient atmospheric conditions (in terms of temperature haidrlatif@gmail.com 2 AL-MALIKI AND KALÁCSKA and humidity) and does not require a vacuum [9,11]. The literature often suggests that plasma treatment may im- prove the hydrophilicity of polymers [12–16], which has also been demonstrated in our previous works [17–19]. Even though plasmas often increase the surface rough- ness of polymers [15, 20, 21], some studies have proven that a decrease in surface roughness might occur after shorter treatment times [16, 22]. The present study attempts to review the tribological aspects of polymeric materials treated by various plas- mas and compared to their pristine surface behaviour by taking into consideration the influence of plasmas on the characteristics of polymer surfaces which vastly governs the tribological behaviour of polymers. Finally, plasma types that may currently be recommended to utilize and reinforce the tribological properties of polymers are high- lighted. 2. Plasma Modification of Plastic Surfaces Plasma can be defined as a chemically active media. The composition of plasmas varies depending on the way they are generated and their working power. Plasmas produce either low or very high temperatures and according to the heat they generate they can be termed as cold or thermal plasmas. Thermal plasmas, especially arc plasmas, were widely industrialized by the aeronautic sector in partic- ular. Cold plasma technologies have evolved in the mi- croelectronics industry, but they have a limited use due to their vacuum equipment. There have been many attempts to transpose plasmas to work under atmospheric pressure without the need for a vacuum. The research has led to various sources that are described in [23]. It is known that plasma is the fourth state of mat- ter and it is more or less an ionized gas that constitutes about 99 % of the universe. Plasma consists of elec- trons, ions and neutrons; these constituents may exist in fundamental or excited states. From a laboratory point of view, plasma is electrically neutral. However, it con- tains some free charge carriers thus is electrically conduc- tive [24, 25]. The degree of plasma ionization can range from small values, e.g. 10−4 − 10−6 for partially ionized gases to 100 % for fully ionized gases. In a laboratory, two types of plasma can be generated; the first are high- temperature plasmas which are also referred to as fusion plasmas, the second are low-temperature plasmas or gas discharges [26]. 2.1 Classification of plasmas Plasmas can be differentiated into several groups depend- ing on the energy supply and amount of energy trans- ferred to them since the properties of a plasma change de- pending on electronic density or temperature as presented in Fig. 1 [23]. There are two major plasma groups - the first are thermal equilibrium plasmas and the second are those not in thermal equilibrium. Plasmas that consist of Figure 1: 2D classification of plasmas (electron tempera- ture versus electron density) [28]. particles (electrons, ions and neutral species) of uniform temperature are known as thermal equilibrium plasmas, for instance, stars and fusion plasmas. Usually they are termed as “local thermodynamic equilibrium plasmas” which is abbreviated to LTE. High temperatures typically ranging from 4,000 K to 20,000 K are required to obtain thermal equilibrium plasmas. Otherwise, plasmas that are not in thermal equilibrium, abbreviated as non-LTEs, will be formed, for example, interstellar plasma matter [25]. LTE and non-LTE plasmas can be distinguished accord- ing to the gas pressure the plasma is subjected to. A high gas pressure is indicative of many collisions in the plasma and it could be argued that just a few collisions occur in the plasma when the gas pressure is low, for ex- ample, dielectric-barrier discharge and atmospheric pres- sure glow discharge plasmas. More details about types, sources and applications of plasmas can be found in [27]. 2.2 Influence of plasmas on the surface char- acteristics of polymers Different types of plasma treatments have exhibited po- tential changes in the physical and chemical surface char- acteristics of polymers. The variation in wettability is a fundamental parameter that controls adhesion, lubrica- tion and/or interactions with molecules. The formation of polar groups at the surface following plasma treat- ments, such as carbonyl, carboxyl and hydroxyl groups, enhances the surface energy. The enhancement of wet- tability following plasma treatment can be a combined effect of surface functionalization and an increase in sur- face roughness. When surface grafting occurs relatively quickly, an increase in surface roughness has mainly been observed following longer treatment times [21]. Depend- ing on the selection of adequate parameters, different types of plasma treatment are used for either enhancing as well as diminishing adhesion or surface hardness. Experimentally, Tóth et al. [29] observed a significant improvement in the surface hardness of ultra-high molec- ular weight polyethylene (UHMWPE) following nitrogen plasma ion implantation (NPII). The hydrogen plasma Hungarian Journal of Industry and Chemistry TRIBOLOGICAL BEHAVIOUR OF POLYMERS 3 Figure 2: F/C atomic ratio vs. voltage. immersion ion implantation (HPIII) treatment of the sur- face of UHMWPE induces amelioration in terms of the scratch resistance, temperature, mean surface roughness, oxygen content, and surface hardness, while the surface slope and elastic modulus often decreased, but it is possi- ble to enhance these characteristics upon treatment. Low values of temperature and mean roughness favour the re- duction of the surface slope [30]. In parallel, the nanome- chanical, chemical and wear properties of the UHMWPE surface have been significantly enhanced following treat- ment with helium plasma immersion ion implantation (HePIII). Over the ranges of the parameters, the surface hardness increased by up to six times, whereas the loss in volume following multipass decreased by up to about 2.5 times [31]. In a related study, the influence of nitrogen plasma immersion ion implantation (NPIII) on the surface of UHMWPE was investigated as well. The results sug- gested a relative increase in surface hardness, macro- scopic temperature and mean surface roughness, while the loss in volume decreased. However, the elastic modu- lus decreased or maybe even increased depending on the actual parameter set applied in the process. According to the parameter range studied, a reduction in wear rate is strongly dependent on thermal effects [32]. A statistical study by Tóth et al. [33] that revised the literature of engi- neering plastics treated by plasma-based ion implantation (PBII) and plasma-based ion implantation and deposition (PBIID) concluded that there is a rapidly trending in the number of related publications. As a consequence, the ef- fect of nitrogen plasma-based ion implantation (NPBII) on poly(tetrafluoroethylene) (PTFE) was discovered by Kereszturi et al. [34]. The study observed that the F/C atomic ratio significantly decreased in an inverse relation- ship with the voltage as shown in Fig. 2. Meanwhile the surface roughness increased inversely with the voltage and correlated directly with fluence as shown in Fig. 3. Figure 3: Mean surface roughness of PTFE vs. fluence and voltage. Although a clear relationship between wear volume and the main process parameters was not observed, in gen- eral this was improved following treatment along with an increase in surface roughness and O/C atomic ratio. Furthermore, the water contact angle recorded increased under low voltages and high fluences. Atmospheric dielectric barrier discharge (DBD) plas- mas enhance the wettability and surface roughness of polypropylene (PP) proportionally to an increase in the duration of plasma exposure [35]. Also, the surface roughness of PP increases linearly with the exposure time of atmospheric DBD plasma due to degradation of the polymer surface and the formation of nodule- like features. These nodules are shaped by highly oxi- dized short fragments of polymer which are referred to as low-molecular-weight oxidized materials (LMWOMs) in the literature [15]. In a subsequent study, Kostov et al. [36] reported that modifications in terms of the sur- face of different engineering plastics, such as polyethy- lene terephthalate (PET), polyethylene (PE) and PP could be achieved by atmospheric pressure plasma jets (APPJ). The primary aim of this research was to identify the op- timal treatment conditions as well as compare the ef- fect of APPJs on another source of atmospheric pres- sure plasmas, e.g., DBD on the characteristics of poly- mer surfaces. As a consequence of APPJ treatment the surface roughness is increased as shown in Fig. 4. How- ever, nodule-like structures were produced as well, but were much smaller compared to those constituted in the previous study when the polymer was treated by DBD. This was attributed to the higher degree of polymer degra- dation during DBD treatment. The adhesion strength of PP and perfluoroalkoxy alkanes (PFAs) has been signifi- cantly enhanced due to atmospheric plasma treatment un- der several gas flows. The characteristics of the surface introduced hydrophilic functional groups where the level 46(2) pp. 1-11 (2018) 4 AL-MALIKI AND KALÁCSKA Figure 4: AFM images of PP (a) untreated; (b) 30 s treated; (c) 30 s treated and washed; (d) 60 s treated; (e) 60 s treated and washed. All treatments were conducted with sample reciprocations using a signal amplitude of 10 kV, frequency of 37 kHz and Ar flow of 1.3 l/min. of improvement changed in proportion to the duration of the treatment as illustrated in Fig. 5 [37]. Although at- mospheric pressure glow (APG) discharge plasma treat- ment is moderate in terms of energy characteristics, APG- derived fluoropolymers exhibit similar surface properties under conventional low-pressure plasmas [38]. Treating metals and polymers by a cold arc-plasma jet under at- mospheric pressure leads to a superficial improvement in hydrophilicity and a decrease in the water contact angle of these materials as shown in Fig. 6 [39]. On the other hand, the literature shows that modifi- cations to the surface of aromatic polymers by dielectric barrier discharge (DBD) can achieve a substantial degree of chemical functionalization on the polymer surface by applying relatively low or intermediate levels of power without suffering severe topographical damage [40]. The surface modification of a PET film by an atmospheric- pressure plasma in combination with different gas flows promptly improved its hydrophilicity and was followed by hydrophobic recovery after longer durations [41]. In parallel, significant changes in the morphology and reac- tivity of PET surfaces have been observed [42,43]. When Figure 5: Effect of gas blowing on wettability of PFA film. Figure 6: Water contact angles of various materials after treatment. exposed to air the processing parameters, such as dis- charge power, processing speed, processing duration, and electrode configurations, affect the nature and scale of changes to the surface. In general, longer durations (low processing speed and a high number of cycles) and high levels of power induced greater changes in the surface wettability of the polymer [44]. Among the various environmental gases studied, air and oxygen yielded the highest levels of hydrophilicity, while argon and nitrogen resulted in lower degrees of hy- drophilicity of the PET surface [45]. Cold atmospheric- pressure plasmas (surface dielectric barrier discharge - SDBD) improve the oxygen and nitrogen contents of PET [46]. In comparison to PET, the effects of plasma treat- ment on polyether ether ketone (PEEK) have been studied less frequently, but also lead to enhanced degrees of hy- drophilicity and adhesion [47] due to the incorporation of functional groups and greater surface roughness follow- ing DBD [48]. The hydrophilicity, which is governed by the oxygenation of PEEK following DBD in the air, also recovered after several months through loss of the struc- turally related functional groups, but it remained more stable than other non-aromatic polymers [49]. Nylon 6 (PA6) exhibited a reduction in surface roughness, and an increase in the O/C and N/C ratios due to diffuse copla- nar surface barrier discharge (DCSBD) plasma treatment in two different gas flows (nitrogen and oxygen). How- ever, the oxygen DCSBD plasma was more efficient in terms of modifying the surface compared to the nitro- gen equivalent [16]. Also, plasma treatment enhances the contact angle and alters the surface topography of Nylon 66 (PA66) [50]. Plasma pre-treatment of the surface of the biopolymer Poly L Lactic Acid (PLLA) leads to the formation of pits in the crystalline phase accompanied by a mild increase in surface roughness [51]. Hungarian Journal of Industry and Chemistry TRIBOLOGICAL BEHAVIOUR OF POLYMERS 5 3. Tribology of Plasma-treated polymer surfaces 3.1 Friction of polymers Many studies have dealt with the tribology of polymers [52, 53]. Hardness and the elastic modulus are governed by the penetration depth, maximum load and strain rate [54]. Microcuttings are a consequence of ploughing, and they may exacerbate the friction force under specific con- ditions. Friction that results from elastic hysteresis is known as the deformation component [55, 56]. “The me- chanical component results from the resistance of the softer material to "ploughing" by asperities of the harder one” [57]. The adhesive bonds generated between the sur- faces in the frictional contact are referred to as the adhe- sion component. The adhesion component is higher than the deformation (mechanical) equivalent [58]. The fric- tion force is equal to the sum of the adhesion and defor- mation components as shown in Eq. 1 [59]. From this, the reason for polymer transferred layers forming on the metal counterface during frictional contact can be deter- mined. The transferred films are an essential factor which must be taken into consideration whilst estimating the tri- bological behaviour of polymers [53]. The effect of load, sliding velocity and temperature on friction are also im- portant parameters that could influence the tribological behaviour of the polymer: Ff=Fa+Fd [N] (1) where Ff represents the friction force, Fa the adhesion component, and Fd the deformation component of fric- tion. Under low loads, Ff ≈ Fa since Fd is far smaller than Fa. 3.2 Wear of polymers Wear is the undesirable removal of layers from the sur- face of a material. Wear occurs when two materials come into contact as a result of movement. Mechanical stress, temperature and chemical reactions directly influence the characteristics of the surface layer. Polymers are sensi- tive to these factors due to their particular structure and mechanical behaviour. The interface temperature can be significantly higher than the temperature of the environ- ment. The wear of some polymers, that were examined by Lancaster [60] whilst being slid against steel, was found to be influenced by temperature with regard to polymers that the pass is minimum at the characteristic tempera- ture. The accurate classification with regard to the wear of a polymer is not a trivial matter due to the highly di- verse nature of such mechanisms [53, 61, 62]. However, abrasion, adhesion and fatigue are the three most com- mon types of polymer wear that occur during the sliding process. Figure 7: Pin-on-disc tribological test system : 1) base frame, 2) pin holder, 3) loading head, 4) positioning rail, 5) rotating steel disc. 3.3 Tribological tests of polymers The tribological behaviour of a specific material is not in- herent of its properties as far as strength, elastic modulus, etc., are concerned. The influence of friction and wear on the overall performance of a polymer is strongly depen- dent on the entire configuration of the test. To evaluate the polymer under operating conditions that occur in actual structures, test configurations have to simulate the main sliding mode as accurately as possible in terms of system pair materials, contact geometry, contact pressure, sliding motion, sliding velocity, environmental conditions, me- chanical stiffness, etc. As a consequence, regular basis tribo-test systems are assembled from test apparatus that has yet to be standardized. Several parameters should be taken into consideration to select the most favourable test system, i.e. the structure of the material (macro- or microstructure), contact con- ditions (whether the contacting bodies possess the same radii of curvature as in a pin-on-disc test or different radii of curvature as in the ball-on-disc test), and energy dis- sipation (sliding temperature) [63]. The real tribosystem of the elements of a polymer is considered to be the most dependable test, however, due to its expense and imprac- tical nature the test cannot be conducted regularly. The scale of tribological tests varies from ‘field tests’ that consist of ‘large-scale simulation tests’ on real com- ponents to ‘laboratory tests’ on artificial samples which are widespread in the field of the tribological research of polymers due to the small apparatus used and their rela- tively low cost and versatility with regard to the testing of various materials under different test conditions, e.g. pin-on-disc Fig. 7). 3.4 Tribological behaviour of the surface of polymers treated by plasmas It is hard to accurately predict the effects of plasma surface treatment on the tribological behaviour of poly- mers, due to the multitude of mechanisms that govern such processes. It can be expected that functionalization, 46(2) pp. 1-11 (2018) 6 AL-MALIKI AND KALÁCSKA (a) (b) (c) Figure 8: Tribological behaviour of pristine and NPIII-treated PA6; (a) dry conditions; (b) water lubrication conditions; and (c) run-out lubrication conditions. crosslinking and chain scission will affect their chemical and mechanical surface properties after plasma treatment, which in turn will alter friction and wear characteristics. However, it cannot be confirmed whether such alterations lead to improved tribological properties or not, this can only be ascertained after the treated surface is tested. The tribological behaviour of rubber treated by plasma has been thoroughly investigated, indicating im- provements in terms of friction and wear resistance [13]. The pin-on-disc test yields the lower friction coefficient of PC and PP, whereas PE and PS exhibit larger coef- ficients of friction after atmospheric plasma treatment compared to their pristine surfaces. Bismarck et al. [64] attributed the significant decrease with regard to the fric- tion coefficient of PC either to the most substantial re- duction in contact angle or the changes in the chemical and simultaneously the physical properties of PC after treatment. On the other hand, the increase in the extent of crosslinking after atmospheric plasma treatment resulted in lower levels of friction and wear of PEEK composites [65], while argon plasma treatment led to a higher friction coefficient of PET [12]. The effects of Nitrogen plasma immersion ion im- plantation (NPIII) on PET indicated improvements with regard to scratch resistance [66]. Kalácska et al. [67] demonstrated that the benefits of sliding tribological properties are strongly dependent on the sliding condi- tions: a lower degree of friction and enhanced wear per- formance of PET treated by PIII only occurred in the presence of low pv factors under dry or water-lubricated sliding conditions. Five minutes of atmospheric plasma treatment is sufficient to reduce the coefficient of fric- tion and enhance the wear properties of a UHMW-PE film under a constant pv factor [68]. In contrast, UHMW-PE treated by atmospheric pressure gas plasma does not ex- hibit a significant change in terms of wear properties after a treatment time of two minutes. Since the level of wear reduced by half after longer treatment times, the duration a polymer is exposed to a plasma plays a major role with regard to the tribological properties of the treated surface, in particular for UHMW- PE [69]. UHMW-PE treated by a cold argon plasma using dielectric barrier discharge (DBD) supports such a find- ing since (under dry conditions) an increase in the friction coefficient with treatment time was observed whereas the wear volume reduced over the treatment time due to mod- ifications of its surface. Under normal saline (N-saline) lubrication conditions, wear volume and friction were re- duced over the treatment time which is indicative of an increase in surface wettability and, therefore, enhanced surface lubrication capability [70]. Sagbas [71] reported an increase in friction and improvement in the wear prop- erties of conventional UHMW-PE after plasma treatment, whereas the friction coefficient was unaffected in terms of Hungarian Journal of Industry and Chemistry TRIBOLOGICAL BEHAVIOUR OF POLYMERS 7 Figure 9: Tribological testing under dry sliding conditions at 0.5; 1; and 2 MPa; including online measurements of coefficients of friction, (specific wear and displacement ∆h), and temperature. vitamin-E-blended UHMW-PE under the same test con- ditions. However, the wear factor slightly decreased com- pared to the significant improvement with regard to the wear properties of conventional UHMW-PE as a conse- quence of the highly cross-linked nature of conventional UHMW-PE. According to the brief review above with regard to the effect of some plasmas on different polymers, the ability of plasmas to alter the surface characterization and thereby the tribological behaviour of polymers is un- questionable. However, the tribological behaviour of the treated surface depends on several factors such as the type of plasma, treatment method, exposure time, operat- ing mechanism and lubrication conditions amongst many other factors. Kalácska et al. [72] studied the tribological behaviour of PA6 treated by nitrogen plasma immersion ion implantation (NPIII) under different conditions (dry, water and oil lubrication) and various pressure velocity factors (pv). The results show that the friction coefficient and specific wear of treated PA6 are lower than that of the untreated one under dry sliding conditions and low pv factors, while the friction coefficient, specific wear and contact temperature of treated PA6 are higher than the pristine equivalent under high pv factors (Fig. 8a). On the other hand, the water lubricant reduces the ad- hesive component of friction after treatment, which was reflected in the fluctuation of the friction behaviour of the treated surface (Fig. 8b). However, under continuous oil lubrication, no difference could be detected between the treated and untreated parameters, therefore, the run-out type was preferred in terms of detecting such a differ- ence. Test conditions in terms of run-out oil lubrication exhibit a lower friction coefficient for treated PA6 than the pristine equivalent in the presence of low pv factors as a consequence of an increase in the dispersive compo- nent (Fig. 8c). In contrast, our last work [73] elaborated on the ef- fect of atmospheric DBD plasma on the tribological be- haviour of PET under various test conditions (3 “dry” normal load and “run-out lubrication” constant normal load conditions). The effect of DBD plasma treatment on the characterization of the surface was interpreted as an enhancement of the surface energy and reduction in the surface roughness due to the melting of surface asperi- ties. However, increasing the surface wettability induces higher coefficients of friction according to Archard’s the- ory of friction [74]. The dry tribological test yielded un- expected behaviour where the coefficient of friction of the treated surface was lower than the pristine equiva- lent under different pv factors. Also, the specific wear and the vertical deformation were enhanced. However, the interface temperature of the treated surface was higher than the untreated one (Fig. 9). The reduction in the co- efficient of friction can be theoretically attributed to the smaller contributions of a deformation component. In a related context, a “run-out” oil lubrication test yielded a lower coefficient of friction for the treated surface due to a rise in the surface energy after treatment, leading to a favourable enhancement with regard to the adsorption of the lubricant as shown in Fig. 10. By using the analy- sis and comparison of the previously reviewed studies, it can be said that atmospheric DBD plasma can be an ef- fective technique nowadays for the treatment of polymer surfaces that aims to reduce friction and improve wear under dry and run-out lubrication conditions under vari- ous pv factors, especially under lower ones compared to other techniques, e.g. NPIII. 4. Conclusion In conclusion, the reviewed research and results have ap- parently shown the capability of plasmas to modify the 46(2) pp. 1-11 (2018) 8 AL-MALIKI AND KALÁCSKA Figure 10: Tribological testing under lubricated sliding and “run-out” conditions at 0.5 MPa. surfaces of polymers which results in a change in the tri- bological properties of surfaces. However, the effect of plasmas depends on several factors such as the sources of plasmas, vacuum, temperature, pressure, etc. The essen- tial points concerning the tribological behaviour of poly- mers that are subjected to plasma treatment are summa- rized below: • Plasmas can efficiently alter the characterization of polymer surfaces by utilizing different sources such as APPJ, PIII, APG, PBII and DBD and various vacuums which results in the enhancement of sur- face wettability and an increase in surface rough- ness with few exceptions. Atmospheric DBD plasma can achieve the optimum surface configuration in a shorter time. • There is a paucity of studies which deal with the tri- bological behaviour of polymers in terms of plasma treatment. Most studies focused on the effect of plas- mas on the tribology of engineering polymers espe- cially PET, PA6, and in some cases PEEK. How- ever, no studies appear to deal with Polyolefins, ex- cept some studies which investigate the tribology of UHMW-PE for medical applications in particular. • UHMW-PE exhibits a higher coefficient of fric- tion and improvements in specific wear after plasma treatment under dry conditions where cross-linking plays a prominent role in terms of controlling the wear rate upon plasma treatment. However, the lu- bricated tribological test of UHMW-PE resulted in a lower coefficient of friction due to an increase in wettability. • The comparative investigation of engineering poly- mers treated by different plasmas under the same conditions (PA6 treated by NPIII and PET treated by atmospheric DBD) can explain the remarkable effect of atmospheric DBD plasma on the tribolog- ical behaviour of PET under dry conditions where the friction coefficient of PET remained lower than the pristine equivalent, whilst subjected to different pv factors. In contrast, PA6 can only sustain low pv factors if a low coefficient of friction is desired in the case of NPIII treatment. • With regard to the aforementioned comparative in- vestigation, atmospheric DBD plasma yielded a unique reduction in the friction coefficient of PET throughout the duration of the test under “run-out” oil lubrication conditions. 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These cross-effects can exhibit adverse or beneficial impacts and may modify the overall corrosiveness of the medium to a great extent. However, there is no standard proce- dure in order to evaluate the cross-effects, i.e. the extent to which the effect of one of the chemicals is modified by the addition of another. The 2N Design of Experiment (DoE) method provides a robust and simple statistical way to evaluate the change in efficiency of oilfield chemicals owing to the addition of other additives. The 2N DoE method can also be applied to other systems. In the present work the effects and cross-effects in systems consisting of a corrosion inhibitor, as well as an oxygen and a hydrogen sulphide scavenger are investigated and successfully demonstrated in a typical oilfield corrosion system with electrochemical corrosion monitoring methods. Keywords: oilfield chemicals, corrosion inhibitor, Design of Experiment 1. Introduction The chemical treatment of wet oils that are produced is a widely used method for mitigating unfavorable phe- nomena in the production, transportation and process- ing of crude oils: corrosion, scaling, emulsion forming, etc. On the way from the oil well to the refinery a vari- ety of oilfield treatment chemicals are added to the oil: corrosion and scale inhibitors, biocides, hydrogen sul- fide and oxygen scavengers (typically with wash waters), demulsifiers, anti-foam agents, etc. [1–4]. The effects of these chemicals are typically well defined in themselves, but the cross-effects, i.e. the influence on each other, are rarely discussed and even more rarely investigated, es- pecially in situ. The reason for this is rather complex. From a practical perspective, there is no standard or well- established procedure for such testing. From a theoretical standpoint, the evaluation of such tests, if any, is rather problematic because if the effects of factors are strongly correlated (i.e. one or more “cross-effects” are significant in the system) then the evaluation of the effects by usual means (i.e. least square model fitting [5–7]) is subject to a significant error, if not impossible. In order to formulate the problem, let us consider a dependent variable, y, e.g. the corrosion rate, and assume that it is a quantitative function of some other quantitative ∗Correspondence: lukacs600131@gmail.com independent variables: y = p1x1 + p2x2 + · · · + pnxn. (1) This is an uncorrelated multilinear model, that is, the (p1, · · · , pn) parameter set, the set of the factor coeffi- cients, is invariant throughout the whole (x1, ·, xn) model variable space. If the (p1, ..., pn) parameter set is depen- dent on the location in the model variable space then the following correlated multilinear model can be applied: y = p1x1 + p2x2 + · · · + pnxn + (2) +q1,2x1x2 + · · · + qn−1,nxn−1xn, where the q1,2, · · · qn−1,n coefficients represent the cross-effects coefficients (the effect of quadratic and higher order contributions is not discussed here). If the cross-effects are significant in a model, i.e. the coeffi- cients of the cross-effects are comparable to the coeffi- cients of the factors, then severe computational difficul- ties may occur, especially if a remarkable error (random or systematic) is superimposed on the measurement data. In such cases conventional parameter-fitting procedures generally fail to provide realistic and accurate model co- efficients. For the investigation of cross-effects, a viable tech- nique is the so-called 2N Design of Experiment (DoE) method. As this method is not widely used in the field of corrosion science and technology, its basic concepts are outlined in brief here. mailto:lukacs600131@gmail.com 14 LUKÁCS AND KRISTÓF In the methodology of the Design of Experiment tech- nique the independent variables are known as factors and the values of the factors are referred to as factor levels. The factor levels are fixed, discrete values (in contrast to the continuous range of the independent variables). The variance in the factor levels, if any, will be transformed into a variance of the dependent variable. The Design of Experiment methods are typically used in industrial quality assurance testing, where the fixed factor levels correspond to certain standardized levels of the factors that are assumed to influence a quality parameter (i.e. the dependent variable). In oilfield chemical performance tests a fixed value with regard to the factor of the “cor- rosion inhibitor” can be the concentration recommended by the supplier. Apart from the fixing of the factor lev- els, the general Design of Experiment schemes and the supporting mathematical apparatus basically do not dif- fer from conventional multilinear parameter fitting. How- ever, a special type of DoE, the 2N Design of Experi- ment method, possesses some noteworthy mathematical properties that make it especially applicable for studying cross-effects. In the 2N DoE method every factor possesses exactly two factor levels and they are normalized to −1 and +1. In some cases, if all the factors are quantitative, a fac- tor level of 0 exists in order to test the linearity of the model. With the normalization of the factor levels to −1 and +1, all the factors and cross-effects are orthogonal, i.e. independently calculable from each other. This is a great advantage, making the method applicable to study cross-effects. On the other hand, the normalization of the factor lev- els to the arbitrary −1 and +1 levels is costly. The coef- ficients of the factors and cross-effects, determined after the calculations, do not have any direct physical mean- ing, they can only be interpreted in terms of a comparison with one another and to the variance of the measurement data. A comparison of the factors and cross-effects with one another can yield a series of more and less significant effects and a comparison to the variance can provide in- formation on the statistical significance of the respective factor/cross-effect. Obviously, the value of the obtained factor and cross-effect coefficients is dependent on the chosen spread between the two factor levels, therefore, this choice must be made with careful consideration. For example, if effects and interactions of oilfield chemicals are investigated, then one of the factor levels would be proposed to be “no chemical added” (concentration = 0) and the other factor level would be termed as the chemi- cal added to the fluid within the recommended range. The purpose of this work was to demonstrate the ap- plicability of the 2N DoE method for studying the factors and cross-effects of oilfield chemicals in a suitably cho- sen model system. 2. Experimental The model system was chosen as a typical corrosion system, containing a carbon steel electrode in a well- buffered, slightly acidic electrolyte (0.1 M NaHSO4 + 0.1 M Na2SO4), which maintains a nearly constant corro- siveness and reduces the accumulation of solid corrosion products on the surface of the electrode which also im- proves the reproducibility of the tests. As the aim was to simulate the effects and cross-effects of oilfield chemical treatment additives (corrosion inhibitor, as well as hydro- gen sulfide and oxygen scavengers), 1 mM of Na2S was added to the solution. The carbon steel plates (three specimens) were ap- plied for three parallel runs in each measurement set. The specimens were abraded with emery paper and then degreased in acetone for one hour. Before each run the species were etched in 5 % HCl, degreased in an alka- line degreasing solution and etched in 5 % HCl again (all dippings lasted for a duration of 5 minutes). 600 cm3 of the solution was poured into a cylindrical test cell of 1000 cm3 in volume and a carbon steel plate electrode with a surface area of 17 cm2 was introduced into the cell, equipped with a silver/silver chloride (3.5 M) ref- erence electrode and two mixed metal oxide-coated tita- nium tube counter electrodes both 3 mm in diameter and 50 mm in length. The solution was not de-aerated and the measurements were conducted at room temperature (25 ◦C). The corrosion rate was determined by impedance measurements carried out at 1 kHz and 0.1 Hz with a 20 mV p-p amplitude AC signal superimposed on the cor- rosion potential, which was established to a satisfactorily stationary level (max. 1 mV/min drift) of no more than 10 minutes. The polarization resistance of the electrode was determined by subtracting the high-frequency resistance (solution resistance) from the low-frequency resistance. The measurements were conducted by an Electroflex EF- 430 potentiostat and a PicoScope 3403D oscilloscope. The results were cross-checked by a Metrohm potentio- stat. In order to simulate the components of a typical oilfield chemical treatment procedure, a commercial cor- rosion inhibitor (BPR 81100, Baker Hughes, 100 ppm), zinc acetate as a model compound for a hydrogen sul- fide scavenger at a concentration of 2 mM, and sodium metabisulfite (Na2S2O5) also at a concentration of 2 mM were added. All chemicals were of p.a. quality. The 2N DoE scheme is shown in Table 1 below. All experimental sets were repeated 3 times with different electrodes. 3. Results and Discussion The effect of three factors (a corrosion inhibitor, as well as hydrogen sulfide and oxygen scavengers) was studied on the polarization resistance (compensated for by the ohmic drop in the solution, see the previous Section) and the corrosion current. The relationship between the po- Hungarian Journal of Industry and Chemistry APPLICATION OF 2N DESIGN OF EXPERIMENT METHOD FOR OILFIELD CHEMICALS 15 Table 1: Levels of factors and cross-effects of factors in the DoE sets. Factors Factor cross effects Set # Corrosion inhibitor Hydrogen sulfide scavenger Oxygen scavenger Corrosion inhibitor × Hydrogen sulfide scavenger Corrosion inhibitor × Oxygen scavenger Hydrogen sulfide scavenger × Oxygen scavenger 1 -1 -1 -1 1 1 1 2 -1 -1 1 1 -1 -1 3 -1 1 -1 -1 1 -1 4 -1 1 1 -1 -1 1 5 1 -1 -1 -1 -1 1 6 1 -1 1 -1 1 -1 7 1 1 -1 1 -1 -1 8 1 1 1 1 1 1 larization resistance and the corrosion current was calcu- lated as: j0[A] = 1 2.303 ( b−1 a [V ] + b−1 c [V ] )−1 Rp[Ω] = 1 2.303 0.04[V ] Rp[Ω] , (3) with a typical value of ba = 0.06 V/decade and bc = 0.12 V/decade, furthermore,Rp is measured in Ohms and j0 in Amperes. The units of measurement are shown in square brackets. The Design of Experiment scheme is shown in Table 1 The scheme consists of 23 = 8 sets. The levels of inter- actions (cross-effects) are simply the product of the levels of the respective factors. The original assumption of the work was that the po- larization resistance and/or the corrosion current of the test specimen depend on the factors according to the fol- lowing model: YS = Y + ∑ f AfEf + ∑ i BiEi, (4) where YS stands for the value of the target function in the respective set (the polarization resistance or corro- sion current), Y denotes the total average of the same,Ef Table 2: Factors (in diagonal cells), cross-effect coeffi- cients and the variance of the measurement data for the evaluation of polarization resistance values. Values larger than the standard deviation are set in bold. Factors Corrosion inhibitor Hydrogen sulfide scavenger Oxygen scavenger Corrosion inhibitor 3.359 −1.086 −3.319 Hydrogen sulfide scavenger 0.022 −0.082 Oxygen scavenger −3.087 Standard deviation of measurement data 2.125 and Ei represent the level of the respective factor/cross- effect in the respective set (−1 or +1), andAf andBi are the values of the respective effect/interaction coefficients. The overall standard deviation of the measurement data was determined via σ(Y ) = √√√√ 1 S(J − 1) S∑ s=1 J∑ j=1 ( Ys,j − Y s )2 , (5) where S = 8 is the number of sets, J = 3 stands for the number of runs per set, Ys,j denotes the measurement re- sult (polarization resistance or the corrosion current) and Y s represents the average of the latter for a certain set. The results based on the model of Eq. 4 are included in Tables 2 and 3 for the polarization resistance and cor- rosion current, respectively. By comparing the coefficients in the tables above it is striking at first sight that – apart from the coefficient of the corrosion inhibitor factor, which possesses the great- est absolute value in both tables – there is great variation in the relative significance of the corresponding values. It could be expected that if a factor/cross-effect is more significant in the model describing the variations of the Table 3: Factors (in diagonal cells), cross-effect coeffi- cients and the variance of the measurement data for the evaluation of corrosion current values. Values larger than the standard deviation are set in bold. Factors Corrosion inhibitor Hydrogen sulfide scavenger Oxygen scavenger Corrosion inhibitor −9.06 · 10−4 7.39 · 10−4 8.71 · 10−4 Hydrogen sulfide scavenger −7.31 · 10−4 7.45 · 10−4 Oxygen scavenger −3.98× 10−4 Standard deviation of measurement data 4.55 · 10−4 46(2) pp. 13-17 (2018) 16 LUKÁCS AND KRISTÓF Table 4: Factors (in diagonal cells), cross-effect coeffi- cients and the variance of the measurement data for the evaluation of the logarithm of the polarization resistance values. Values larger than the standard deviation are set in bold. Factors Corrosion inhibitor Hydrogen sulfide scavenger Oxygen scavenger Corrosion inhibitor 0.275 −0.143 −0.266 Hydrogen sulfide scavenger 0.110 −0.117 Oxygen scavenger −0.110 Standard deviation of measurement data 0.172 polarization resistance, then the same factor/cross-effect will exhibit approximately the same relative significance in the model of the corrosion current. However, in this case great differences exist in terms of the relative sig- nificance. The coefficient of the factor concerning the hydrogen sulfide scavenger and its cross-effect with the oxygen scavenger are both negligible in the model of the polarization resistance ( Table 2) and much more signifi- cant (compared to the standard deviation of the measure- ment data in Table 3). This magnitude of the differences cannot simply be attributed to some changes with regard to the weighing of measurement data due to the recipro- cal transformation from the polarization resistance to the corrosion current (cf. Eq. 3 and raises doubts suggesting that the model in Eq. 4 is invalid. Eq. 4 suggests that the contribution of the additives (corrosion inhibitor and the scavengers) to the dependent variable is a linear function of the concentration. However, if it is taken into consider- ation that the effects of the additives are basically kinetic, then it can be implied that instead of the linear Eq. 4 a logarithmic approximation might exist: lnYS = lnY + ∑ f Af lnEf + ∑ i Bi lnEi, (6) which is in agreement with the general experience that the effects (activities) of components are proportional to the logarithm of concentration. By applying Eq. 6, the factors and cross-effect coefficients of the models for the polar- ization resistance and corrosion current will be identical apart from a multiplicator of (−1). The model-fitting results of Eq. 6 are shown in Table 4 for the polarization resistance data. From the results it can be concluded that the corrosion inhibitor has the great- est effect on the system and it increases the polarization resistance significantly. The hydrogen sulfide scavenger also decreases the corrosion rate in itself, but its applica- tion along with the corrosion inhibitor is less favorable. The use of an oxygen scavenger is not at all advisable under these conditions. 4. Summary The general aspects of the 2N Design of Experiment method and also a specific application for a chemical treatment model system were discussed. The effects and interactions of a corrosion inhibitor, as well as hydrogen sulfide and oxygen scavenger model compounds were studied. The linear model for these additives yielded con- troversial results, namely the fitting of the model on the polarization resistance data provided totally different re- sults to those on the corrosion current data. By applying the logarithmic model, the results are consistent and their interpretation straightforward. It has been proven that – by carefully selecting the appropriate mathematical model – the proposed method is applicable for the investigation of the effects and cross- effects of different oilfield treatment chemicals. Acknowledgement Present article was published in the frame of the project GINOP-2.3.2-15-2016-00053 (“Development of engine fuels with high hydrogen content in their molecular struc- tures (contribution to sustainable mobility)”). REFERENCES [1] Rahmani, Kh.; Jadidian, R.; Haghtalabb, S.: Eval- uation of inhibitors and biocides on the corrosion, scaling and biofouling control of carbon steel and copper–nickel alloys in a power plant cooling wa- ter system, Desalination, 2016 393(1), 174–185 DOI: 10.1016/j.desal.2015.07.026 [2] Barmatov, E.; Hughes, T.; Nagl, M.: Efficiency of film-forming corrosion inhibitors in strong hydrochloric acid under laminar and turbulent flow conditions, Corr. Sci., 2015 92, 85–94 DOI: 10.1016/j.corsci.2014.11.038 [3] Papavinasam, S.: Corrosion Control in the Oil and Gas Industry, Chapter 7 – Mitigation – Internal Cor- rosion (Elsevier, Amsterdam) 2014 p. 361 ISBN: 978-0-12-397022-0 [4] Song, G.-L.: The grand challenges in electrochemical corrosion research, Front. Mater., 2014 1(2), 1–3 DOI: 10.3389/fmats.2014.00002 [5] Giunta, A.A.; Wojtkiewicz Jr., S.F.; Eldred, M.S.: Overview of modern design of experiments meth- ods for computational simulations, Proceedings of 41st Aerospace Sciences Meeting and Exhibit 2003; Reno, NV; USA. AIAA 2003-0649 Hungarian Journal of Industry and Chemistry https://doi.org/10.1016/j.desal.2015.07.026 https://doi.org/10.1016/j.desal.2015.07.026 https://doi.org/10.1016/j.corsci.2014.11.038 https://doi.org/10.1016/j.corsci.2014.11.038 https://doi.org/10.3389/fmats.2014.00002 https://doi.org/10.3389/fmats.2014.00002 APPLICATION OF 2N DESIGN OF EXPERIMENT METHOD FOR OILFIELD CHEMICALS 17 [6] Garud, S.S.; Karimi, I.A.; Kraft, M.: Design of computer experiments: A review, Comput. Chem. Eng., 2017 106, 71–95 DOI: 10.1016/j.compchemeng. 2017.05.010 [7] Kemény, S.; Deák, A.: Kísérletek tervezése és kiértékelése [Design and Evaluation of Experiments, in Hungarian] (Műszaki Könyvkiadó, Budapest) 2002 ISBN: 978-963-2799-12 46(2) pp. 13-17 (2018) https://doi.org/10.1016/j.compchemeng. 2017.05.010 https://doi.org/10.1016/j.compchemeng. 2017.05.010 HUNGARIAN JOURNAL OF INDUSTRY AND CHEMISTRY Vol. 46(2) pp. 19-25 (2018) hjic.mk.uni-pannon.hu DOI: 10.1515/hjic-2018-0013 STRONG REACHABILITY OF REACTIONS WITH REVERSIBLE STEPS ESZTER VIRÁGH ∗1 AND BÁLINT KISS1 1Department of Control Engineering and Information Technology, Budapest University of Technology and Economics, Magyar Tudósok krt. 2, Budapest, 1117, HUNGARY The controllability of reactions is an important issue in the chemical industry. The control of reactions is of great practical interest in order to ensure the energy- and time-efficient production of compounds. This paper studies the dynamical models of some chemical reactions in order to verify their controllability with regard to a candidate input signal, namely the change in the ambient temperature of a reaction. Keywords: reversible reaction, strong reachability, controllability, Lie algebra 1. Introduction Chemical reactions are widely applied during the synthe- sis and transformation processes of organic compounds. The reaction mechanism and resulting products depend mainly on the concentrations of the species, the catalyst used, the ambient temperature, and the ambient pressure. If the values of these parameters are changed, one can obtain different products from the original ones but it is also possible to increase the productivity and energy- efficiency of the reaction. Hence the application of a proper feedback law to ensure the latter scenario may be envisaged. A study of the local controllability by considering the reaction rate coefficient as an input has been presented in Ref. [1]. The authors of Ref. [2] have also consid- ered the reaction rate coefficient as an input and extended the results by claiming that global controllability holds. The controllability of another control input, namely the dilution ratio, is studied in Ref. [3]. General conditions for strong reachability in the case of a temperature input were reported earlier in Ref. [4]. Moreover, the conditions of strong reachability for polymer electrolyte membrane fuel cells (PEMFC), controlled by concentrations, have also been analysed. The motivation to consider the con- centrations and temperature (or their rate of change) as input signals is due to the fact that these quantities can be easily modified efficiently by industrial equipment that is currently in use, thus these results can be used as a ba- sis to establish control laws to stabilize a desired reaction performance without major changes being made to the equipment used in production. The oxidation of acetone with hydroxylamine (the oximation reaction) was inves- tigated by Raman spectroscopy [5]. Knowing the mecha- ∗Correspondence: viragh.eszter@gmail.hu nism, the controllability is important for this reaction. Throughout this paper, the candidate variable for con- trol is the rate of change in the temperature Ṫ , i.e. the first time derivative of the ambient temperature. From a practical point of view, this is a simplification since the variable which can be changed externally, denoted by u, is not Ṫ but an algebraic expression involving u and other variables of the system as well. For the dynamics consid- ered in this paper it is always possible, however, to obtain the values of u as a function of Ṫ and other state vari- ables. The remaining part of this paper is organized as fol- lows. Sec. 2 briefly revisits the concepts related to the strong reachability of nonlinear dynamical systems and conditions of strong reachability. The differential equa- tions describing the dynamics of reactions are presented so that the rate of change in temperature is considered as the controlled input in Sec. 3. In Sec. 4 the strong reach- ability of the oximation reaction is studied. The systems in the case of acidic medium in Subsection 4.1 and in weakly basic medium in Subsection 4.2 are analyzed. In Ref. [4] a sufficient condition for strong reachabil- ity was given for reactions with general dynamics. In Sec. 5, the conditions for strong reachability are given, if the reaction also contains reversible steps. In the last section the conclusions of the paper are drawn. 2. Study of strong reachability Consider the following nonlinear dynamical system, given by the differential equation: ξ̇ = f(ξ) + g(ξ)u, ξ(0) = ξ∗ ∈ Rn, (1) where f, g ∈ C∞(Rn,Rn) are smooth vector fields and u ∈ R is the control-input variable. The vector fields mailto:viragh.eszter@gmail.hu 20 VIRÁGH AND KISS f and g are often referred to as drift and control vector fields, respectively. For the sake of completeness, let us revisit some definitions used in Refs. [4, 6]. Definition 1 (Reachability set). Consider the system given by Eq. 1. The set R(ξ∗, t) ⊂ Rn is referred to as the reachability set from the point ξ∗ at time t and it is the union of values at t of the solutions to Eq. 1 for some admissible input function u with the initial condi- tion ξ(0) = ξ∗. Definition 2 (Strong reachability). The system Eq. 1 is referred to as strongly reachable from the point ξ∗, if the setR(ξ∗, t) has an interior point for all t > 0. Definition 3 (Lie bracket). Suppose that f ∈ C∞(Rn,Rn) and g ∈ C∞(Rn,Rn), then the Lie bracket of the vector fields f and g is [f, g] = Dg f −Df g. (2) The operator adng f : C∞(Rn,Rn) × C∞(Rn,Rn) → C∞(Rn,Rn) is defined as: ad0 gf = f, adng f = [g, adn−1g f ]. (3) Definition 4 (Lie algebra). Consider the vector fields f, g ∈ C∞(Rn,Rn). The Lie algebra generated by f and g is denoted by Λ = Lie(f, g) and is the smallest lin- ear subspace of C∞(Rn,Rn) that satisfies the following conditions: 1. f , g ∈ Λ , 2. for any a, b ∈ Λ, [a, b] ∈ Λ. It should be noted that Λ also defines a distribution. Definition 5 (Distribution). The distribution ∆ is the op- erator which assigns a linear subspace of RN to ∀x ∈ RN . Definition 6 (Controllability distribution). The controlla- bility distribution ∆c of Eq. 1 is the smallest distribution which satisfies the following conditions: 1. g ∈ ∆c, 2. ∆c is invariant to the vector field f (∀η ∈ ∆c, [η, f ] ∈ ∆c), 3. ∆c is involutive (∀η1, η2 ∈ ∆c, [η1, η2] ∈ ∆c). The controllability distribution has a subspace spanned by vector fields g and [f, g]. The following theo- rem is a fundamental result used in Ref. [6]. Theorem 1 (Reachability rank condition). Consider the controllability distribution ∆c of Eq. 1. The sys- tem Eq. 1 is strongly reachable at point ξ∗ ∈ Rn if dim{∆}c (ξ∗) = n. 3. Strong reachability of kinetic equations The active control of chemical processes may be nec- essary to maximize the amount of target products and minimize the amount of by-products. To achieve such a control objective, a suitable input variable must be se- lected so that the resulting dynamical system is control- lable from that input. To check if this requirement is sat- isfied, the tools introduced in the previous section will be applied to the equations describing the reaction dynam- ics. Consider a system of R reaction steps and with M species (R,M > 0). By borrowing notational conven- tions from chemistry, each reaction step can be generally defined by M∑ m=1 α(m, r)X(m) kr−−→ M∑ m=1 β(m, r)X(m), r = 1, 2, . . . , R, (4) where α(·, r) = (α(1, r), α(2, r), . . . , α(m, r))T denotes the reactant complex vector, β(·, r) = (β(1, r), β(2, r), . . . , β(m, r))T represents the product complex vector, X(m) is themth species and kr is the re- action rate coefficient of the rth reaction step. The species on the left-hand side of Eq. 4 are referred to as reactant species and reactant complexes refer to their formal lin- ear combinations. Similarly, one may find the products and their linear combinations (product complexes) on the right-hand side of the reaction described in Eq. 4. Let us also define the stoichiometric matrix, denoted by γ. The matrix γ consists of R columns and M rows, such that each column is obtained by γ(·, r) = β(·, r)− α(·, r). (5) Eq. 4 defines the reaction but it does not specify its mass action kinetics. However, in order to study the controlla- bility, the differential equations of the reaction dynamics need to be obtained in the form of differential equation Eq. 1. These equations are obtained from the heat bal- ance [7–9] of reaction Eq. 4 as ẋm = R∑ r=1 γ(m, r)krx α(·, r) m = 1, 2, . . . ,M, (6) Ṫ = R∑ r=1 1 βr,0 krx α(·, r) + u, (7) where xm denotes the concentration of species m, T is the temperature, and xα(·, r) = ∏M p=1 x α(p, r) p . Re- call that the single input u appears in the expression of Ṫ . The state vector ξ for the dynamics Eqs. 6–7 reads ξ = (x1, x2, . . . , xm, T )T . The reaction rate coefficient kr can be given as kr = kr,0e − Er R0T (8) Hungarian Journal of Industry and Chemistry STRONG REACHABILITY OF REACTIONS WITH REVERSIBLE STEPS 21 where kr,0, Er, R0 ∈ R+. To study reachability, one has to determine the num- ber of linearly independent Lie brackets spanning the Lie algebra generated by the vector fields g and adgf . Thanks to the special structure of the reaction dynamics, the lin- ear independence can be examined by factorizing the ma- trix of Lie brackets and checking the rank of the factors. First, let us define the reaction dynamics matrix: Definition 7 (Reaction dynamics matrix DR). Introduce the notation k (i) j := ∂i ∂T i kj i, j ∈ {1, 2, . . . , R} (9) The matrix of sizeR×R of the derivatives of the reaction rate coefficient defined as DR =  k (1) 1 k (2) 1 . . . k (R) 1 k (1) 2 k (2) 2 . . . k (R) 2 ... ... . . . ... k (1) R k (2) R . . . k (R) R  (10) is referred to as the reaction dynamics matrix. The following Lemma and Theorem have been shown in Ref. [4]. They are also provided here for completeness. Lemma 1. Consider a reaction with R steps. Suppose that the activation energies E1, E2, . . . , ER of the reac- tion steps are all different and strictly positive, then the reaction dynamics matrix DR is of full rank for every T > 0. Theorem 1 cannot be applied directly to the reaction dynamics Eq. 6–7, because the right-hand sides (RHS) of some equations in Eq. 6 may be linearly dependent. Let δ denote the number of linearly dependent RHSs in Eq. 6. The system of chemical reactions is considered to be strongly reachable from a point ξ∗ ∈ RM+1 if and only if the dimension of the controllability distribution is M − δ+ 1. The additional dimension is due to Eq. 7 with the temperature T as an additional variable. Using Theorem 1, the controllability subspace for par- ticular reactions can be deduced, so the conditions for strong reachability of the reactions can be determined. Theorem 2. Consider a reaction with M species and R reaction steps. Suppose that the activation energies E1, E2, . . . , ER of the reaction steps are all different and strictly positive. Then the reaction dynamics with the tem- perature change (Ṫ ) as an input variable are strongly reachable if the concentrations of all reactant species are positive. Theorem 2 provides a condition for the strong reach- ability of reactions in a general form. However, for some reactions where the reaction dynamics have additional properties, weaker conditions may be sufficient to ensure strong reachability. In Sec. 4, the strong reachability con- ditions in the case of oximation reactions were investi- gated. 4. Controllability study of the oximation re- action The oxidation of acetone with hydroxylamine was inves- tigated by Raman spectroscopy in Ref. [5]. The reaction is strongly exothermic and the concentration of the inter- mediate highly depends on the pH and temperature. The process can be hazardous, however, it is not dangerous to run in a laboratory with low concentrations and in a con- trolled manner. Strong reachability is a necessary condi- tion to be able to control the reaction. 4.1 Oximation reaction in acidic medium In oximation reactions, the sequence (number and nature) of reaction steps depends on the pH. The equations of the reaction steps are different in acidic and weakly basic media. In the case of acidic media the reaction takes place over two reaction steps as given by For the sake of notational simplicity, the symbols A, B, C, D, E, and F will denote the species such that the two reaction steps above read: A + B k1−−→ C (11) C + D k2−−→ E + F. (12) Let us denote the concentrations of the species by a, b, c, d, e, f ≥ 0. It is assumed that the reaction rate coefficients k1, k2 > 0. Theorem 2 implies that the reaction is strongly reach- able, provided that the conditions are met. It follows from strong reachability that it is possible to arrive at any con- centrations of M − δ species and at any temperatures by suitable manipulation of the input. Recall that there is no guarantee that such concentrations and temperatures also define a steady-state for the system. Note that Theorem 2 only provides a sufficient condi- tion for strong reachability. For chemical reactions, the positivity condition of activation energies is almost al- ways satisfied. Considering the reaction steps of the ox- imation reaction in acidic media the two remaining con- ditions of strong reachability will be studied: (1) the pos- itivity of the concentration of all reactant species; (2) the distinctness of activation energies. Let us now suppose that the system in Eqs. 11–12 is strongly reachable. The stoichiometric matrix for the re- 46(2) pp. 19-25 (2018) 22 VIRÁGH AND KISS action steps reads: γ =  −1 0 −1 0 1 −1 0 −1 0 1 0 1  (13) and it is easy to verify that δ = 2 in this case. The differ- ential equation of the reaction: ȧ ḃ ċ ḋ ė ḟ Ṫ  =  −k1ab −k1ab k1ab− k2cd −k2cd k2cd k2cd k1 β ab+ k2 β cd  +  0 0 0 0 0 0 1  u = = f(ξ) + g(ξ)u (14) is in a form similar to Eq. 1, where ξ = (a, b, c, d, e, f, T )T and the vector field g(ξ) is constant. Since the rank of the stoichiometric matrix γ is 2 and the temperature is a scalar quantity, Theorem 1 im- plies that the system is strongly reachable if dim{∆}c = 2 + 1 = 3. Hence, to study strong reachability, the num- ber of linearly independent vector fields spanning the Lie algebra generated by the vector fields adgf and g must be determined. The Lie brackets adgf and ad2 gf read: ad(i) g f =  −k(i)1 ab −k(i)1 ab k (i) 1 ab− k(i)2 cd −k(i)2 cd k (i) 2 cd k (i) 2 cd k (i) 1 β ab+ k (i) 2 β cd  , (15) where i ∈ {1, 2}. To study the dimension of the controllability distribu- tion ∆c one has to determine the rank of the matrix whose columns are g, adgf and ad2 gf which reads: ( adgf ad2 gf g ) = =  −k(1)1 ab −k(2)1 ab 0 −k(1)1 ab −k(2)1 ab 0 k (1) 1 ab− k(1)2 cd k (2) 1 ab− k(2)2 cd 0 −k(1)2 cd −k(2)2 cd 0 k (1) 2 cd k (2) 2 cd 0 k (1) 2 cd k (2) 2 cd 0 k (1) 1 β ab+ k (1) 2 β cd k (2) 1 β ab+ k (2) 2 β cd 1  . (16) The last row is linearly independent of all other rows in the matrix of Eq. 16, hence, by deleting the last row and column from the matix, the rank will be decreased by 1. The remaining matrix is denoted by Θ and defined as Θ =  −k(1)1 ab −k(2)1 ab −k(1)1 ab −k(2)1 ab k (1) 1 ab− k(1)2 cd k (2) 1 ab− k(2)2 cd −k(1)2 cd −k(2)2 cd k (1) 2 cd k (2) 2 cd k (1) 2 cd k (2) 2 cd  . (17) It is clear that the condition dim{∆c} = 3 holds true if and only if rank(Θ) = 2. It is easy to see that the matrix Θ can be factorized as Θ =  −ab 0 −ab 0 ab −cd 0 −cd 0 cd 0 cd  ( k (1) 1 k (2) 1 k (1) 2 k (2) 2 ) = A ·D2. (18) The condition of rank(Θ) = 2 can hold true if and only if the matrices A and D2 are of full rank according to the multiplication theorem of determinants. Matrix A is of full rank (rank(A) = 2) if and only if a 6= 0, b 6= 0, c 6= 0 and d 6= 0. The reaction dynamics matrix D2 is of full rank if and only if there is no constant c ∈ R \ {0} such that k(2)1 = ck (1) 1 and k(2)2 = ck (1) 2 , hence k (2) 1 k (1) 1 = k (2) 2 k (1) 2 (= c) (19) cannot be true. Recalling that the reaction rate coeffi- cients are kr = kr,0e − Er R0T (kr,0, Er, and R0 are positive constants), it is easy to determine the time derivatives: k(1)r = ( Er R0T 2 ) kr,0e −Er R0T , (20) k(2)r = kr,0 ( E2 r R2 0 T 4 − 2Er R0 T 3 ) e −Er R0T . (21) The ratios of the first- and second-order time derivatives are obtained as k (2) r k (1) r = kr,0 ( E2 r R2 0 T 4 − 2Er R0 T 3 ) e −Er R0T( Er R0T 2 ) kr,0e −Er R0T = Er − 2R0T R0T 2 . (22) Based on Eq. 22, the equality in Eq. 19 holds true if and only if E1 = E2. As a result it has been proven that if the reaction dynamics are strongly reachable then the concentrations a, b, c and d are positive and E1 6= E2. Thus the condi- tions of Theorem 2 are also necessary for strong reacha- bility in the case of oximation reactions in acidic media. 4.2 Oximation reaction in weakly basic medium In the case of weakly basic media the reaction occurs ac- cording to the reaction steps given by: Hungarian Journal of Industry and Chemistry STRONG REACHABILITY OF REACTIONS WITH REVERSIBLE STEPS 23 Since the specific chemical compositions of the species are irrelevant to the controllability analysis, the symbols A, B, C, D, E, F, and G will denote the species such that the above reaction steps read: A + B k1−−→ C, (23) C k2−−→ D + E, (24) D + F k3−−⇀↽−−− k−3 G + E. (25) Let us denote the concentration of the species by a, b, c, d, e, f , g ≥ 0. It is assumed that the reaction rate coeffi- cients are strictly positive: k1, k2, k3, k−3 > 0. Recall that Theorem 2 only provides a sufficient con- dition for strong reachability. By considering oximation reactions in weakly basic media the remaining conditions of strong reachability will be studied. Let us suppose now that the system of Eqs. 23–25 is strongly reachable. The stoichiometric matrix for the re- action steps reads: γ =  −1 0 0 0 −1 0 0 0 1 −1 0 0 0 1 −1 1 0 1 1 −1 0 0 −1 1 0 0 1 −1  . (26) The differential equation of the reaction ȧ ḃ ċ ḋ ė ḟ ġ Ṫ  =  −k1ab −k1ab k1ab− k2c k2c− k3df + k−3ge k2c+ k3df − k−3ge −k3df + k−3ge k3df − k−3ge k1 β ab+ k2 β c+ k3 β df + k−3 β ge  + +  0 0 0 0 0 0 0 1  u = f(ξ) + g(ξ)u (27) is in a form similar to Eq. 1, where the vector field g(ξ) is constant and ξ = (a, b, c, d, e, f, g, T )T . Since the rank of the stoichiometric matrix γ is 3 and the temperature is a scalar quantity, Theorem 1 implies that the system is strongly reachable if dim{∆}c = 3 + 1 = 4. Hence, the number of linearly independent vector fields spanning the Lie algebra generated by the vector fields adgf and g must be determined. The Lie–brackets adgf , ad2 gf and ad3 gf read: adigf =  −k(i)1 ab −k(i)1 ab k (i) 1 ab− k(i)2 c k (i) 2 c− k(i)3 df + k (i) −3ge k (i) 2 c+ k (i) 3 df − k(i)−3ge −k(i)3 df + k (i) −3ge k (i) 3 df − k(i)−3ge k (i) 1 β ab+ k (i) 2 β c+ k (i) 3 β df + k (i) −3 β ge  , (28) where i ∈ {1, 2, 3}. To study the dimensions of the controllability distribution ∆c one has to give the rank of the matrix whose columns are adgf , ad2 gf , ad3 gf , and g:( adgf ad2 gf ad3 gf g ) . (29) The last row is linearly independent of all other rows in matrix Eq. 30, hence, by deleting the last row and column from the matrix, the rank will be decreased by 1. The remaining matrix is denoted by Θ and defined as Θ =   −k(i)1 ab −k(i)1 ab k (i) 1 ab− k(i)2 c k (i) 2 c− k(i)3 df + k (i) −3ge k (i) 2 c+ k (i) 3 df − k(i)−3ge −k(i)3 df + k (i) −3ge k (i) 3 df − k(i)−3ge  i=1,2,3  (30) The condition dim{∆}c = 4 holds true if and only if rank(Θ) = 3. It is easy to see that the matrix Θ can be factorized as Θ = A ·D = −ab 0 0 0 −ab 0 0 0 ab −c 0 0 0 c −df ge 0 c df −ge 0 0 −df ge 0 0 df −ge   k (1) 1 k (2) 1 k (3) 1 k (1) 2 k (2) 2 k (3) 2 k (1) 3 k (2) 3 k (3) 3 k (1) −3 k (2) −3 k (3) −3  (31) The condition rank(Θ) = 3 can hold true only if rank(A) ≥ 3 and rank(D) ≥ 3. T he 3rd and 4th columns in matrix A are linearly dependent, thus rank(A) ≤ 3. The condition rank(A) = 3 can hold true only if the concentrations a, b, and c as well as the 46(2) pp. 19-25 (2018) 24 VIRÁGH AND KISS concentrations d and f , or the concentrations g and e are strictly positive. Matrix D is of full rank only if D con- sists of a 3 × 3 times full-rank matrix. Lemma 1 implies that the reaction dynamics matrix D3 is of full rank if the activation energies are different. Hence, matrix D is of full rank, if 3 different activation energies exist. The system was proven to be strongly reachable if 3 of the activation energies are all different and concentrations a, b, c and d, f , or g, e are positive. Thus a condition for strong reachability coule be given more precisely in the case of oximation reaction in weakly basic media. 5. Reversible reaction step For reactions of general types, Theorem 2 provides a con- dition for strong reachability. However, it will be shown that if the reaction contains one or more reversible steps, weaker conditions are sufficient for strong reachability. The concentrations are defined by x1, x2, . . . , xM , as in the previous sections. The notationA is introduced for the matrix describing the effect of concentrations: A := γ diag(xα(· ,1), xα(·, 2), . . . , xα(·, R)), (32) where xα(·,r) = ∏M m=1 x α(m, r) m and γ is the stoichio- metric matrix as introduced by Eq. 5. The vector k = (k1, k2, . . . , kR)T is composed of the reaction rate coef- ficients. The notation D is introduced for the following matrix composed of the derivatives of reaction rate coef- ficients: D := ( k(1) k(2) ... k(rank(γ)) ) . (33) Lemma 2. The reaction dynamics in Eqs. 6–7 with the input variable Ṫ are strongly reachable, if rankγ = rank(AD), where γ is the stoichiometric matrix and A and D are defined as above. Proof The differential equation of the reaction reads: ( ẋ Ṫ ) =  v R∑ r=1 kr βr,0 xα(·, r) + ( 0 1 ) u, (34) where ẋ = (ẋ1, ẋ2, . . . , ẋM )T , u is the control input and the vector field v stands for the vector composed of the right-hand sides of Eq. 6. As in the previous sections, the study of strong reach- ability means verification of the dimension of the control- lability distribution ∆c. The dimension of the controlled input (the dimension of the change in temperature) is 1, thus, Theorem 1 implies that the system is strongly reach- able if and only if dim{∆}c = rank(γ) + 1. The vector fields spanning the controllability distri- bution are g and adigf for i > 0. The Lie bracket adigf reads: adigf=  v(i) R∑ r=1 k (i) r βr,0 xα(·, r) =  A · k(i) R∑ r=1 k (i) r βr,0 xα(·, r)  (35) for i ∈ {1, 2, . . . , rankγ}. The rank of the controllability distribution is hence the rank of the matrix( adgf ad2 gf . . . adrankγ g f g ) = A · k(1) . . . A · k(rankγ) 0 R∑ r=1 k (1) r βr,0 xα(·, r) . . . R∑ r=1 k(rankγ) βr,0 xα(·, r) 1  (36) The last row in Eq. 36 is linearly independent of the oth- ers, hence, the same reasoning as earlier is followed and the last row and columns are eliminated, thus, decreasing the rank by one. The resulting matrix is denoted by Θ and reads: Θ = ( A · k(1) A · k(2) . . . A · k(rankγ) ) = = AD. (37) Since the dimension of the controllability distribution is rank(Θ) + 1, the reaction dynamics are strongly reach- able if rankγ = rankΘ or if rankγ = rank(AD). Theorem 3. Consider the reaction dynamics Eqs. 6–7 such that the activation energies E1, E2, . . . , ER are positive and different in pairs. Suppose that the concen- trations of reactant species are positive in the case of one- way reaction steps and at least one of the ways is positive in the case of reversible reaction steps. Then, the reaction dynamics controlled by Ṫ are strongly reachable. Proof If the system does not contain reversible reaction steps, Theorem 2 is obtained. Without loss of generality, it can be supposed that the system contains one reversible reaction step. This step can be replaced by pairs of irreversible reaction steps, with reaction rate coefficients denoted by ke and k−e. The changes in the concentrations are equal in the reac- tion step with rate coefficient ke and in the reaction step with rate coefficient k−e, only the direction is different. Thus, the two columns in matrix γ for the reversible re- action steps are always linearly dependent. Lemma 2 im- plies that the system is strongly reachable if and only if rankγ = rank(AD). If the activation energies are pos- itive and all different, Lemma 1 implies that matrix D is of full rank. The matrix A is defined by Eq. 32, thus, the columns for ke and k−e are linearly dependent. The column for ke contains the factor of the concentrations of the reactant species in the transformation step and k−e contains the factor of the concentrations of the re- actant species in the transformation step in the opposite direction with the arbitrary sign in the place of non-zero elements. By substituting one of the two vector fields with a zero vector field, the rank of matrix A remains unchanged. Thus, in the case of reversible reactions for strong reachability, it is sufficient if the reactant species have positive concentrations only in one of the directions, and the activation energies are positive and all different. Hungarian Journal of Industry and Chemistry STRONG REACHABILITY OF REACTIONS WITH REVERSIBLE STEPS 25 6. Conclusion The reaction dynamics of strong reachability where the control variable is selected as the rate of change in the ambient temperature (Ṫ ) have been studied. First, the strong reachability was analyzed in the case of the oxi- mation reaction. Since the processes depend on the pH, conditions that facilitate strong reachability in acidic as well as weakly basic media were studied. For our anal- ysis, Theorem 2 was used. It provides sufficient condi- tions to facilitate strong reachability, however, these con- ditions are not always necessary. It was proven that the conditions in Theorem 2 are necessary to facilitate strong reachability of the oximation reaction in the case of acidic media. In weakly basic media, the system contained a re- versible reaction step, thus, the conditions of Theorem 2 could be determined. Strong reachability has also been studied for reaction dynamics of a general type that contain at least one re- versible reaction step where the conditions of Theorem 2 could also be further refined. For reversible reaction steps it has been shown that positive reactant concentrations are unnecessary to facilitate strong reachability in both direc- tions of the reversible steps, in one direction is sufficient. Acknowledgement The chemistry-related comments from Zsombor Kristóf Nagy and György Marosi at the BME Department of Or- ganic Chemistry and Technology are gratefully acknowl- edged. REFERENCES [1] Farkas, G.: Local controllability of reac- tions, J. Math. Chem., 1998 24, 1–14 DOI: 10.1023/A:1019150014783 [2] Drexler, D.A., Tóth, J.: Global controllability of chemical reactions, J. Math. Chem., 2016 54, 1327– 1350 DOI: 10.1007/s10910-016-0626-7 [3] Dochain, D., Chen, L.: Local observability and con- trollability of stirred tank reactors, J. Math. 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Theory and applications of deterministic and stochastic models (Princeton University Press, Princeton, New Jersey), 1989 ISBN: 9780719022081 [8] Turányi, T., Tomlin, A.S.: Analysis of Kinetic Reac- tion Mechanisms (Springer Berlin Heidelberg), 2014 ISBN: 9783662445624 [9] Atkins, P.W.: Physical Chemistry (Oxford University Press), 2010 ISBN: 9780199543373 46(2) pp. 19-25 (2018) https://doi.org/10.1023/A:1019150014783 https://doi.org/10.1023/A:1019150014783 https://doi.org/10.1007/s10910-016-0626-7 https://doi.org/10.1016/0959-1524(92)85003-F https://doi.org/10.1016/j.fuel.2017.09.095 https://doi.org/10.1016/j.fuel.2017.09.095 https://doi.org/10.1021/op500015d https://doi.org/10.1007/978-1-84628-615-5 HUNGARIAN JOURNAL OF INDUSTRY AND CHEMISTRY Vol. 46(2) pp. 27–31 (2018) hjic.mk.uni-pannon.hu DOI: 10.1515/hjic-2018-0014 PRODUCTION OF A BIOLUBRICANT BY ENZYMATIC ESTERIFICATION: POSSIBLE SYNERGISM BETWEEN IONIC LIQUID AND ENZYME ZSÓFIA BEDŐ1, KATALIN BÉLAFI-BAKÓ1, NÁNDOR NEMESTÓTHY1, AND LÁSZLÓ GUBICZA *1 1Research Institute of Bioengineering, Membrane Technology and Energetics, University of Pannonia, Egyetem u. 10, Veszprém, 8200, HUNGARY The possible replacement of lubricants with fossil-fuel sources and the manufacture of biolubricants with more beneficial features were studied. Oleic acid and isoamyl alcohol were reacted with an enzyme in an ionic liquid. During the reaction conventional as well as microwave heating was applied. After the experimental determination of the optimal reaction parameters, it was unexpectedly found that a synergistic effect occurred by applying ionic-liquid and microwave-heat treatment simultaneously. The enzyme exhibited a much higher level of activity than the value expected based on the measurements carried out separately by using an ionic liquid instead of an organic solvent and microwave-heat treatment or a conventional method. In the experiments with recycled enzyme it was found that ionic liquid maintained the enzyme more effectively, as if it was immobilized by it: the enzyme managed to maintain its activity and recycling ability. Keywords: synergistic effect, ionic liquid and microwave heating, biolubricant production, enzyme reuse 1. Introduction Lubricants from mineral oils have a considerable detri- mental effect on the environment due to the aromatic or- ganic compounds within their chemical structures. Min- eral oils that have leached into water or soil are toxic for living organisms, they substantially decrease the level of dissolved oxygen in the water. These lubricants can hardly be degraded biologically. During their manufac- ture several by-products form and further additives are needed for the lubricants. Hence the demand for bi- olubricants from plant oils has been growing recently, since they are natural, renewable, non-toxic as well as environmentally-friendly compounds, and often cheaper than synthetic oils. Therefore, they are suitable for elim- inating the disadvantages of mineral oil, moreover, our dependence on mineral oils and other non-renewable sources might be decreased [1, 2]. The production of synthetic and semi-synthetic lubri- cants is necessary since now it is not possible to conduct all lubrication tasks by using lubricants derived exclu- sively from mineral oils. In several cases non-coking lu- bricants with extremely high degrees of viscosity are able to operate at low temperatures (below -50 °C). Biolubri- cants are used in numerous fields of application, but in all of them it is vital to prevent the contamination (only a negligible level is acceptable) of the product and envi- ronment. These provide an alternative to the mineral oil- based lubricants in industrial applications that are used in *Correspondence: gubiczal@almos.uni-pannon.hu the automotive industry as hydraulic fluids during metal processing and oils for driving gears [3]. They are not considered as biological hazards in water systems when applied in watercrafts. In biotechnological methods for the manufacture of biolubricants, raw materials with a high oleic acid content are generally used for the transesterification processes. Biolubricants are mainly produced from plant oils, e.g. sunflower oil, soybean oil and castor oil [4, 5]. The life- time of these biolubricants that possess esters is usually longer than those obtained from mineral oils. On the other hand, their widespread industrial usage is hindered by the fact that certain equipment must be converted to run on biolubricants [6]. Various esters can be enzymatically produced from acids and alcohols of different chain lengths in non- conventional systems (organic solvents, ionic liquids, su- percritical fluids, solvent-free media). Thus, the ester- ification of acids and alcohols of short chain lengths by lipase results in flavour esters [7, 8]. The esterifica- tion of fatty acids (acids with carbon numbers of be- tween 12 and 18) and alcohols may yield both biolubri- cants and biofuels depending on alcohols’ chain lengths [9,10]. Biodiesel is obtained when alcohols of short chain lengths are used, while biolubricants can be manufac- tured by alcohols of long chain lengths. The formation of a biolubricant from oleic acid and isoamyl alcohol in organic solvents has been studied pre- viously [11–13]. The term ‘biolubricant’ may be used since both isoamyl alcohol and oleic acid are considered mailto:gubiczal@almos.uni-pannon.hu 28 BEDŐ, BÉLAFI-BAKÓ, NEMESTÓTHY, AND GUBICZA to occur naturally and the reaction is carried out by a naturally-occurring catalyst, an enzyme. Koszorz et al. studied the same reaction and stated that the water formed as a by-product of the esterification reaction had a nega- tive effect on the rate of reaction and activity of the en- zyme. To enhance the effectiveness of the process, water had to be removed by an integrated system where the re- action was combined with a pervaporation unit [14]. Turkish researchers applied fusel oil – a by-product of bioethanol production – containing a significant amount of isoamyl alcohol that was used to synthesize a biolubri- cant with high yield [15]. In addition to organic solvents, good results were achieved recently using ionic liquids as solvents. In the field of heat treatment microwave irradiation has yielded excellent results in both organic synthetic and enzymatic reactions [16, 17]. In transesterification reactions even a synergy effect was observed between the enzyme and ionic liquid [18–20]. The aim of this paper was twofold: (i) to study the possibility of applying ionic liquids instead of organic solvents; (ii) to investigate the role of microwave irradia- tion to achieve the highest possible degree of conversion in the minimum amount of time. 2. Experimental The reactions were conducted in an incubator shaker and microwave equipment using conventional heating and microwave irradiation, respectively. Similar compo- sitions and reaction volumes were used in the measure- ments to be able to compare the experimental results. 2.1 Samples and Measurements All chemicals were commercially available and used without further purification. Novozym 435 (immobilised Candida antarctica li- pase B, CALB), a triacylglycerol acylhydrolase (E.C. 3.1.1.3.) immobilized on an acrylic resin, was a gift from Novozymes (Bagsvćrd, Denmark). Its nominal catalytic activity and water content were 7000 propyl laurate units (PLU)/g and 1-2 %, respectively. Isoamyl alcohol (98 %) and oleic acid (99 %) were used as received from Sigma- Aldrich. The ionic liquid 1-butyl-3-methylimidazolium hexafluorophosphate ([bmim]PF6) (≥98.5 %) was pur- chased from Sigma-Aldrich while n-hexane and isooc- tane (99 %) were acquired from Reanal. To follow the yield of the ester, a HP-5890A gas chro- matograph (GC) was used. The device was equipped with a split/splitless injector, flame ionization detector (FID), and DB-FFAP column (length: 10 m, inner diameter: 0.53 mm, film thickness: 1.00 µm). The following heating pro- gramme was applied: 130 °C, 3 mins.; temperature ramp up: 10 °C min−1; 240 °C, 5 mins. Isooctane was used as an internal standard. For the analysis, a 10 µL sample of the reaction mixture was extracted. Reaction mixtures that contain ionic liquids cannot be injected into the GC, since they – as a viscous liquid – form a deposit on the inner side of the column that causes fouling. Moreover, they may be degraded due to the high temperature, thus, the precision of the measurements will be affected and undesirable peaks may appear in the chro- matograms. During the measurements the components are usually separated from the ionic liquid by extraction and injected into the column. In our measurements – to preserve the GC column – fiberglass and adsorbent material were placed inside the injector, which retained the ionic liquid after injec- tion while the component to be analysed was transferred in a gas phase to the column as a result of the high tem- perature. In this way extraction of the product from the reaction mixture could be avoided, therefore, the errors that originate from the incomplete extraction (effective- ness) could be eliminated. 2.2 Experimental setups Two different procedures were used for the production of biolubricants. Firstly, by using conventional heating the synthesis of biolubricants was conducted in Eppendorf tubes (1.5 mL) at 40 °C rotated at 200 rpm (IKA incuba- tor shaker KS 4000i). In a typical experiment 5 cm3 of reaction mixture (22.5 mmol of isoamyl alcohol and 3.75 mmol of oleic acid dissolved in n-hexane or [bmim]PF6) was prepared in a volumetric flask, and the Eppendorf tubes were each filled with 1 cm3 of the reaction mix- ture. The reaction started when 10 mg of the enzyme was added. Tests under microwave conditions were performed in a commercial microwave synthesizer (Discover se- ries, BenchMate model, CEM Corporation, USA). It was equipped with a magnetic stirrer and a fibre-optic sensor to monitor the temperature, which was set by varying the power of the microwave. For the esterification of biolu- bricant, 10 W of energy was used to maintain the temper- ature of the reaction between 40 and 60 °C. The volume and composition of the reaction mixture was identical to under conventional conditions. Experiments to study the reusability of enzymes were conducted by separating the enzyme from the reaction mixture and starting a novel reaction with a reaction mix- ture of the same volume. 3. Results and Analysis 3.1 Experiments Certain ionic liquids may catalyse esterification reac- tions. Even though in the case of [bmim]PF6 this phe- nomenon does not occur according to earlier publica- tions, measurements were conducted in reaction mixtures which did not contain enzymes to be able to exclude this effect. Our experiments confirmed previous results from the literature: [bmim]PF6 did not catalyse the reactions. Hungarian Journal of Industry and Chemistry PRODUCTION OF A BIOLUBRICANT BY ENZYMATIC ESTERIFICATION 29 Figure 1: Biolubricant production in the organic solvent (dashed lines) and ionic liquid (solid lines) using conven- tional heating. The experimental conditions were selected according to data from the literature in addition to our earlier ob- servations, and they were checked by preliminary mea- surements. Thus, the molar ratio of isoamyl alcohol to oleic acid was adjusted to 6:1, with a shaking rate of 200 rpm. The measurements were conducted at a temperature of between 30 and 50 °C to follow the eventual changes at various temperatures. It would have been possible to carry out measurements at higher temperatures using the enzyme Novozym 435 or the ionic liquid [bmim]PF6, fur- thermore, changes over longer reaction times could be more suitable to follow and evaluate. 3.2 Experiments using conventional heating Firstly, measurements under the conditions described in section 2.2 were conducted using conventional heating (Fig. 1). As can be seen esters were produced in high yields during the reactions in the ionic liquid as well as expected, and the yield was always higher in the ionic liquid at the same temperature. 3.3 Experiments using microwave heating The results of the measurements using microwave irradi- ation are presented in Fig. 2. As can be observed, a much shorter time was necessary to reach equilibrium, and the reaction rate was also faster in the ionic liquid. 3.4 Investigation of enzyme reuse The reusability of the enzyme Novozym 435 was studied under similar conditions in an ionic liquid (i.e. using con- ventional and microwave heating). The results indicated Figure 2: Biolubricant production in the organic solvent (dashed lines) and ionic liquid (solid lines) using mi- crowave irradiation. that the activity of the enzyme declined more rapidly us- ing conventional heating. 4. Discussion The results of the experiments conducted in the organic solvent, n-hexane, and in the ionic liquid, [bmim]PF6, un- der similar conditions provided a good basis to compare the effects of conventional and microwave heating during the production of biolubricants using enzymes since in both cases the same reaction volumes were used. As can be seen in Fig. 1, the reaction rate was higher in the ionic liquid (IL) than in n-hexane (n-H), the organic solvent that was usually applied. The data in Table 1 can be further compared. By comparing the values of C, IL/C and n-H (the ratio of enzyme activities in the ionic liquid and n-hexane using conventional (C) heating), it can be seen that the activity of the enzyme increased by a factor of 1.2 (on average) at each temperature due to the pres- ence of the ionic liquid. In the organic solvent the activity of the enzyme was found to be 2.8 times greater as a result of the microwave irradiation at each temperature (data of MW, n-H/C, n-H) compared to the conventional heating. In similar experi- ments in ionic liquids even more significant increases in the activity of enzymes were observed: microwave irradi- ation (MW) resulted in a 5.8-fold rise (data of MW, IL/C, IL). A possible explanation for the significant increase is that the ionic liquid and microwave irradiation have a positive synergistic effect on the activity of the enzyme. Previously it was observed that ionic liquids seem to pro- tect the enzyme in a similar way to the immobilising sup- Table 1: Comparison of the activity of the enzyme under various conditions. T / °C Activity / µmol·min−1·g−1 Conventional heating Microwave heating C, IL/C, n-H MW, n-H/C, n-H MW, IL/C, IL n-H IL n-H IL 30 162 194 475 1120 1.19 2.93 5.77 40 342 444 990 2510 1.29 2.89 5.65 50 575 660 1650 3840 1.15 2.86 5.82 46(2) pp. 27–31 (2018) 30 BEDŐ, BÉLAFI-BAKÓ, NEMESTÓTHY, AND GUBICZA Figure 3: Reusability of the enzyme in the ionic liquid using microwave and conventional heating port of the enzymes. In this work an immobilised enzyme was applied, thus, the synergistic effect simply strength- ened the enzyme preparation or stabilised the active site of the enzyme. A similar effect has already been de- scribed in transesterification reactions in some papers in the literature [18,20], but not with regard to esterification reactions. The stabilisation effect of the ionic liquid was con- firmed by the results presented in Fig. 3. By re-using the enzyme 5 times under conventional heating, the activity of the enzyme decreased much more rapidly than in the case of microwave heating. While in the first case 50 % of the original activity of the enzyme was maintained af- ter the fifth application, using microwave irradiation this value was 70 %. 5. Conclusion The experiments led to a definite answer to the original question, namely whether microwave irradiation may en- hance the effectivity of the enzymatic production of a bi- olubricant from isoamyl alcohol and oleic acid. It was observed that microwave heating increased the rate of re- action. During the evaluation of the experiments an unex- pected effect was discovered: a synergistic effect was ob- served between microwave irradiation and the ionic liq- uid. 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Fat blends composed of different ratios (fully hydrogenated coconut oil / non-hydrogenated coconut oil: 25/75, 50/50 and 75/25) were prepared and examined for solid fat content. The solid fat content of samples was determined as a function of temperature by pNMR. The DSC technique determines the solid fat index by measuring the heat of fusion successively at different temperatures. DSC calculates the actual content of solids in fat samples and how it changes throughout the duration of heating or cooling. A characteristic curve is constructed by the correlation of enthalpies. Based on our results, it is clear that both DSC and pNMR techniques provide very practical and useful information on the solid fat content of fats. DSC is dynamic and pNMR is static. A difference in the values of the solid fat indexes of samples was observed which may be due to a fundamental difference between the two techniques. These data can be used by food manufacturers to optimize processing conditions for modified coconut oil and food products fortified with coconut oil. Keywords: solid fat content, solid fat index, pNMR, DSC, and Coconut oil 1. Introduction Nowadays, a proper understanding of the crystallization and melting properties of coconut oil systems is essential to increase the number of applications in the food indus- try. Coconut oil is considered as a multi-component mix- ture of various triglycerides which determines the physi- cal properties that affect the structure, stability, flavor as well as sensory and visual characteristics of foods [1]. Modification of the properties of solid fat has received much attention in research recently because of its impor- tance during the processing and production of new food products. The crystallization and melting properties of modified fat used as a shortening in bakery products are critical [2]. The crystal networks present in modified fat strongly enhance its texture, stability and acceptance of fatty-food products. An essential aspect of the industrial manufacture of edible oils and fats is the ability to measure the physical and thermal properties of the materials such as melting and crystallisation profiles, solid fat content (SFC), solid fat index (SFI) and enthalpy. Nuclear magnetic resonance (NMR) spectroscopy and differential scanning calorime- try (DSC) are easier to implement and faster techniques than dilatometry which is time-consuming and inaccurate *Correspondence: vinod.dhaygude05@gmail.com [3]. NMR has been widely used for the analysis of food materials such as dairy products, fats and oils, in addi- tion to wine and beverages. Over the past two decades, DSC has been increasingly utilised for the thermody- namic characterisation of edible oils and fats as well as the SFI determination of food fats. Considering the significant scientific and practical im- portance of the physical properties of coconut oil from a few studies, the solid fat content determined by NMR and DSC methods was investigated and the obtained results compared. Ultimately, this research study is beneficial to the food industry which continues to reformulate many products. 2. Experimental 2.1 Materials In this research study, Barco coconut oil was used as a source of non-hydrogenated coconut oil (NHCO) which was kindly provided by Mayer’s Kft. in Budapest. The fully hydrogenated coconut oil (FHCO) was obtained from local industry in Hungary. Blends of NHCO and FHCO were mixed in 25:75, 50:50 and 75:25 (w/w) pro- portions. The blends were melted and maintained at 80 ◦C for 30 mins to erase crystal memory. Subsequently, mailto:vinod.dhaygude05@gmail.com 34 DHAYGUDE, SOÓS, ZEKE, AND SOMOGYI Table 1: Fatty acid composition (%) of NHCO, FHCO and their blends. Fatty acid FHCO FHCO:NHCO NHCO (%) 75:25 50:5 25:75 C6:0 0.1 0.225 0.35 0.475 0.6 C8:0 1.9 3.175 4.45 5.725 7 C10:0 2.7 3.4 4.1 4.8 5.5 C12:0 53.3 51.425 49.55 47.675 45.8 C12:1 0.1 0.075 0.05 0.025 − C14:0 21.3 20.675 20.05 19.425 18.8 C16:0 10 10.025 10.05 10.075 10.1 C18:0 10 8.25 6.5 4.75 3 C18:1 trans 0.03 0.0575 0.085 0.1125 0.14 C18:1 cis 0.3 2.0 3.7 5.4 7.1 C18:2 trans − 0.02 0.05 0.08 0.11 C18:2 cis 0.1 0.5 0.9 1.3 1.7 C20 0.1 0.1 0.1 0.1 0.1 Other 0.02 0.03 0.05 0.065 0.08 all blends and pure samples of fat were stored in a refrig- erator at 10 ◦C until use. 2.2 Methodologies Static analysis The static analysis of the solid fat con- tent was conducted by pulsed nuclear magnetic resonance (pNMR) apparatus (Bruker Minispec 300, Bruker GmbH, Germany) according to the official method Cd 16b-93 of the American Oil Chemists’ Society (AOCS) [4]. The solid fat content was measured at 5 ◦C, 10 ◦C, 15 ◦C, 20 ◦C, 25 ◦C and 30 ◦C. Three parallel measurements were conducted and average values reported (Fig. 1). Ad- ditionally, these SFC values were converted into percent- ages where the initial value was considered to be 100 %. These percentage SFCs were compared with the SFIs. Dynamic Analysis Dynamic analyses of the samples were studied by DFC according to AOCS official method Cj 1–94 [4]. Samples of nearly 20 mg were loaded onto the middle of the aluminum pans using a small spatula and hermetically sealed by an empty pan that served as a reference. Samples were cooled to 0 ◦C at a rate of 1 ◦C min−1 and maintained at this temperature for 10 mins. The heating of blends and pure samples of oil was performed until a temperature of 80 ◦C was achieved at the same rate as for the cooling. The samples were maintained at 80 ◦C for 30 mins. The cooling process started after this period and the rate of cooling was 1 ◦C min−1 until the temperature reached −20 ◦C. Before being heated again to ambient temperature, the samples were maintained at this temperature for 10 mins. After that, heating commenced once more at a rate of 5 ◦C min−1 up to 20 ◦C at which point calorimetric measure- ments ended. Three parallel measurements were taken and the average thermogram was reported. The SFI of fat is expressed as a function of temper- ature. The numbers of solids in the samples of oil in re- lation to the temperature were estimated on the basis of the calorimetric results. Areas of the thermograms were Figure 1: Solid fat content profiles of two coconut oils and their blends. calculated and correlated with the percentage of solids in the samples. 3. Results and Discussion 3.1 Fatty acid composition Samples were characterized by their fatty acid composi- tion (see Table 1). The dominant fatty acids in the sample of coconut oil were lauric acid (C12:0) 45.8-53.3 % and myristic acid (C18:0) 18.8-21.3 %. The NHCO exhibited a higher percentage of medium-chain fatty acids and a lower percentage of unsaturated fatty acids. The FHCO was rich in polyunsaturated fatty acids (PUFA) and mo- nounsaturated fatty acids (MUFA). 3.2 Solid fat content according to NMR The composition of fatty acids and triacylglycerols (TAG) would contribute to the percentage of solid fat par- ticles in liquid oil at various temperatures. The SFC pro- files of the original fats and their blends at temperatures ranging from 5 ◦C to 30 ◦C are presented in Fig. 1. The SFC profile of NHCO exhibited low values of 81.06 %, 69.70 %, 54.61 %, 34.54 %, 25.86 % and 0.17 % over the temperature range of 5 ◦C – 30 ◦C because of the concentration of fatty acids. In the case of FHCO, the solid fat content was high at 90.49 %, 81.28 %, 69.29 %, 54.15 %, 48.30 % and 4.46 % over the same temperature range. The SFC profiles of blends changed following the addition of FHCO to NHCO. An increase in the maxi- mum values of SFC was also observed by Ribeiro et al. following the addition of fully hydrogenated soybean oil to soybean oil [5]. This can be explained by the changes in the composition of triacylglycerols of the blends. At 5 ◦C, the blends exhibited SFCs ranging from 84.94 % to 90.02 %, which decreased non-linearly until melting completely at 30 ◦C. During the blending, the concen- tration of TAGs with high melting points increased and subsequently the SFC values of blends were modified. In all blends, the SFC values at 30 ◦C were almost identical to the SFC of the FHCO. Hungarian Journal of Industry and Chemistry STATIC AND DYNAMIC ANALYSES OF THE SOLID FAT CONTENT OF COCONUT OIL 35 Figure 2: Melting profiles of two coconut oils and their blends. Table 2: Thermal properties of NHCO, FHCO and their blends. Sample Max. Peak temperature Enthalpy (◦C) (J/g) FHCO 24.61 80.24 75:25(w/w)FHCO:NHCO 24.30 76.21 50:50(w/w)FHCO:NHCO 23.96 63.44 25:75(w/w)FHCO:NHCO 23.52 55.84 NHCO 23.27 46.38 3.3 Melting characteristics The melting profiles of NHCO in the presence of fully hydrogenated coconut are depicted in Fig. 2. The melt- ing behavior of the original oils and blends was charac- terized by only one endothermic peak. A similar ther- mal behavior of coconut oil and hydrogenated coconut oil was observed by one major peak in various studies [6, 7]. Components with the lowest melting points tend to melt first and represent the most unsaturated triglyc- erides, while components with higher melting points that represent the most saturated triglycerides melt later. Sim- ilarly, results showed that NHCO started melting first compared to other samples because of its higher con- tent of unsaturated triglycerides. The addition of FHCO to NHCO did not alter the melting behavior but as the content of FHCO was increased, the peaks according to the melting profiles of blends shifted towards the high- melting temperatures (Fig. 2). This melting profiles provided an indication of the amount of crystallized fat and the occurrence of polymor- phic transitions. The thermal characteristics of the original oils and their blends are shown in Table 2. No significant differ- ences were observed between the values of onset temper- ature (Ton) and peak temperature (Tp) in addition to the enthalpies of NHCO and FHCO. Ton ranged from 15.60 ◦C to 20.50 ◦C while Tp ranged from 23.27 ◦C to 24.61 Figure 3: Solid fat index profiles of two coconut oils and their blends. ◦C. Melting enthalpies of NHCO following the addition of FHCO increased from 46.38 J/g to 80.24 J/g (see Table 2). 3.4 Solid fat index (SFI) The solid-liquid ratio in fats expressed as solid fat con- tent is determined from the melting curves that result from DSC by partial integration. The heat flow into or out of samples of fat was measured as they were heated and cooled isothermally. The estimation of the SFIs of samples is dependent upon the onset and final tempera- tures of melting. The SFI profiles of all samples calcu- lated by melting thermographs are shown in Fig. 3. Non- hydrogenated coconut oil exhibited a characteristic steep slope and a rapid decrease in the percentage of solids at 20 ◦C. This ratio of solids to liquids decreases differently in these blends of fat as the temperature rises and is at its minimum for all blends at around 30 ◦C (see Fig. 3). 4. Discussion The results obtained from two methods exhibited a wide range of solid fat content values of the same samples. The values of SFC calculated from pNMR results were lower than values of SFI according to DSC where DSC is a dy- namic method and NMR is a static method. The values of the percentages of SFC for each blend at 15 ◦C calculated by DSC were 87.55 %, 88.38 % and 95.95 % (see Fig. 3) but 68.05 %, 68.83 % and 72.35 % when calculated by pNMR, respectively (see Fig. 4). DSC samples exhibited a sharp decline in their SFI or ratio of solids to liquids when heated from 15◦C to 25◦C, however, the SFC of samples according to NMR exhibited a gradual slope. DSC measurements of physical behavior were ob- served under controlled heating conditions. The results of DSC describe the whole melting process whilst be- ing heated. The NMR results indicate the statistical val- ues of solid fat content. The difference between the two measurements was possibly due to the time-dependent process concerning the development of crystal structure where SFI describes the status of the fat system and SFC 46(2) pp. 33–36 (2018) 36 DHAYGUDE, SOÓS, ZEKE, AND SOMOGYI Figure 4: Solid fat content (%) of two coconut oils and their blends. the solid status after stabilization. In addition NMR iden- tified state vise crystals at respective temperatures. The difference in values may be due to the method of tem- pering, the rate of heating or cooling, and the degree of accuracy. 5. Conclusion The results revealed that by combining FHCO with NHCO the melting behavior of blends of coconut oils was modified, leading to significant increments in the melt- ing point and in the maximum solid fat content. These two methods yielded more descriptive and clear informa- tion about melting behaviour by determining amounts of solids in the samples of coconut oil in relation to the tem- perature. Static and dynamic analytical methods showed a difference in the solid-to-liquid ratio of samples which may be due to fundamental differences. The blending of FHCOs with vegetable oils can produce valuable blends of fat of good consistency and with reduced or even in the absence of trans-isomers of unsaturated fatty acids suit- able for margarine. Acknowledgement This research was supported by the Doctoral School of Food Sciences at Szent István University. REFERENCES [1] Dayrit, F. M.: The properties of lauric acid and their significance in coconut oil. J. Am. Oil Chem. Soc., 2015 92, 1–15 DOI: 10.1007/s11746-014-2562-7 [2] O’brien, R. D.: Fat and oils formulating and processing for applications Boca Raton, FL CRC/Taylor & Francis, 2009, USA ISBN: 9781420061666 [3] Walker, R. C.; Bosin, W. A.: Comparison of SFI, DSC and NMR methods for determining solid- liquid ratios in fats. J. Am. Oil Chem. Soc., 1971 48, 50–53. 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Soc., 2001 78, 387–394 DOI: 10.1007/s11746-001-0273-4 Hungarian Journal of Industry and Chemistry https://doi.org/10.1007/s11746-014-2562-7 https://doi.org/10.1007/BF02635684 https://doi.org/10.1016/j.foodres.2009.01.012 https://doi.org/10.1016/j.foodres.2009.01.012 https://doi.org/10.1016/S0308-8146(01)00241-2 https://doi.org/10.1016/S0308-8146(01)00241-2 https://doi.org/10.1007/s11746-001-0273-4 https://doi.org/10.1007/s11746-001-0273-4 HUNGARIAN JOURNAL OF INDUSTRY AND CHEMISTRY Vol. 46(2) pp. 37–42 (2018) hjic.mk.uni-pannon.hu DOI: 10.1515/hjic-2018-0016 MONITORING OF CHEMICAL CHANGES IN RED LENTIL SEEDS DURING THE GERMINATION PROCESS ILDIKÓ SZEDLJAK *1, ANIKÓ KOVÁCS1, GABRIELLA KUN-FARKAS2, BOTOND BERNHARDT3, SZABINA KRÁLIK1, AND KATALIN SZÁNTAI-KŐHEGYI1 1Department of Grain and Industrial Plant Processing, Szent István University, Villányi út 29-43, Budapest, 1118, HUNGARY 2Department of Brewing and Distilling, Faculty of Food Science, Szent István University, Villányi út 29-43, Budapest, 1118, HUNGARY 3Department of Soil Chemistry and Turnover, Institute for Soil Sciences and Agricultural Chemistry, Centre for Agricultural Research, Hungarian Academy of Sciences, Herman Ottó út 15, Budapest, 1022, HUNGARY Red lentils are a very important raw material in the food industry due to their high protein content and high level of health- promoting components. The nutritive value of red lentils is the most important attribute from a research point of view; it can be increased by germination, soaking as well as physical and biochemical processes. The antinutritive materials are reduced or denatured by the germination process and indigestible components become available to the human body. Heat treatment was applied to achieve different temperatures and increase the microbiological stability of germinating samples. The effect of heat treatment on the amounts of certain components and the activity of oxidative enzymes was tested during our experiments; the nutritional characteristics (water-soluble total polyphenol content (WSTPC), water- soluble protein content (WSPC), water-soluble antioxidant capacity, in addition to peroxidase and polyphenol oxidase enzyme activities) of different treatments in red lentil samples were monitored. The WSTPC in our samples ranged from 0.726 mg Gallic Acid Equivalent GAE/g DW (DW being dry weight) to 1.089 mg GAE/g DW, and the WSPC varied from 19.078 g / 100g DW to 29.692 g / 100 g DW. Results showed that germination led to an increase in the WSTPC and WSPC. The peroxidase enzyme activity also exhibited an increase during germination which could result in deepening of the colour of the finished products. Germination resulted in the water-soluble antioxidant capacity of red lentil samples decreasing. Keywords: red lentil, germination, antioxidant activity, protein, enzyme 1. Introduction Lentils (Lens culinaris M.) are bushy annual plants of the legume family. Lentils are grown for the high pro- tein content and high nutritive value of their lens-shaped seeds. Lentils are primarily a cool-season crop; they are moderately resistant to high temperatures and droughts. Lentils are characterized by their high levels of plant pro- tein, complex carbohydrates (resistant starch, slowly di- gestible starch and oligosaccharides), fibres (soluble and insoluble) as well as very low sodium and fat content. Additionally, lentils are rich in B-vitamins, e.g. folate, thiamin and niacin, and key minerals, namely iron, potas- sium, magnesium and zinc, make them a highly nutritious food. The most common types of lentils are red, green and black of which red and green are the most commonly traded. The cultivation and consumption of red lentils are considerable in Asian countries. On the other hand, con- *Correspondence: ildiko.szedljak@gmail.com sumer demand for red lentils in the Western Hemisphere is not high [1]. Red lentils are a valuable source of macronutrients (proteins, fats, carbohydrates) and other important com- ponents (phytochemicals: phytic acid, phenolic acids, flavonols, flavanols and condensed tannins). Lentils have demonstrated many health benefits, e.g. lowering the glycemic index and their gluten-free status for people with metabolic disorders. The consumption of lentils can also lead to weight loss, which is recommended for all overweight and obese individuals [2, 3]. The germinated seeds and their compounds are pos- sible components of functional foods. Functional foods play an important role in health promotion and disease prevention. Different scientific papers suggest that lentils provide protection against chronic diseases through a multitude of biological activities including anticancer, antioxidant and angiotensin-converting enzyme inhibi- tion. Lentils also reduce blood lipid levels and the risk of developing cardiovascular diseases [4, 5]. mailto:ildiko.szedljak@gmail.com 38 SZEDLJAK, KOVÁCS, KUN-FARKAS, BERNHARDT, KRÁLIK, SZÁNTAI-KŐHEGYI The nutritive value of lentil seeds can be improved by the germination process. Germination is a complex metabolic process during which the lipids, carbohydrates and storage proteins within seeds are broken down in or- der to obtain the necessary energy and amino acids. These changes influence the bioavailability of essential nutri- ents [6]. The presence of antinutritional factors might be reduced by germination. Red lentils have been gaining increasing attention due to their health benefits as part of the human diet and they are considered to be an ex- cellent source of dietary antioxidants largely because of their high level of bioactive phytochemicals [1, 7] In Hungary, small-scale (20 seeds) red lentil germi- nation experiments have already been conducted during which the effect of germination on the lectin content was studied [8]. The main purpose of our research was to ex- amine the suitability of the germinated red-lentil grist as a raw material of dry pasta. Red lentils were selected for our experiments due to their aforementioned favourable nutritional characteris- tics. In addition, its flour can be suitable in the devel- opment of gluten-free pasta products in the form of en- richment and gluten-free raw materials. The formation of more digestible water-soluble components was conduced by seed germination, but at the same time a loss may be observed due to the heat treatments (drying pasta) used in the manufacture of the products. The same loss may oc- cur during the boiling process. Therefore, it is important to check for all kinds of changes that occur during heat treatment. The control of the activity of enzymes which generate oxidation processes is also essential during ger- mination as is technological / kitchen-technological pro- cessing from the point of view of the expected quality of the finished products. Developing food diversity by incorporating red lentil seeds and its flour into western diets is highly recom- mended. 2. Experimental The aim of our study was to examine the chemical changes in red lentil seeds during the germination pro- cess. The effect of different heat treatments on the amount of certain components and the activity of oxidative en- zymes were monitored. Moreover, a connection between the parameters and the extent to which these variables in- teract was sought. 2.1 Samples and Measurements Samples 10 kg of raw organic whole red lentil was pur- chased from BiOrganik Online Kft. 3 kg of which was added to the germination device. 500 g of both soaked and sprouting seeds were sampled and heat-treated at three different temperatures. The heat-treated seeds were milled using a hammer grinder and then homogenized. The aqueous extracts were made from the control sam- ples and the heat-treated grists. Steeping, Germination and Heat Treatment Steep- ing and germination were performed in a Schmidt- Seeger, KMA-A1-2008 micromalting plant. The micro- malting plant was controlled by a personal computer with a special controlled by a personal computer with special software. During germination the temperature of the air was regulated and wetted with special jets. During the steeping process compressed air was dis- persed in the steeping water. Alternate wet and dry pe- riods were implemented during steeping, because during the latter the oxygen uptake of grains is more effective. Wet steeping lasted for 3 hours at 20 ◦C with aerations of 6.67 minutes in duration every 8 minutes. This was followed by a 2 hour-long dry period at 22 ◦C with hu- midification. The second 2-hour-long wet period was per- formed at 20 ◦C. Steeping was stopped when an adequate moisture content was achieved. Germination lasted for 96 hours at 22 ◦C with humidification. During the first 48 hours, the germinating seeds were rotated 30 times ev- ery two hours, then every three hours. Germinating seeds were not sprayed during the process. Germinating red lentil samples were taken daily at the same time. Heat treatment was applied at different tem- peratures (60 ◦C, 80 ◦C, 100 ◦C) in order to increase the microbiological stability of germinating samples. The ef- fect of heat treatment on the amount of certain compo- nents and the activity of oxidative enzymes was tested during our experiments. Chemical Analysis The samples were homogenized and 0.10 ml of distilled water was added to each sample. The centrifugation process was conducted after extrac- tion for 10 minutes at 4 ◦C and 10,000 rpm. The water- soluble polyphenolic content was measured by colorimet- ric analysis using Folin & Ciocalteu’s phenol reagent [9] and the results were expressed in Gallic Acid Equivalent (GAE) (mg GAE/g DW – DW being dry weight). The WSPC was measured by a method discovered by Layne [10]. The water-soluble antioxidant activity was deter- mined using a Ferric Reducing Antioxidant Power (FRAP) Assay Kit [11]. The polyphenol oxidase (PPO) enzyme activity was measured by using a synthetic sub- strate, pyrocatechol. The oxidized form of the substrate can be synthesized photometrically at 420 nm by a spec- trophotometer [12]. The peroxidase (POD) enzyme activ- ity of the extracts was determined using o-Dianisidine as a hydrogen donor in sodium acetate (pH 5.1) [13]. The reagents for the chemical measurements were provided by Sigma-Aldrich Kft. Statistical Methods All of the measurements were replicated five times. The Kruskal-Wallis test was ap- plied to calculate the exact p-value (α = 0.05) and Dunn’s post hoc pair-wise test was chosen with an adjustment by Bonferroni. The relationship between the parameters was determined by Spearman’s rank correlation coeffi- Hungarian Journal of Industry and Chemistry CHEMICAL CHANGES IN RED LENTIL SEEDS DURING THE GERMINATION PROCESS 39 Figure 1: Water-soluble total polyphenol content in red lentil samples. Different letters indicate significant differ- ences between treatments (p ≤ 0.05). cient (non-parametric equivalent of Pearson’s correlation coefficient) (α = 0.05) using the XLSTAT-Sensory so- lution software, version 2013.1.01 (Addinsoft, 28 West 27th Street, Suite 503, New York, NY 10001, USA). During the correlation test the correlation between the variables regardless of their units was examined. 3. Results and Evaluation 3.1 Water-soluble total polyphenol content (WSTPC) Zhang et al. [14] measured the total polyphenol content (soluble and insoluble in water) using Folin Ciocalteu’s reagent in raw red-lentil extracts (5.04 ± 0.36 mg GAE/g DW – 7.02 ± 0.48 mg GAE/g DW). According to their data all extracts of lentils cultivated in Canada were sig- nificantly different from each other. In contrast to this TPC values changed over a very narrow range (from 5.9 ± 0.1 mg GAE/g DW to 5.93 mg GAE/g DW) in the sam- ples of red-lentil flour tested [15–17]. The results of TPC are shown in Fig. 1. The WSTPC in our samples ranged from 0.726 mg GAE/g DW to 1.089 mg GAE/g DW. Our WSTPC values were 5 to 10 times smaller than in the aforementioned experiments. By comparing the control and soaked samples, it can be observed that the WSTPC increased during the soak- ing process. These values were higher than the measured data from germinated samples (Fig. 1). According to our experiments heat treatment at high temperatures (80 ◦C and 100 ◦C) equalized the WSTPC values in red lentil samples. Furthermore, germination and heat treatments did not effect the WSTPC of the seeds. 3.2 Water-soluble antioxidant capacity The results of water-soluble antioxidant capacity were measured using a FRAP Assay Kit. The values ranged be- tween 0.177 mg Ascorbic Acid Equivalent (AAE)/g DW Figure 2: Water-soluble antioxidant capacity of red lentil samples. Different letters indicate significant differences between treatments (p ≤ 0.05). and 0.815 mg AAE/g DW. As a result of the germinating process, the antioxidant capacity of the samples was sig- nificantly reduced compared to that of the control sample. However, treatment at a high temperature (100 ◦C) led to a further increase in the amount of new water-soluble components with antioxidant capacity. Samples that were not dried during the first 3 days were significantly dif- ferent from the control samples in all of the categories. Moreover, they differed from the sample dried at 100 ◦C on the 4th day (Fig. 2). The highest water-soluble antioxidant capacities were measured in the control samples, except for the control sample treated at 100 ◦C. By comparing control samples to germinated samples, it is evident that the germinating process did not result in an increase in the water-soluble antioxidant capacity. Our results showed that whilst being soaked the water-soluble antioxidant capacity started to decrease. The water-soluble antioxidant capacity in the heat- treated sample on the 3rd day of germination at 80 ◦C de- creased drastically compared to the control sample. The same change occurred with the samples that were not dried. Nevertheless, the significant decrease had already occurred on the 1st day of germination. No correlation was found between the WSTPC and water-soluble antioxidant capacity. 3.3 Water-soluble protein content (WSPC) WSPCs, given in Fig. 3, ranged from 19.078 g / 100 g DW (dry weight) to 29.692 g / 100 g DW. By comparing the control and soaked samples, it is evident that the WSPC increased during the soaking pro- cess. In the case of samples that were not dried in addi- tion to those treated at 80 ◦C and 100 ◦C, no significant differences were observed between treatments except for samples treated at 60 ◦C where those soaked and on their 2nd day of germination had significantly higher values compared to the control sample. The highest WSPC was 46(2) pp. 37–42 (2018) 40 SZEDLJAK, KOVÁCS, KUN-FARKAS, BERNHARDT, KRÁLIK, SZÁNTAI-KŐHEGYI Figure 3: Water-soluble protein content in red lentil sam- ples. Different letters indicate significant differences be- tween treatments (p ≤ 0.05). measured on the 2nd day of germination at 60 ◦C, which was significantly higher than all the heat-treated control samples as well as samples treated at 100 ◦C except for the value on the 1st day of germination. As the germination process advanced – especially on the 3rd and 4th days – the WSPC of samples heat-treated at 80 ◦C and 100 ◦C started to decrease compared to the same phenophases of those that were not dried or heat- treated at 60 ◦C. This may be explained by the fact that plant proteins are more easily degraded at higher temper- atures over prolonged periods of time. A negative correla- tion was observed between the WSPC and water-soluble antioxidant capacity. The total protein content was determined using the Dumas method as described by Hefnawy [18]. In this study the total protein content was 26.6 ± 0.50 g / 100 g DW and the effect of the heat treatment was insignifi- cant. 3.4 Peroxidase (POD) Enzyme Activity The changes in POD enzyme activity of red-lentil sam- ples are shown in Fig. 4. The POD adversely affects the nutritive value, taste, texture and colour of food products. These enzymes are referred to as heat-tolerant enzymes and can regain their activity following heat treatment and storage (Fig. 4). POD enzyme activity ranged from 10.815 U/g DW to 215.785 U/g DW with statistically significant differences. The highest value (215.785 U/g DW) was found in the sample dried at 100 ◦C on the 4th day. The samples that were not dried or heat-treated were identical to each other on the same level (control, soaked, 1st-4th day). POD activity progressively increased during the germination process in almost all cases. The POD ac- tivity of the sample dried at 100 ◦C was 20-fold higher than that of the control sample. The POD activity of different tempered lentil samples was also measured by Pathiratne et al. [19] and their maximum value was 186.4 Figure 4: Peroxidase enzyme activity of red lentil sam- ples. Different letters indicate significant differences be- tween treatments (p ≤ 0.05). U/g protein. However, in another study by Świeca et al. [20], the POD activity of germinated lentil samples was much higher than the aforementioned ones, 10.3 ± 0.24 kU/mg protein. Elevated temperatures of heat treatment resulted in an increase in the POD activity during the germination pro- cess. 3.5 Polyphenol oxidase (PPO) enzyme activ- ity PPOs and PODs are the most studied enzymes in fruit and vegetables. Świeca et al. [20] studied the PPO enzyme activity in sprouts of lentils according to the method de- scribed by Galeazzi et al. [21] and measured 2.24 ± 0.05 kU/mg protein. They reported that enzymatic markers of the stress metabolism of plants, e.g. PPO activities, did not differ significantly between sprouts. In our study a catechol substrate was also used but no PPO enzyme ac- tivity was detected in the samples. 4. Conclusion Of all the parameters studied, the WSPC of red lentils strongly correlated with the values of water-soluble an- tioxidant capacity measured using the FRAP Assay Kit (data not shown). The correlation is inversely propor- tional, hence, the greater the WSPC, the lower the water- soluble antioxidant capacity. Seed germination is one of the most important stages in the life cycle of plants and germinated seeds may be a useful source of healthy food. Germinated seeds are very complex living matrices and it is very difficult to understand the biochemical changes that occur during sprouting. 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LWT - Food Sci. Tech., 2016 65, 762–769. DOI: 10.1016/j.lwt.2015.08.073 [23] Gere, A.; Kovács, S.; Pásztor-Huszár, K.; Kókai, Z.; Sipos, L.: Comparison of preference mapping meth- ods: a case study on flavoured kefirs. J. Chemom., 2014 28(4), 293–300. DOI: 10.1002/cem.2594 [24] Gere, A.; Sipos, L.; Héberger, K.: Generalized pairwise correlation and method comparison: Im- pact assessment for JAR attributes on overall lik- ing. Food Qual. Prefer., 2015 43, 88–96. DOI: 10.1016/j.foodqual.2015.02.017 [25] Gere, A.; Danner, L.; De Antoni, N.; Kovács, S.; Dürrschmid, K.; Sipos, L.: Visual attention accom- panying food decision process: An alternative ap- proach to choose the best models. Food Qual. Pre- fer., 2016 51, 1–7. DOI: 10.1016/j.foodqual.2016.01.009 Hungarian Journal of Industry and Chemistry https://doi.org/10.1016/j.lwt.2015.08.073 https://doi.org/10.1016/j.lwt.2015.08.073 https://doi.org/10.1002/cem.2594 https://doi.org/10.1016/j.foodqual.2015.02.017 https://doi.org/10.1016/j.foodqual.2015.02.017 https://doi.org/10.1016/j.foodqual.2016.01.009 HUNGARIAN JOURNAL OF INDUSTRY AND CHEMISTRY Vol. 46(2) pp. 43–46 (2018) hjic.mk.uni-pannon.hu DOI: 10.1515/hjic-2018-0017 RECOVERY OF ITACONIC ACID BY ELECTRODIALYSIS VERONIKA VARGA1, KATALIN BÉLAFI-BAKÓ1, DÁVID VOZIK1, AND NÁNDOR NEMESTÓTHY *1 1Research Institute of Bioengineering, Membrane Technology and Energetics, University of Pannonia, Egyetem u. 10, Veszprém, 8200, HUNGARY Itaconic acid is an organic acid produced mainly for non-food purposes. It can be manufactured by biotechnological syn- thesis using various strains which results in the salt form of the acid. In this work, the separation of sodium itaconate by electrodialysis was studied. Homopolar cation- and anion-selective membranes were applied and the module was operated under a constant voltage. The transport of the acid was followed by on-line ultraviolet and visible absorption spectroscopy, where the detector was installed in the system. The experiments with models of aqueous solutions con- firmed that the technique is suitable for the effective recovery of itaconic acid. Keywords: ultraviolet and visible absorption spectroscopy, on-line detection, monopolar membranes 1. Introduction Itaconic acid was discovered by Baup in 1837 as the coproduct resulting from the degradation of citric acid [1]. Itaconic acid (2-methylene,1,4-butanedioic acid) is an unsaturated dicarboxylic acid, a rather reactive com- pound due to its conjugated double bond and two car- boxyl groups. Therefore, it can easily participate in poly- merisation reactions. Itaconic acid – unlike citric acid – is applied exclu- sively for non-food purposes [2]. It is used mainly in the production of synthetic fibres and ion-exchange resins as well as in the pulp and paper industry. Itaconic acid can be synthesized biotechnologically. Kinoshita was first to describe the process in 1932 when it was isolated from the broth of Aspergillus itaconicus [3]. Later a similar strain, Aspergillus terreus, was found to produce itaconic acid. Other microbes suitable for the fermentation of itaconic acid are listed in Table 1. The main problem with downstream processing is that several similar organic acids are present in the broth, thus, recovery of itaconic acid is difficult. Separation of ita- conic acid can be conducted by filtration with the aid of activated carbon and crystallisation (consecutive steps) or adsorption by strong anion-exchange resins, like Purolite A-500 P or PFA-300 [10]. The efficiency of the separa- tion depends mainly on the temperature, pH and concen- tration. An application of electrodialysis (ED) as a membrane process is the separation of organic acids [11–14]. Malic acid and galacturonic acid amongst others can be sepa- rated by ED using monopolar and bipolar membranes by *Correspondence: nemesn@almos.uni-pannon.hu Table 1: Biotechnological synthesis of itaconic acid Strain Reference Aspergillus itaconicus Kinoshita et al. (1932) [3] Ustilago maydis Steiger et al. (2013) [4] Pseudozyma antarctica Levinson et al. (2006) [5] Yarrowia lipolytica Kuenz et al. (2018) [6] Synechocystis cyanobacteria Heidorn et al. (2011) [7] Chin et al. (2015) [8] Aspergillus terreus Karaffa et al. (2015) [9] implementing batch and continuous modes of operation. The majority of these acids are produced as a salt, thus, the aim of the separation by ED is to transport the organic acid through the anion-selective membrane, while the cation should pass through the cation-selective membrane. The other neutral components remain in the feed solution. Usually the mobility of the acid is sufficient for effective transport, hence both the acid and cation can be recovered by ED. The aim of this paper was to study the possibility of applying ED for the recovery of sodium itaconate. 2. Experimental Itaconic acid, sodium sulphate, sulphuric acid, sodium hydroxide and all the other chemicals used were of an- mailto: nemesn@almos.uni-pannon.hu 44 VARGA, BÉLAFI-BAKÓ, VOZIK, AND NEMESTÓTHY Table 2: Features of the membranes Feature Fumasep FAA Fumasep FKS selectivity >92 % >96 % electrical resistance <2 Ωcm2 <8 Ωcm2 pH stability in acidic media 5-13 thickness 0.13-0.15 mm 0.11-0.13 mm ion-exchange capacity >1.2 meq/g >1.0 meq/g conductivity >8 mS/cm >5 mS/cm alytical grade and purchased from Sigma-Aldrich. The anion- and cation-selective membranes were Fumasep FAA and FKS membranes, respectively. The main fea- tures of the membranes are summarized in Table 2. The membranes were activated by sodium chloride and sul- phuric acid before usage. For analytical purposes a Young Lin Instrument Co., Ltd. (YL9100-type) high-performance liquid chromatog- raphy (HPLC) system (including a YL9109 vacuum de- gasser, YL9110 quaternary pump and YL9150 automatic sample dispenser) was used to determine the concentra- tion of itaconic acid with a Hamilton HPLC column (15 cm in length, 4.6 mm inner diameter, 5 µm particle size) and a YL9120 UV/Vis detector. The Luff-Schoorl method was used to determine the glucose concentration which is based on the reduction of cupric (Cu(II)) cations in a boiling alkaline solution of cuprous (Cu(I)) oxide [15]. The surplus of Cu(II) was measured by iodometry using a titration with sodium thiosulfate. The conductivity of the solutions was measured by a Radelkis OK-102/1 conductivity meter equipped with a Radelkis OK-9023 bell electrode using a cell constant of 0.7 cm−1. Data concerning the voltage and current were measured by a National Instruments USB-600866009 de- vice. All the experimental data were collected online us- ing LabVIEW software. An electrodialysis module was constructed from 2 anion- and 2 cation-selective membranes using spacers between them. The electrode solution was an aqueous so- lution of sodium sulphate. Electrodialysis measurements were conducted using diluted (aqueous) model solutions of sodium itaconate and sodium itaconate mixed with glucose. The module was operated under a constant voltage. 3. Results In this project, the final aim was to connect the ED de- vice to the fermentation of itaconic acid in order to set up an integrated system. For this purpose, firstly the opera- tion of ED was investigated by using model solutions of sodium itaconate and a simple ED device with monopolar Figure 1: Percentages of the four distinct forms of itaconic acid. ion-exchange membranes. The transport of the itaconic acid through the anion-selective membranes was the fo- cus of the study To follow the process, it was important to determine the exact concentration of itaconic acid. If the acid is the only compound in the solution, measuring the conduc- tivity is a simple method for detection. However, if any other charged compound is present, it will disturb such measurements. In this case, HPLC is suggested for the analysis [9]. Itaconic acid is a dicarboxylic acid (consisting of three different ionic forms) and its dissociated forms and ionic strengths vary according to the pH. Thus, four dis- tinct peaks over different retention times can be detected in HPLC chromatograms. The percentages of the four distinct forms as a function of pH were determined and are presented in Fig. 1. Since it is quite difficult to measure the actual con- centration of itaconic acid, another method was chosen. Itaconic acid has a UV absorption maximum at 243 nm which can be used for detection. This method seemed suf- ficiently sensitive for our purposes. In our work, a loop was constructed from the solution (recirculated in the ED module) to the UV detector. Thus, online detection was applied to follow the concentration Figure 2: Calibration curve for the determination of ita- conic acid concentration by UV detection Hungarian Journal of Industry and Chemistry RECOVERY OF ITACONIC ACID BY ELECTRODIALYSIS 45 Figure 3: Polarization curves of itaconic acid as a function of operating time. Firstly, a calibration curve was recorded (Fig. 2) over the con- centration range of itaconic acid that was planned to be used. The data measured by the online UV system were checked by HPLC. To test the ED module, polarization curves were taken using a potentiostat by applying a range of voltages from 0 to 10 V (Fig. 3). The current data were recorded as a function of the voltage data. The measurements were re- peated in various electrode solutions. It seems that beyond a sodium sulphate concentration of 0.125 M, the ED operated properly. Experiments were conducted in the ED module by us- ing aqueous model solutions of itaconic acid (with an ini- tial concentration of 3-3 g/l). The electrode solution was a 0.16 M Na2SO4 solution. The experiments were con- ducted under a constant voltage (10 V) and the current intensity varied between 0.11 and 0.15 A. Subsequently, the conductivity in the diluate solution was measured. The concentration of the acid decreased gradually to half its initial value after an operating time of 70 mins as can be seen in Fig. 4. This means that ita- conic acid was able to pass through the anion-selective membrane, while sodium ions were able to diffuse across the cation-selective membrane. Therefore, the measure- ments confirmed that the mobility of this acid is sufficient to separate it by ED. Figure 4: Conductivity data of the diluate of ED Figure 5: Concentration of itaconic acid in the diluate so- lution In the next series of experiments, glucose was added to the acid (4 g/L) to investigate whether the ED module was able to separate the two compounds. The concentra- tion of itaconic acid in the diluate was followed online by the UV detector installed in the loop. The concentra- tion of the glucose was determined by the Luff-Schoorl method. The concentration of the acid decreased from 3.0 to 1.5 g/L during the experiment (Fig. 5), while the glucose concentration was monitored in all three streams. In the diluate (originally feed) solution, a slight decrease in glu- cose concentration was observed (to 3.52 g/L), its con- centration was negligible (0.20 g/L) in the electrode so- lution, while in the concentrate solution 0.59 g/L glucose was measured probably due to its diffusion from the feed solution. 4. Conclusion The measurements provided a definite answer to the orig- inal question, namely whether ED is a suitable technique for the recovery of itaconic acid. The results of the ex- periments using model solutions (sodium itaconate on its own as well as a mixture of sodium itaconate and glucose) confirmed that ED is an effective method for the separa- tion of itaconic acid. Based on these results, further ex- periments are being planned using more complex model solutions, similar to the composition of the fermentation broth. Subsequently, it is our intention to connect the ED module to the fermentation process. Acknowledgements This research was supported by the National Research, Development and Innovation Fund project OTKA K 119940 entitled “Study on the electrochemical effects of bioproduct separation by electrodialysis” and by the fi- nancial support of Széchenyi 2020 within project EFOP- 3.6.1-16-2016-00015. 46(2) pp. 43–46 (2018) 46 VARGA, BÉLAFI-BAKÓ, VOZIK, AND NEMESTÓTHY REFERENCES [1] Baup, S.: Über eine neue Pyrogen- Citronensäure, und über Benennung der Pyrogen Säure über- haupt, Ann. Chim. Phys., 1837 9, 29–38 DOI: 10.1002/jlac.18360190107 [2] Delidovich, I.; Hausoul, P. J.; Deng, L.; Pfutzen- reuter, R.; Rose, M.; Palkovits, R.: Alternative monomers based on lignocellulose and their use for polymer production, Chem. 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Process., 2001 79, 41–45 DOI: 10.1205/09603080151123353 Hungarian Journal of Industry and Chemistry https://doi.org/10.1002/jlac.18360190107 https://doi.org/10.1002/jlac.18360190107 https://doi.org/10.1021/acs.chemrev.5b00354 https://doi.org/10.3389/fmicb.2013.00023 https://doi.org/10.1016/j.enzmictec.2006.01.005 https://doi.org/10.1007/s00253-018-8895-7 https://doi.org/10.1016/B978-0-12-385075-1.00024-X https://doi.org/10.1016/j.jbiotec.2014.12.016 https://doi.org/10.1007/s00253-015-6735-6 https://doi.org/10.1007/s00253-015-6735-6 https://doi.org/10.1021/acs.jced.5b00620 https://doi.org/10.1016/j.memsci.2009.07.013 https://doi.org/10.1515/186 https://doi.org/10.1016/j.memsci.2013.11.008 https://doi.org/10.1016/j.memsci.2013.11.008 https://doi.org/10.1515/343 https://doi.org/10.1205/09603080151123353 HUNGARIAN JOURNAL OF INDUSTRY AND CHEMISTRY Vol. 46(2) pp. 47–54 (2018) hjic.mk.uni-pannon.hu DOI: 10.1515/hjic-2018-0018 THE INITIAL MAGNETIC SUSCEPTIBILITY OF DENSE AGGREGATED DIPOLAR FLUIDS SÁNDOR NAGY *1 1Institute of Mechatronics Engineering and Research, University of Pannonia, Gasparich M. u. 18/A, Zalaegerszeg, H-8900, HUNGARY To correlate the dipole moment and density dependence of the initial magnetic susceptibility on the basis of the former related theories and the probability analysis of chain formation, physically based analytical correlation equation was derived. After the local magnetic field strength and the chaining probability between two particle have been determined the chain and particle distributions came from the geometric distribution. The initial magnetic susceptibility was resulted from the summation of Langevin initial susceptibility of k-length chains. Two particles were considered in a chain if the interaction energy between them was below a certain limit. By varying slightly this energy limit around 70–75 % good agreement has been obtained between the simulation and theoretical data. Monte Carlo simulations were used to calculate the initial magnetic susceptibility of dipolar hard sphere system at different dipole moments and densities. Keywords: dipolar fluids, initial susceptibility, Monte Carlo simulation 1. Introduction The investigation of dipolar fluids has been induced by the evolution of magnetorheology and electrorheology over the last two decades. The viscosity of electrorheo- logical (ER) fluids increases dramatically due to an ex- ternal electric field. ER fluids can be obtained by dispers- ing solid particles with dielectric permittivity εp in a fluid with dielectric permittivity εf , where εp > εf . The dis- persed particles are of between 0.1 mm and 100 mm in diameter. The polarized particles are organized into pairs and chains. The magnetic analogy of the phenomenon de- scribed above is the magnetorheological (MR) effect. If the magnetic permeabilities of the liquid and dispersed particles differ, then in an external magnetic field the par- ticles are also arranged in chains. The dispersing medium can be water, oil, an organic solvent, etc. while the dis- persed particles can be some kind of iron oxide or ferrit. In this paper, the magnetic terminology and centimetre- gram-second (CGS) system of units are used. In the fig- ures, the reduced quantities are applied. Electro- and magnetorheological fluids typically ex- hibit a reduced density of up to ρ∗ = 0.4 (where ρ∗ = ρσ3; ρ and σ are the concentration and diameter of the suspended particles, respectively). The magnetic proper- ties, e.g. magnetization curve and initial magnetic suscep- tibility, are well described by the various theories within this range of reduced density. The magnetization M can be obtained by summation of the dipole moments in the *Correspondence: sata123.sandor@gmail.com unit volume: M = 1 V ∑ i mi. (1) In the absence of any external magnetic field the fluid is isotropic and according to Eq. 1 the magnetization is zero. When any external magnetic field is present, the field-oriented components of dipole moments should be summarized as M = ρm 〈cos Θ〉 H0 H0 , (2) where H0 = |H0| and 〈cos Θ〉 is the ensemble aver- age of the cosine of the angle between mi and H0, and m = |mi|. Since the directions of H0 and M are identi- cal, vector notation can be omitted. The initial magnetic susceptibility is equal to the initial gradient of the mag- netization curve χ0 = ∂M ∂H0 ∣∣∣∣ H0=0 . (3) In practice, ER and MR fluids can be used for the trans- mission of torque or force, in vibration dampers and brak- ing systems, etc. The magnetic properties generally are calculated from Monte Carlo simulations because it is not necessary to know the velocity and acceleration of the particles nor the forces between them. The expressions of the related models are listed in Ta- ble 1. (One line belongs to one theory and the first line is the head of the table, e.g. Table 1: 2.4 refers to the 4th cell in the 2nd line within the 1st table.) Three different mailto:sata123.sandor@gmail.com 48 NAGY Table 1: The expressions of the effective magnetic field, the magnetization and the initial magnetic susceptibility of the related theories. Model He – Effective magnetic field M – Magnetization χ0 – Initial magnetic susceptibility 1 “Langevin” [1] H0 ρmL ( mH0 kBT ) ρm2 3kBT = χL 2 “Weiss” [2] H0 + 4π 3 M(He) ρmL ( mHe kBT ) χL 1− 4π 3 χL 3 “Pshenichnikov” [3] H0 + 4π 3 M(H0) ρmL ( mHe kBT ) χL ( 1 + 4π 3 χL ) 4 “Ivanov” [4] H0 + 4π 3 M(H0) ( 1 + 4π 48 ∂M ∂H0 ) ρmL ( mHe kBT ) χL ( 1 + 4π 3 χL + (4π) 2 144 χ2 L ) 5 “Tani” and “Szalai” [5, 6] M(H0) = ρmL+ 4π 3 ρ 2βm3LL ′ + 1 10ρ 2β2m5ζ ′ Idd∆ − 16π2 27 ρ3β2m5LL ′ + 1 3ρ 3β2m5LL ′ Idd∆ χL ( 1 + 4π 3 χL + (4π)2 144 χ2 Lf(ρ) ) magnetic fields will be used. The applied external mag- netic field is denoted by H0 and the sum of the external and generated magnetic fields by He. He is always par- allel to H0. The third one is the local magnetic field Hl which is of chain-parallel orientation and its formation is due to dipole-dipole interactions between the particles. The well-known Langevin function is applied from the initial theory [1] in the magnetization formula (Ta- ble 1: 1.3), where L(α) = cothα − 1/α. The magnetic dipole moment of the particles is denoted by m and the applied external magnetic field by H0, while the Boltz- mann constant is represented by kB. The expression of magnetic susceptibility can be written as in Table 1: 1.4. This is known as Langevin susceptibility which is indi- cated by χL as well. In this approach the effective mag- netic field He exerted on the given particle is equal to the external magnetic field (Table 1: 1.2). According to the more accurate model by Weiss [2] the effective magnetic field is equal to the sum of the ex- ternal magnetic field and the magnetic field induced by the magnetization (Table 1: 2.2). The formula of the mag- netization (Table 1: 2.3) is similar to the previous one but H0 is substituted by He. Due to the iterative nature of the magnetization expression the initial magnetic suscep- tibility (Table 1: 2.4) exhibits divergence at χL = 3/4π, therefore, overestimates the real values. Above this initial magnetic susceptibility limit, when χL ≥ 3/4π, the zero- field magnetization is not equal to zero: M(H0) 6→ +0, ifH0 → +0. Moreover, in weak external magnetic fields, one H0 value belongs to three equilibrium magnetization values. The effective magnetic field has been substituted for the external magnetic field in the expression of the ef- fective magnetic field (Table 1: 3.2) in the theory by Pshenichnikov et al. [3]. The magnetization formula (Ta- ble 1: 3.3) is the same as in Weiss’ theory. The initial magnetic susceptibility (Table 1: 3.4) is in good agree- ment with the simulations but underestimates them at higher densities or higher dipole moments. That is why it seems to be a good method to extend the expression of the effective magnetic field (Table 1: 4.2) by Ivanov et al. [4]. The magnetization formula is once again identical (Table 1: 4.3) but a new term is in- troduced in the initial magnetic susceptibility (Table 1: 4.4). Although at higher densities it yields higher val- ues than in Pshenichnikov’s model, it underestimates the simulation data as well. The factor of the third term is (4π)2/144 = 1.0966 and perhaps it could be higher, but in this case at low densities the initial magnetic suscepti- bility overestimates the simulations. The perturbation theory by Tani et al. [5] is worth mentioning because a density-dependent correction was used to complete the third term of the susceptibility (Ta- ble 1: 5.4), where f (ρ) = 9Idd∆/π 2 − 16, and Idd∆ = 17π2 9 [ 1− 0.93952ρ∗ + 0.36714(ρ∗) 2 1− 0.92398ρ∗ + 0.23323(ρ∗) 2 ] . The formula of the magnetization curve for this pertur- bation theory was calculated by Szalai et al. The ex- pressions that are not mentioned in Table 1: 5.2 can be found in Ref. [6]. The values of the susceptibility more closely resemble the simulation data but still underesti- mate those. It is worth mentioning the study by Huke and Lücke [7] who introduced the so-called “dipolar coupling con- stant” into the second term of the initial magnetic sus- ceptibility, but the third term was ignored in expressions in Table 1: 4.4 and 5.4. Thereby their theory at higher densities underestimates and at lower densities overes- timates the simulation data. Furthermore, the theory of mean-spherical approximation (MSA) [8–10] should also Hungarian Journal of Industry and Chemistry THE INITIAL MAGNETIC SUSCEPTIBILITY OF DENSE AGGREGATED DIPOLAR FLUIDS 49 be mentioned which provides a formula for initial mag- netic susceptibility and magnetization as well, but the va- lidity of these are within the range of up to m∗ < √ 1.5. With regard to the distribution of chain aggregates in ferrofluids [11, 12], it has been found that in the ab- sence of any external magnetic field, the chain size dis- tribution is proportional to pk exp(−ε), where the chain length is denoted by k and the dimensionless energy pa- rameter ε is a function of the maximum dipole interaction energy but independent from the density, therefore, it is a constant here and the probability of bond formation be- tween two adjacent particles in a chain is p. Subsequently, the chain size distribution decreases according to an ex- ponential function because pk = exp(−k/k0), where k0 = −1/ ln p. Based on some publications [13, 14], in the case of high dipole moments this exponential expres- sion turns into a power law: g(k) ∝ k−ι, with exponent ι ≈ 2.0− 2.5. Our investigation was performed in a dipolar hard- sphere (DHS) monodisperse system with a permanent magnetic dipole moment and of fixed density. It is sup- posed that the chains are perfectly straight and parallel to the local magnetic field. Furthermore, the average dis- tance between two neighbouring particles in a chain is the same as the distance between two neighbouring par- allel chains. The particles interact with each other only by the evolved mean magnetic field and the applied external magnetic field is superimposed on this, thus, the chains influence each other only by this mean magnetic field. 2. Theory 2.1 The appearance of probability analysis in the initial magnetic susceptibility The distribution of chains was calculated with the aid of probability analysis in a zero applied magnetic field. As was mentioned in the “Introduction”, Weiss’ theory states that the effective (now “local”) magnetic field converges to zero when χL < 3/4π and non-zero values when χL ≥ 3/4π. The central and surrounding particles are un- der the influence of this local magnetic field. The chain is oriented in the same direction as the local magnetic field. Let us denote the probability of chain formation between two particles whose direction relative to each other is par- allel to the local magnetic field by p. Now using this approach the exact distribution of chain length can be calculated because the probability that the chain length ought to be equal to k follows the geometric distribution with parameter q: gk = qpk−1, (4) where q = 1−p and the “chain distribution” is denoted by gk. According to its definition the geometric distribution shows the probability that a kth particle is connected to a chain of length k − 1 thus forming a chain of length k. A geometric sequence is described in Eq. 4, where the common ratio is denoted by p and the first term by q. The sum of the terms of a geometric sequence is S∞ = ft 1−cr , thus, ∑∞ k=1 gk = q 1−p = q q = 1. It is also important to calculate the so-called “particle distribution” that implies the number of those particles which are members of the chains of length k: hk = q2kpk−1. (5) The detailed deduction of hk and the sum of hk terms are described in Appendix A. The expected value of the geometric distribution with parameter q is 1/q, thus, here the average chain length is 1/q. The number of chains is equal to the number of par- ticles divided by the average chain length: n 1/q = nq, where the number of particles is denoted by n. Until now only the local magnetic field which arises from the strength of interaction energies between neigh- bouring particles and induces spontaneous magnetization in a random direction has been discussed, thus, the total magnetization of the system of volume V is equal to zero. When an infinitesimal external magnetic field H0 is switched on, non-zero total magnetization is formed. Since H0 is parallel to M, scalar notations are used in the following. As was observed from Pshenichnikov’s model the effective magnetic field is the sum of the external H0 and secondary (4π/3)M(H0) magnetic fields. The ques- tion arises why it is legitimate to use the expression of effective magnetic field from “Pshenichnikov” (Table 1: 3.2) instead of from “Weiss” (Table 1: 2.2). The answer is because H0 modifies infinitesimally the orientation of the chains but does not align them with its own direction, thus, the average angle between the local and external or even the effective magnetic fields is not equal to zero. When calculating the initial magnetic susceptibility, a chain of length k is considered as a particle with a dipole moment km, thus, in terms of magnetization the argu- ment of the Langevin function is kmHe kBT . The Langevin function is weighted by the distribution hk, and finally the gradient of magnetization in an infinitesimal external magnetic field is calculated as χ0 = ∂ ∂H0 ∣∣∣∣ H0=0 ρm ∞∑ k=1 hkL ( kmHe kBT ) . (6) An infinitesimally weak external magnetic field can be written as χ0 = 1 + p 1− p χL ( 1 + 4π 3 χL ) , (7) where the following infinite expression is used (|p| < 1): ∞∑ k=1 pk−1k2 = 1 + p (1− p)3 . (8) The detailed derivation of the initial magnetic suscepti- bility (Eq. 7) is given in Appendix B. 46(2) pp. 47–54 (2018) 50 NAGY Figure 1: The rates of the local magnetic field as a function of the density from Eq. 9 at three different dipole moments in the absence of any external magnetic field. 2.2 The numerical calculation of the probabil- ity of chain formation “p” The main challenge of our approach is the determina- tion of p. The particles form chains because of the lo- cal magnetic field even in the absence of any applied ex- ternal magnetic field. According to Weiss’ model when χL ≥ 3/4π this local magnetic field predicts an infi- nite initial magnetic susceptibility. The problem with this model is that it assumes that the orientation of the lo- cal magnetic field is parallel with the external magnetic field. Nevertheless, Weiss’ model is applicable to predict the extent of the local magnetic field by the expression (when H0 = 0): Hl = 4π 3 ρmL ( mHl kBT ) . (9) H∗l as a function of the reduced density ρ∗ at three dif- ferent dipole moments is presented in Fig. 1. The defini- tions of the reduced quantities are H∗ = H √ σ3/kBT ; M∗ = M √ σ3/kBT ; m∗ = m/ √ σ3kBT . All particles are considered to be influenced by this local magnetic field Hl, in the absence of any external magnetic field H0 when calculating the initial magnetic susceptibility. As was mentioned before, the most ac- cepted criterion for chaining is to determine an energy level and if the dipolar energy between two given parti- cles is under this level, the particles are in a bound re- lationship. Generally [15–17], this energy level is 70-75 % of the minimum of the dipolar energy, i.e. U∗lim = −0.7 ∗ 2(m∗)2. Here the well-known dipolar energy is defined as the interaction between point dipoles: Udd ij = −m 2 r3 ij [3 (m̂i · r̂ij) (m̂j · r̂ij)− (m̂i · m̂j)] , (10) where the particles have dipole moments of strength m as well as an orientation given by unit vectors m̂i and Figure 2: The feasible location of a particle between two fixed particles. m̂j . Furthermore, the distance between the centers of the particles is denoted by rij and r̂ij = rij/rij . As is shown in Fig. 2, according to our model parti- cle j can move along the direction of the chain between the two fixed adjacent particles, namely i and the grey one, in the tube with a light blue background. Logically, the minimum distance between two particles in a hard sphere system is σ, on a reduced scale d∗min = 1, while for the maximum distance d∗max = 2 〈r∗〉 − 1, where the reduced average distance between two adjacent particles is denoted by 〈r∗〉. Obviously the maximum distance between two neigh- bouring particles could be greater than d∗max but at higher densities in particular the surrounding particles obstruct the movement of the central particle. Assuming that the distance distribution is isotropic, it is given by 〈r∗〉 = 3 √ 1/ρ∗. Taken all round to calculate p the probability of those states of particle pairs should be totalled when the dipolar interaction energy is less than or equal to the aforemen- tioned energy limit Ulim and the interval of integration in distance is [d∗min, d ∗ max], that is p = ∫ Udd≤Ulim P (θi)dθiP (θj)dθjP (φi)dφiP (φj)dφj , (11) where 0 ≤ θ < π and 0 ≤ φ < 2π are the usual spherical angles of the dipoles and the probabilities when magnetic field H (here H = Hl) is applied in general are P (θ)dθ = exp ( mH kBT cos θ ) sin θdθ ∫ π 0 exp ( mH kBT cos θ ) sin θdθ (12) and P (φ) dφ = dφ/2π. The calculation of p was performed by numerical in- tegration. Particles i and j (Fig. 2) are under the influ- ence of the local magnetic field independently from each other. For both particles, all possible values of θ, φ, and r are swept and taken into account if the dipolar interaction energy between particles i and j is less than or equal to Ulim. This is expressed by Eq. 11. For instance, when ρ∗ = 0.8 and m∗ 2 = 3.0 then H∗l = 5.154 and d∗max = 1.154435. The probability of chaining between particles i and j as a function of dis- tance is shown in Fig. 3. The requested probability p is Hungarian Journal of Industry and Chemistry THE INITIAL MAGNETIC SUSCEPTIBILITY OF DENSE AGGREGATED DIPOLAR FLUIDS 51 Figure 3: An example calculation of p. The parame- ters are rho∗ = 0.8, (m∗)2 = 3.0, H∗ l = 5.154, d∗max = 1.154435, and U∗ lim = 0.7U∗ min. The requested probability p is the average of this curve in the interval [d∗min, d ∗ max]. the average of this curve from 1 to d∗max, i.e. p = 0.3454, if U∗lim = 0.7U∗min. 3. Simulation results and discussion To determine the initial magnetic susceptibility, Monte Carlo simulations of DHS fluids were performed using a canonical NVT ensemble. Boltzmann sampling [18], pe- riodic boundary conditions and the minimum-image con- vention were applied. In order to take into account the long-range character of the dipolar interaction, the re- action field method under boundary conditions of con- duction was used. After 100,000 equilibration cycles, be- tween 1 and 10 million production cycles were conducted involving N = 512 particles. In the absence of an exter- nal magnetic field, the initial magnetic susceptibility was obtained from the following fluctuation formula: χ0 = 1 3kBTV (〈 M2 〉 0 − 〈M〉20 ) , (13) where M = ∑N i=1 mi. The exact results of the probability of chain formation from Eq. 11 applied to the local magnetic field, given by Eq. 9, are shown in Table 2. The data associated with the aforementioned dipole moments were rounded to three non-zero decimals. According to Fig. 1 at low densities the values of the local magnetic field are zero, neverthe- less, the rates of the probability of chaining are not equal to zero. The value of the energy limit was fitted to the best agreement between the simulation data and our the- ory lines. Our theoretical findings (green lines, Eq. 7 ) in terms of the initial magnetic susceptibility according to our Monte Carlo simulation data (blue dots) and the values of Ivanov’s theory (grey lines, Table 1: 4.4) are compared in Figs. 4-6. The variability is not indicated where its mag- nitude is comparable to the size of the dot. The values of dipole moments in the order m∗ = 1, m∗ = √ 2 and m∗ = √ 3 are shown in Figs. 4-6. Table 2: The probability of chaining at three different dipole moments. The applied energy limit at m∗ = 1 and m∗ = √ 2 is Ulim = 0.77Umin and Ulim = 0.71Umin at m∗ = √ 3. p ρ∗ m∗ = 1 m∗ = √ 2 m∗ = √ 3 0.1 0.000260 0.000263 0.000580 0.2 0.000426 0.000429 0.000943 0.3 0.000615 0.000617 0.00794 0.4 0.000852 0.00292 0.0250 0.5 0.00117 0.0110 0.0521 0.6 0.00164 0.0253 0.0953 0.7 0.00241 0.0515 0.170 0.8 0.0135 0.107 0.320 0.85 0.0269 0.164 0.471 0.9 0.0539 0.273 0.649 0.95 0.101 0.416 0.775 In the case of m∗ = 1 (Fig. 4), the energy limit is Ulim = 0.77Umin. A significant difference was only observed between Ivanov’s theory and the simulation data beyond a reduced density of 0.8 and the simu- lation dots were tracked by our present theory. The maximum relative deviation from the simulation data is |χ0 sim − χ0 th| /χ0 sim = 4.175%. When m∗ = √ 2, the appropriate energy criterion is Ulim = 0.77Umin as well. Up to a reduced density of 0.6 the former theory and simulation are in good agreement (Fig. 5), but in the present theory more than double the surplus is shown in the region of high density compared to Table 1: 4.4. The maximum relative deviation from the simulation data is 8.024 %. Here it is quite conceivable that the simple series ex- pansion of initial magnetic susceptibility as the summa- tion of positive integer powers of Langevin susceptibil- ity is unsatisfactory. By increasing the third coefficient in Figure 4: Initial magnetic susceptibility of DHS fluid as a function of reduced density with dipole moment m∗ = 1. Monte Carlo simulation results are denoted by symbols and the solid lines correspond to the present (Eq. 7) and Ivanov’s (Table 1: 4.4) theories. 46(2) pp. 47–54 (2018) 52 NAGY Figure 5: Initial magnetic susceptibility of DHS fluid as a function of reduced density with dipole moment m∗ =√ 2. Monte Carlo simulation results are denoted by sym- bols and the solid lines correspond to the present (Eq. 7) and Ivanov’s (Table 1: 4.4) theories. Figure 6: Initial magnetic susceptibility of DHS fluid as a function of reduced density with dipole moment m∗ =√ 3. Monte Carlo simulation results are denoted by sym- bols and the solid lines correspond to the present (Eq. 7) and Ivanov’s (Table 1: 4.4) theories. Table 1: 4.4, the initial magnetic susceptibility at lower densities is also increased. When m∗ = √ 3 the difference is even more spec- tacular between the theories (Fig. 6). At high densities the uncertainty of initial magnetic susceptibility is quite large with regard to the simulation data. The best fit curve belongs to an energy limit of 71 %, which is very close to the value from references [15–17] of 70 %. The maxi- mum relative deviation from the simulation data is 15.850 %. When m∗ = 1 and ρ∗ = 0.95, with an energy limit of 70 %, the theoretical value of initial magnetic suscep- tibility is χ0 = 1.042, and if the energy limit is 75 %, χ0 = 0.937. Both values are higher than the correspond- ing simulation data, thus, the energy limit has to be raised to 77 %. The situation is similar when m∗ = √ 2 and ρ∗ = 0.95, namely χ0 = 8.701 when the energy limit is 70 % and χ0 = 6.363 when it is 75 %. Probably at lower dipole moments and higher densi- ties the two adjacent particles cannot be considered as a chain even though the interaction energy exceeds an en- ergy limit of 70 % or 75 % for example because the av- erage kinetic energy is closer to this interaction energy than is the case when m∗ = √ 3. Therefore, the duration of chain formation is short to draw the particles together. 4. Conclusion The initial magnetic susceptibility of dipolar hard sphere fluids was described by the help of the probability vari- able p supplemented by Pshenichnikov’s well-known the- ory. The validity of the present theory is up to ρ∗ = 0.95 and at leastm∗ = √ 3. In addition to the theoretical work, Monte Carlo simulations were run to confirm our investi- gation. At higher densities, especially with higher dipole moments, the former related theories significantly under- estimate the simulation data but good results are also pro- vided by the presented theory within this range. By con- sidering the green curves and blue dots in Figs. 4-6, it is obvious that the simple quadratic or tertiary polynomial approach is outdated, therefore, the Taylor series expan- sion of (1 + p)/(1− p) contains powers even as high as infinity. 5. Appendix 5.1 Appendix A The particle distribution can be obtained by di- viding the number of particles in chains of length k by the total number of particles: hk = kgk∑ kgk = kqpk−1∑ kqpk−1 = kpk−1∑ kpk−1 = kpk−1 1 + 2p+ 3p2 + · · · = = kpk−1 (1+p+ p2 + · · · ) + (p+ p2 + p3 + · · · ) + (p2 + p3 + p4 + . . .) + · · · = = kpk−1 (1 + p+ p2 + · · · ) + (p+ p2 + p3 + · · · ) + (p2 + p3 + p4 + · · · ) + · · · = = kpk−1 1 1− p + p 1− p + p2 1− p + · · · = qkpk−1 1 + p+ p2 + · · · = qkpk−1 1 1− p = q2kpk−1. (14) Hungarian Journal of Industry and Chemistry THE INITIAL MAGNETIC SUSCEPTIBILITY OF DENSE AGGREGATED DIPOLAR FLUIDS 53 The sum of hk terms must be equal to one: ∞∑ k=1 hk = ∞∑ k=1 q2kpk−1 = q2 ( 1 + 2p+ 3p2 + . . . ) = q2 [( 1 + p+ p2 + · · · ) + ( p+ p2 + p3 · · · ) + · · · ] = = q2 [ 1 1− p + p 1− p + p2 1− p + · · · ] = q [ 1 + p+ p2 + . . . ] = q 1 1− p = 1. (15) 5.2 Appendix B χ0 = ∂ ∂H0 ∣∣∣∣ H0=0 ρm ∞∑ k=1 hkL ( kmHe kBT ) = ∂ ∂H0 ∣∣∣∣ H0=0 ρm ∞∑ k=1 q2kpk−1L km ( H0 + 4π 3 ρmL ( mH0 kBT )) kBT  = = q2ρm ∂ ∂H0 ∣∣∣∣ H0=0 ∞∑ k=1 kpk−1L kmH0 kBT + 4π 3 kρm2L ( mH0 kBT ) kBT  = = q2ρm ∞∑ k=1 kpk−1 1 3  km kBT + 4π 3 kρm2 1 3 m kBT kBT  = q2 ∞∑ k=1 k2pk−1 ( 1 3 ρm2 kBT + 1 9 4π 3 ρ2m4 k2 BT 2 ) = q2 ( χL + 4π 3 χ2 L ) ∞∑ k=1 k2pk−1 = 1 + p 1− p χL ( 1 + 4π 3 χL ) . (16) REFERENCES [1] Langevin, P.: Sur la théorie du magnétisme, Jour- nal de Physique Théorique et Appliquée, 1905 4(1), 678–693 DOI: 10.1051/jphystap:019050040067800 [2] Weiss, P.: L’hypothése du champ moléculaire et la propriété ferromagnétique, Journal de Physique Théorique et Appliquée, 1907 6(1), 661–690 DOI: 10.1051/jphystap:019070060066100 [3] Pshenichnikov, A. F.; Mekhonoshin, V. 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J.: Computer Simulation of Liquids (Clarendon Press, Oxford) 1987 ISBN: 978-0198556459 Hungarian Journal of Industry and Chemistry https://doi.org/10.1103/PhysRevLett.71.2729 https://doi.org/10.1103/PhysRevE.49.5131 https://doi.org/10.1103/PhysRevE.49.5131 https://doi.org/10.1103/PhysRevE.51.5962 HUNGARIAN JOURNAL OF INDUSTRY AND CHEMISTRY Vol. 46(2) pp. 55–62 (2018) hjic.mk.uni-pannon.hu DOI: 10.1515/hjic-2018-0019 WORKER MOVEMENT DIAGRAM BASED STOCHASTIC MODEL OF OPEN PACED CONVEYORS TAMÁS RUPPERT1 AND JÁNOS ABONYI *1 1MTA-PE Lendület Complex Systems Monitoring Research Group, Department of Process Engineering, University of Pannonia, Egyetem u. 10, Veszprém, H-8200, HUNGARY Human resources are still utilized in many manufacturing systems, so the development of these processes should also focus on the performance of the operators. The optimization of production systems requires accurate and reliable models. Due to the complexity and uncertainty of the human behavior, the modeling of the operators is a challenging task. Our goal is to develop a worker movement diagram based model that considers the stochastic nature of paced open conveyors. The problem is challenging as the simulator has to handle the open nature of the workstations, which means that the operators can work ahead or try to work off their backlog, and due to the increased flexibility of the moving patterns the possible crossings which could lead to the stopping of the conveyor should also be modeled. The risk of such micro-stoppings is calculated by Monte-Carlo simulation. The applicability of the simulator is demonstrated by a well-documented benchmark problem of a wire-harness production process. Keywords: Industry 4.0, Operator 4.0, Monte-Carlo simulation, Process development, Line balanc- ing, Wire-harness assembly 1. Introduction Conveyor lines are more productive than regular assem- bly lines [1]; therefore there are more prevalent in the au- tomotive industry [2]. The movement of these conveyors mostly has paced and cyclic characteristic where at the beginning of the cycle, every station moves to the next position [3]. It can happen that the operator cannot finish his/her work before the product leaves the workstation. There are two alternative approaches for completing the unfinished work. We speak about close station produc- tion when the operator must stop the conveyor even in case of a minor delay [4]. Such processes are typical in Japan. In U.S.-type production systems, the operator does not have to finish his or her job, he or she can move with the product to the next station to work off the backlog. In these open stations the operators can work ahead or can be delayed [5], and the production stops only when the delay exceeds a critical limit. These open workstations reduce capacity loss by decreasing the risk of stopping the conveyor, but the modeling and optimization of these processes is much more challenging as the model has to handle idle and delay times [6]. Worker movement dia- grams are widely used to model the work of operators at conveyor belts [7]. Such models can be used to reduce the risk of conveyor stoppage [8] and optimize production se- quence [9], since the optimal distribution of the products can also reduce the probability of critical backlogs [10]. *Correspondence: researcher@abonyilab.com Worker movement diagrams focus only one station. In open paced conveyors the operators effect on each other; therefore the model should handle the interactions be- tween the workstations, especially for the prediction of the conveyor stoppage. Our goal is to develop a worker movement diagram based model for open paced conveyors, which model con- siders the stochastic nature of production and recognizes the meeting point of operators and analyzes the idle times due to working in the same zones and risk of stopping the production in case of unmanageable backlogs. We in- troduce stochastic variables into the movement diagram representation based model and apply Monte-Carlo sim- ulation to evaluate the risk of conveyor stoppage and give robust estimates of the effects of different parameter set- tings. The simulator is developed in Python environment. The applicability of the proposed model and simulator is demonstrated by a well-documented benchmark problem of a wire-harness production process. Section 2 describes the worker movement diagram and the sections defined based on the relative position of the operators and the conveyor. The model of the paced conveyor is based on equations that represent the movement of the operators in these sections. Based on these equations we calculate when the conveyor should be stopped. Section 3 describes the applicability of the developed simulator in a wire harness production system. mailto:researcher@abonyilab.com 56 RUPPERT AND ABONYI 2. Model of the paced conveyor 2.1 Problem definition The most widespread paced open station conveyors are used to produce wire harnesses in the automobile in- dustry. The optimization and cost estimation of these processes are an economically significant problem [11]. These modular assembly lines consist of manual work- stations (tables) shown in Fig. 1. Human operators work at the tables that are moving similarly as a conveyor belt (see Fig. 2). These tables move with a fixed speed which is determined based on the tact time, tc. After the cycle, every table moves to the next station. The modeling the relative position of the operators and the tables can be represented by worker movement diagrams that will be presented in the next section. 2.2 Movement diagram of an open station The paced conveyor has k, k = 1, . . . ,K is number of workstations that moves in every n = 1, . . . , N cycle. The speed of the conveyor is vc, and the walking speed of operator is vw. The tc is the tact time determines the assembly speed: vkn = L tkπ(n−k) (1) where L represents the length o the workstation, the tkπ(n−k) the assembly time which is dependent on the produced product. The sequence of the products is rep- resented by a π vector of the labels of the types, so π(k) = pj states that type product pj started to be pro- duced during the k-th production cycle. The modeling of the paced conveyor is complex task as the conveyor moves only for a tcm < tc period of the time, which de- fines several sections of the tack time according to the speed and position of the table and the operators. As it is depicted in Figs. 3 and 4, the worker move- ment diagram is divided for six sections (s = 1, . . . , 6) . 1. The operator moves to the starting point of the table Figure 1: An example assembly table in wire harness man- ufacturing. The dashed line with an arrow represents the worker motion at the table. The operator works on the ta- ble from left to right. The assembly speed is vkn. Figure 2: The most widely used open station paced con- veyors are used in wire harness assembly, where the oper- ators are working at tables that moving in every cycle of the production [12]. 2. The operator works before the new cycle 3. The operator and the table move together 4. The operator works and the table stays 5. The operator and the table move together after the end of tact time 6. The operator works and the table stays after the end of tact time In the first section, s = 1, the operator walks to the left side of the table, F (1)kn. After reaching this posi- tion the operator starts the assembly process and moves with the conveyor till the conveyor moves to its next workspace. After this F (3)kn position the operator works at the standing table with a vkn speed. When the job is fin- ished, the operator reaches the end of the table, F (4)kn = kL, as it is shown at Fig. 5). The second, fifth and sixth sections happen when operator deviates from this normal case (work ahead or delayed). In the following, we present a model that describes how the positions of the table and the operators are chang- ing in time. In the model F (s)kn denotes the position of kth operator at nth cycle step in sth section of diagram, where the positions are measured from the starting point of the first table. Section 1. - The operator moves to the starting point of the table At the beginning of the cycle, the operator moves the starting point of the next table which is 2L far from its actual position. The F (1)kn position when the kth opera- tor reaches the staring point of table should be calculated as F (1)kn = F (6)kn−1 − T (1)knvw (2) T (1)kn = NWT+DWT+CDWT+ IWT (3) where F (6)kn−1 is the kth operator finishing position in the previous cycle step (n− 1), while the T (1)kn required Hungarian Journal of Industry and Chemistry Worker Movement Diagram Based Model Of Open Paced Conveyors 57 Figure 3: Worker movement diagram of the sections when the operator works ahead. Lines with arrow represent the motion of the operator, while dashed lines represent movement of the table. Figure 4: Worker movement diagram of the sections when the operator has a backlog. Lines with arrow represent the motion of the operator, while dashed lines represent movement of the table. Figure 5: Worker movement diagram of one station. The first meeting point with the table and the operator is F (1)kn. F (3)kn and F (4)kn are the positions at the end of the second and third sections. When there is no delay or the operator does not work ahead F (4)kn = F (6)kn, where F (6)kn is the finishing position. 46(2) pp. 55–62 (2018) 58 RUPPERT AND ABONYI time can be decomposed into four components, which will be modeled in the following subsections: • NWT - Normal Walking Time • DWT - Delayed Walking Time • CDWT - Critically Delayed Walking Time • IWT - Idle Walking Time NWT: Normal Walking Time In the normal case, the operator and the conveyor move together at the beginning of the cycle with vc+vw relative speed. The effect of the akn−1 idle time and the lkn−1 late time of the previous cycle is represented by the NWTa and NWTb variables that are used to calculate the NWT walking time: NWT = max[min(NWTa; NWTb); 0] (4) NWTa = max ( 2L− akn−1vw vc + vw ; 0 ) (5) NWTb = min ( tcm − lkn−1, 2L vc + vw ) , (6) where akn−1vw represents the walking distance of opera- tor at the end of the previous cycle. When tcm − lkn−1 is less than zero, then operator does not have to walk, be- cause he or she still works on the last (n− 1) product (In this case we should calculate DWT). DWT: Delayed Walking Time When the assembly time in the previous cycle exceeds tc, DWT is equal to the time which necessary for the reaching the table after tc. DWT = IF [tcm − lkn−1 > 0 OR lkn−1 = 0]; (7) THEN DWTh; ELSE 0 DWTh = (8) max [ 2L vc + vw −max ( tcm − lkn−1; 0 ) ; 0 ] vcw where vcw = vc+vw vw is the walking speed of operator, when the conveyor is moving. CDWT: Critically Delayed Walking Time When lkn−1 is more than tcm, the operator moves to the beginning of the table when the conveyor is standing. CDWT = IF [tcm − lkn−1 <= 0 (9) OR lkn−1 = 0]; THEN 2L vw ; ELSE 0 IWT: Idle Walking Time When the conveyor does not move and akn−1 is bigger than the necessary walking time, 2L vw , then IWT = min ( akn−1, 2L vw ) (10) Section 2. - The operator works before the new cycle TheF (2)kn staring position and T (2)kn duration of the The second section is calculated as: F (2)kn = F (1)kn + T (2)knv k n (11) T (2)kn = max ( akn−1 − 2L vw ; 0 ) (12) where vkn is the average speed of the assembly. Section 3. - The operator and table move together In this section, operator and the conveyor are moving to- gether for a time period shorter than tcm, so they will meet at: F (3)kn = F (2)kn + T (3)kn(vc + vkn) (13) T (3)kn = min ( max [ (n− 1)tc + tcm − T k; 0 ] ; tcm ) (14) where (n− 1)tc + tcm describes the time instant the sec- tion will finish. In normal situation T (3)kn equals to tcm, while in extreme case the operator has as significant idle time as he or she finishes his or her job before the end of this section. Section 4. - The operator works and table stays In this section the operator works with vkn linear speed until the conveyor does not move, so this section finishes at: F (4)kn = F (3)kn + T (4)knv k n (15) T (4)kn = min{max[ntc − T ; 0]; (16) L vkn − T (2)kn − T (3)kn} , where L vkn −T (2)kn−T (3)kn defines the remaining assem- bly time before the end of the tact time. The idle and delay times At the end of the cycles the akn idle or lkn delay time is calculated as: lkn = max ( L vkn + T (1)kn − akn−1 + lkn−1 − tc; 0 ) (17) akn = max ( tc − L vkn − T (1)kn + akn−1 − lkn−1; 0 ) (18) The prediction of conveyor stoppage is the most impor- tant ability of the model which will be calculated based on the delay time as it will be presented in the following subsection. Hungarian Journal of Industry and Chemistry Worker Movement Diagram Based Model Of Open Paced Conveyors 59 Section 5. - The operator and the table move together after the end of tact time This section can be considered as the modification of the third section with the delay of the operator. As we already know lkn and the operator can work in this section maxi- mum till tcm, the calculation is straightforward: F (5)kn = F (4)kn + T (5)kn(vc + vkn) (19) T (5)kn = min ( lkn, tcm ) (20) Section 6. - The operator works and the conveyor stays after the end of tact time As the duration of this section is limited as tc − tcm, the variables that define the end of the section are calculated as: F (6)kn = F (5)kn + T (6)knv k n (21) T (6)kn = min [ max ( lkn − tcm; 0 ) ; tc − tcm ] (22) Calculation of the stoppage and the idle time The open station type operation of the paced conveyor has increased flexibility as the conveyor has to be stopped only when the delay of the kth operator is as significant as it disturbs the work of the neighboring k−1th operator. We define this situation as: T k + T (1)kn <= T k−1 + T (1)k−1 n−1 + tc 4 (23) In this case the idle Ikn time has to be modified by T (1)kn and reset the value of akn to zero. Ikn = (n− 1)tc − T (1)kn (24) When the lkn − T (6)kn is smaller than tcm, the operator stops the conveyor. The lkn is reset and the stoppage time is: Skn = max(lkn − T (6)kn − tcm; 0) (25) 2.3 KPIs and the developed simulator The developed simulator handles the stochastic and open nature of the conveyor, simulates all workstations, the in- teractions between the operators and predicts stoppage. The worker movement diagram representation helps in the stoppages prediction (see Fig. 6). Production planners can use the developed simulator to try sequencing strategies and analyze a new production lines capability. The following key performance indica- tors (KPIs) calculated based on Monte-Carlo simulation gives a realistic picture about the production. • The balance of conveyor line is depended on the maximum of the late times of operators, lk = [lk1 , l k 2 , . . . , l k n]: B = K∑ k=1 max(lk) K 1 tc (26) • The efficiency of production is calculated based on to the sum of the L vkn assembly times di- vided by the maximum of the T(6) k = T (6)k1 , T (6) k 2 , . . . , T (6) k n) finishing times and the sum of stoppage times multiplied by the number of workstations. P = K∑ k=1 L vkn {max[T(6) k ] + N∑ n=1 K∑ k=1 Skn}K (27) • The sum of the S stoppage times (Eq. 25). • The mean of the assembly times. The simulator and the movement diagram are devel- oped in Python environment. d The developed simulator and the related dataset is freely and fully available on the website of authors: www.abonyilab.com. 3. Application to wire harness production To demonstrate the applicability of the simulator three typical types of production sequencing strategies were analyzed. In the first case, the sequence follows the ran- dom customer demand which case often happens in Just In Time (JIT) production. Batch production is a more ef- ficient sequencing strategy. In this case, batches of lower and higher complexity products are following each other. One of the best solutions is the π = m1,m2,m1, . . . high/low sequencing strategy because it utilizes the open station nature of the conveyor. The studied conveyor contains K = 5 workstations. The number of manufactured products is N = 100, and two different group of products (M = 2) are produced. The assembly times are represented by a normal distribu- tion, which is t1 = N (250, 30) for the lower complexity product and t2 = N (310, 30) for the higher complexity product. The tact time of the conveyor is constant and set to tc = 280s which is the average assembly time of the products. Fig. 7 shows the results of 1,000 simulations of the three sequence types. This scatter matrix plot shows the main KPIs, the balance, the number of the manufactured products, the number of stoppages, and the average as- sembly times. The green dots represent the High/Low, the blues the batched, and the red the random sequences. As shown in Fig. 7, the difference between the ran- dom (blue) and high/low (green) sequences is significant on all KPIs. The batched sequence (red) has similar per- formance to the high/low sequence, but many times this batch production is not manageable because of the high variance of the products and the short delivery times. 4. Conclusions As human resources are still necessary for many man- ufacturing systems, the development of production pro- cess should also focus on the performance of operators. 46(2) pp. 55–62 (2018) www.abonyilab.com 60 RUPPERT AND ABONYI −5 0 5 10 15 20 25 30 Distance [m] 0 1000 2000 3000 4000 5000 6000 Ti m e [s ] Figure 6: The developed worker movement diagram of five stations and 18 cycle steps. The distance begins at −5 m to represent the previous workstation. Figure 7: The result of a Monte-Caro simulation of three different sequencing strategies. The scatter plot shows all of KPIs. The high/low sequence is denoted by green, the batch by red, and the random by blue dots. The difference between the random and high/low sequences is significant on all KPIs. Hungarian Journal of Industry and Chemistry Worker Movement Diagram Based Model Of Open Paced Conveyors 61 According to the digital twin concept, this development should be based on the model of the production sys- tem, which necessaries the development of simulators that can handle uncertainties related to the human nature of the operators. The developed worker movement dia- gram based model handles the paced and open worksta- tions of the conveyors and the stochastic nature of pro- duction. The worker movement representation helps in the analysis of the operators which is needed to predict production stoppages. The introduction of stochastic vari- ables and the Monte-Carlo simulation-based evaluation of the key performance indicators provide a realistic pic- ture about the production. The applicability of the simula- tor in the analysis of the effect of production sequencing is demonstrated by a well-documented benchmark prob- lem of a wire-harness production process. The developed simulator is not specialized to the studied wire harness production; it can be used to model all of the types of paced conveyors even open or closed workstations. Acknowledgement This research was supported by the National Research, Development and Innovation Office NKFIH, through the project OTKA-116674 (Process mining and deep learn- ing in the natural sciences and process development) and the EFOP-3.6.1- 16-2016- 00015 Smart Specialization Strategy (S3) Comprehensive Institutional Development Program. Notations KPI Key Performance Indicator NWT Normal Walking Time DWT Delayed Walking Time CDWT Critically Delayed Walking Time IWT Idle Walking Time k index of workstation k = 1, . . . ,K K number of workstations n index of cycle step n = 1, . . . , N N number of cycle steps s index of section s=1, . . . , 6 vkn assembly speed of th operator [ms ] vw walking speed of the operator [ms ] vc speed of the conveyor [ms ] vcw walking speed of the operator when the conveyor is moving [ms ] tc tact time [s] tcm conveyor movement time [s] tk(π(n) assembly time of actual the product at kth operator [s] T (s)kn duration of the actual s section in nth cycle step a kth workstation [s] T(6)k finishing times of the kth operator [s] akn work ahead time in nth cycle step at kth operator [s] lkn late time in nth cycle step at kth operator [s] lk late times of kth operator [s] T actual simulated time [s] Ikn final idle time in nth cycle step at kth workstation [s] Skn stoppage time in nth cycle step at kth workstation [m] F (s)kn position of operator at the actual s section in nth cycle step a kth workstation [m] Tablekn table position in nth cycle step at kth operator [m] π(n) sequence of products [−] L length of the workstation [m] T kn position of the tables [m] REFERENCES [1] Estrada, F., Villalobos, J.R., Roderick, L., Estrada, F., Villalobos, J.R., Roderick, L.: Evaluation of Just- In-Time alternatives in the electric wire-harness in- dustry, Taylor and Francis, 1997 35(7), 1993–2008, DOI: 10.1080/002075497195038 [2] Lodewijks, G.: Two Decades Dynamics of Belt Conveyor Systems Bulk Solids Handling, 2002 22(2), 1–2 [3] Xiaobo, Z., Zhou, Z., Asres, A.: Note on Toyota’s goal of sequencing mixed models on an assembly line, Computers and Industrial Engineering, 1999 36(1), DOI: 10.1016/S0360-8352(98)00113-2, 57–65 [4] Sarker, B.R., Pan, H.: Designing a Mixed-Model, Open-Station Assembly Line Using Mixed-Integer Programming, The Journal of the Operational Re- search Society Palgrave Macmillan Journals, 2001 52(52), 545–558 DOI: 10.1057/palgrave.jors.2601118 [5] Bukchin, J., Tzur, M.: Design of flexible assembly line to minimize equipment cost, IIE Transactions (Institute of Industrial Engineers), 2000 32(7), 585– 598 DOI: 10.1080/07408170008967418 [6] Bautista, J., Cano, J.: Minimizing work overload in mixed-model assembly lines, International Journal of Production Economics, 2008 112(1), 177–191 DOI: 10.1016/j.ijpe.2006.08.019 [7] Xiaobo, Z., Ohno, K.: Algorithms for sequencing mixed models on an assembly line in a JIT pro- duction system, Computers ind. 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They were tested for their rheological behaviour over the first 3 days of storage at room temperature, and for their characteristics based on a Hungarian Standard. Parameters were set such as the volume of the baked product, baking loss, crumb characteristics and elasticity of crumbs. The behaviour of flour from einkorn wheat is different to that of Tr. spelta. The properties of the tested flour mixes measured by a farinograph show that Tr. spelta produces an acceptable dough, on the other hand, the dough of Tr. monococcum develops quickly but is very unstable so weakens within minutes of being kneaded. This also suggests that doughs composed of einkorn wheat flour require a different type of kneading than those of Tr. spelta (or Tr. aestivum, also referred to as common wheat) flours. Breads composed of Tr. spelta were comparable with those made with Tr. aestivum, the crumb elasticity was above 90 % on the day of baking, which indicates high quality. The Tr. monococcum breads, however, were of low grade: the volume of the breads decreased by increasing the ratio of Tr. monococcum to Tr. spelta and the elasticity reduced to unacceptable levels (less than 60 %). It should be mentioned that the grading was based on breads made purely from Tr. aestivum flours. Keywords: spelt, einkorn, bread, texture analysis 1. Introduction As a result of the increasing number of cases of celiac disease and allergies, as well as the growing popularity of conscious nutrition, interest in older varieties of wheat is once again on the rise. In general, consumers think that these species of wheat are potentially less immunogenic than their modern equivalents. The manufacturing prop- erties of doughs produced from ancient varieties of wheat are much weaker than those of common wheat. In order to obtain good quality bakery products, it may be neces- sary to use mixtures of flours from different varieties. In our research, the properties of the flour of einkorn and spelt wheats in addition to breads that consist of dif- ferent proportions of these flours were prepared and in- vestigated. During measurements, attempts were made to determine whether these wheat species – which are in the- ory suitable for baking bread – could improve the baking performance or whether a significant difference exists be- tween the characteristics of the finished products of vari- ous compositions. Crossing more modern varieties results in higher yields, greater resistance, more uniform ripening times and higher gluten contents. Although these breeding pro- cedures facilitated processing, the genetic diversity and nutritional value decreased significantly which virtually *Correspondence: koczan.gyorgyne@etk.szie.hu resulted in the total displacement of indigenous species [1, 2]. One reason for this is that Tr. monococcum was consumed primarily as a mush or simply cooked; these methods did not require proofing, which was originally used in ancient Egypt during bread baking [3]. Bread made from spelt flour is also of lower quality than that of common wheat, both in terms of specific volume and crumb structure [4]. According to previous research, spelt wheat flour pro- duces less stable and elastic but stickier dough than plain flour. Due to its sticky and soft nature after kneading, it is difficult to handle [5, 6]. Breads made from einkorn flour exhibit a wide range of possible specific volumes, ranging from very low to high. Although only a few subtypes are suitable for making breads, most versions are suitable for preparing pasta or biscuits [7], or utilisation for special purposes like fermentation processes [8]. The first phase of the investigations concerned the quality of the gluten, followed by the preparation and testing of loaves of bread. The main question concerned how the blends of flours of these species of wheat influ- ence the quality of the final products. mailto: koczan.gyorgyne@etk.szie.hu 64 KÓCZÁN-MANNINGER AND BADAK-KERTI 2. Experimental 2.1 Samples and Measurements Triticum monococcum (einkorn) and Triticum spelta wheat flours were manufactured by Szabó Hengermalom Kft. using conventional technology and contained no ad- ditives or bread improvers. For the measurements fine flours were used, i.e. small grain particles with low bran content, to ensure they contained only a negligible amount of outer shell. The determination of wet gluten content was per- formed according to a standard using the Glutomatic Sys- tem. After gluten washing, a gluten index was also calcu- lated using a gluten centrifuge. The moisture content was determined by a Sartorius moisture analyser. The uniformly dispersed sample of 2.5 g was dried at 105 ◦C to a constant weight (which has not changed for 20 seconds more than 1 mg). The change in mass could be deduced from the moisture content of the whole test substance. The determination of water absorption was conducted by a Brabender farinograph in accordance with a Hungar- ian standard (MSZ 6369-6:2013) in duplicates, followed by further experimentation using a baking test (MSZ 6369-8:1988). The volume of the bread samples was measured by placing a loaf in a container of known volume and pour- ing in a known quantity of mustard seeds around the loaf until the container was full. By measuring the amount of seeds remaining once the container was full, the volume of the loaf could be calculated. The quality of the bread texture was evaluated by a TA.XTplus texture analyser (Stable Micro Systems, Sur- rey, UK), following a modified American Association of Cereal Chemists (AACC) International approved method (74-09) and expressed as crumb firmness (force, 1/g) and relative elasticity (%). A 40 % compression of a 25 mm- thick sample was achieved, following a resting time of 30 seconds (at the same compression depth) and then the measuring head was slowly lifted and the springiness of the sample calculated. Thus, it was a “measure of force in compression” test using an AACC 36mm-diameter cylin- der probe with radius (P/36R). The analyser was set at a ‘return to start’ cycle with a pre-test speed of 1 mm s−1, a test speed of 0.5mm s−1, a post-test speed of 10 mm s−1 and a pre-defined percentage (40 %) of the original sam- ple height. The relative elasticity was calculated from the difference between the original height and the height to which the sample recovered (after pressing and releasing the pressure). Measurements were conducted in triplicates. Statisti- cal evaluations were carried out using ANOVA (analysis of variance) tests in Excel. Bread samples were stored at room temperature in plastic bags. Texture measurements were taken on the day of baking after the bread had been cooled to room temper- ature (Day 0) and on the following 2 days, namely Days 1 and 2. Table 1: Composition of the samples (%) 100A 80A 60A 40A 20A 100T Tr. monoc. (A) % 100 80 60 40 20 0 Tr. spelta (T) % 0 20 40 60 80 100 Water % 57 62 64 65.4 65.8 71 Yeast % 4 4 4 4 4 4 Salt % 1.2 1.2 1.2 1.2 1.2 1.2 The ingredients consisted of 250 g of flour, 10 g of yeast and 3 g of salt, the only variable parameter was the amount of water used to make the dough. Initially, the dough consisted of approximately 60 % (150 ml) water based on the weight of the flour, and the amount of water was increased to form a homogeneous dough. The final compositions are shown in Table 1. 3. Results and Discussion 3.1 Experiments In the case of the einkorn flour, gluten washing was in- effective as it could not be washed out. After the mixing phase, a yellowish substance remained on the bottom of the washer. In the case of spelt flour, gluten tests could be conducted without any problems. The wet gluten content of the Tr. spelta flour was 46.73 %. According to the Hungarian regulations bread wheat flours must have a minimum wet gluten content of 28 % and for wheat flours used to improve the bak- ing quality a minimum of 34 %. Bakers consider a gluten content in excess of 30 % to be good. The wet gluten con- tent of the spelt flour examined is well above this value, but other factors are also taken into account to determine the quality of flour. The gluten index, a measure of gluten quality, of spelt flour was 45.73 %. A value of between 60 and 90 % is considered to be ideal, below 60 % weak and in excess of 90 % too strong. Thus, the gluten quality of the spelt flour was clearly weak. The gluten quality calculated from the results of the farinograph tests for spelt flour was 98 % which is ac- ceptable but does not fully reflect the quality of the flour. Although the kneading and stability times of the doughs fell within the range of expected values, the planimetric area was greater due to the degree of softening. Thus, the quality score obtained by Hankóczy’s evaluation method was smaller. The farinogram of spelt flour more closely resembles a flour of medium quality (Fig. 1). This is especially true for the Tr. monococcum flour. It reaches its maximum consistency very quickly; the top of the curve barely exceeds the consistency line (500 BU – Brabender Units). The degree of softening is enormous, as is reflected well by the large planimetric area. The qualitative value assigned to the curve is very low (Fig. 2). Hungarian Journal of Industry and Chemistry INVESTIGATIONS INTO FLOUR MIXES OF TRITICUM MONOCOCCUM AND TRITICUM SPELTA 65 Figure 1: Farinogram of Triticum spelta flour. A direct correlation was identified between the vol- ume of the bread samples and the amount of spelt flour in the flour blend (Fig. 3). This is in accordance with the gluten quality of the flour blends, as is seen from the re- sults of the farinograph measurements. The crumb hardness of the bread samples is shown in Fig. 4. As the samples started to age the compression force increased. By examining the initial and final forces (measures of crumb hardness), it can be stated that sam- ple 60A showed the best results. In this case, the force in- creased by 29 % between Day 0 and Day 2. For samples containing less einkorn flour the crumbs seemed to be softer and the relative increase in hardness during storage less (when values on Day 2 were compared to those on Day 0). Even though sample 80A was initially even softer than 60A, by the end of Day 2 it needed 1.7 times the force to compress it. An explanation of this phenomenon can also be given with regard to the different composi- tions of the starch molecules in einkorn flour compared to those in spelt flour. The staling of bread is related to the crystallization processes of starch molecules. Significant differences between samples consisting of 100 % spelt flour and those of 20 % einkorn flour mixed with 80 % spelt flour were shown by the results. The in- crease in crumb hardness during storage resulted in sig- nificant differences in all samples of identical composi- tions. Figure 2: Farinogram of Triticum monococcum flour Figure 3: Volume of bread samples (A – einkorn flour, T – spelt flour; the numbers are the percentages of einkorn flour in the flour blend) The elasticity of the bread crumbs increased as the amount of spelt flour increased in the flour blend (Fig. 5). This tendency persisted during storage as well. The slight increase in the elasticity of the bread composed of 100 % Triticum monococcum flour was probably due to improper handling of the samples, i.e. improper cooling before being packed, although it is questionable whether any moisture originating from the headspace of the pack- aging could cause such a change. Taking into account that the results obtained could be derived from measurement and/or calculation errors, it may be worthwhile to consider the role of the chemical structure of einkorn flour during the baking process, and its effect on the elasticity during further targeted experi- ments. By using a rating system for the Tr. aestivum flours, the bread samples can be classified. Although the same judgment about the “marketability” of the bread sam- ples cannot be made for breads based on these special types of flour, trends can clearly be observed. By adding more einkorn flour to the flour blends, the “quality” of the crumb structure decreased. Most of the samples did not achieve an elasticity of 80 % meaning that they did not return to 80 % of their orig- inal height after compression. With these values, most of the breads fall into the non-marketable category. Elastic- Figure 4: Crumb hardness (Force, 1/g) as a function of different flour compositions over 3 days 46(2) pp. 63–66 (2018) 66 KÓCZÁN-MANNINGER AND BADAK-KERTI Figure 5: Change in the elasticity of the bread samples during storage at room temperature ities of between 90 and 95 % are indicative of good qual- ity breads. Such values were only achieved when 100 % Triticum spelta flour was used. After 2 days of storage at room temperature, the crumbs of 100 % spelt flour bread degraded to an average quality. 4. Conclusion The purpose of our investigations was to examine the quality of flours from varieties of ancient wheats. Gluten could not be washed out of einkorn samples and the wet gluten content of Tr. spelta was also very low. Farinograph measurements revealed that when only einkorn flour is used, the dough forms very fast but is very soft and almost completely unstable. By mixing einkorn and spelt flours bread can be made, however, an acceptable ratio would not exceed 20 % of einkorn to 80 % of Tr. spelta flour. With this flour blend, the resulting bread volume is comparable to the accepted low values of bread composed of 100 % spelt flour. The hardness and elasticity of the bread crumbs al- ready changed significantly at the lowest mixing ratios. Further studies on the sensory characteristics of these breads and consumer tests are needed before deciding on the use of flour blends of Triticum monococcum and Triticum spelta in the absence of any addition of Triticum aestivum flour. REFERENCES [1] Draskovics, M. R.: Seed plants (Spermatophyta) In: Turcsányi, G. (ed.) Agricultural botany, Mezőgaz- dasági Szaktudási Kiadó, Budapest, Hungary, 2000 pp 363-365 ISBN: 9633563593 [2] Dinu, M.; Whittaker, A.; Paglia, G.; Benedet- telli, S.; Sofi, F.: Ancient wheat species and human health: biochemical and clinical impli- cations. J. Nutr. Biochem., 2018 52, 1-9 DOI: 10.1016/j.jnutbio.2017.09.001 [3] Brandolini, A.; Hidalgo, A.: Chapter 8: Einkorn (Triticum monococcum) Flour and Bread in Flour and Breads and their Fortification In: Preedy V. R.; Watson R. R.; Patel V. B.: Health and Disease Pre- vention, Academic Press/Elsevier, UK, 2011 pp 79- 88 ISBN: 978-0-12-380886-8 [4] Abdel-Aal, E-S. M.; Hucl, P.; Sosulski, W.; Bhirud, P. R.: Kernel, milling and baking properties of spring-type spelt and einkorn wheats. J. Cereal Sci., 1997 26, 363-370 DOI: 10.1006/jcrs.1997.0139 [5] Callejo, M. J.; Vargas-Kostiuk, M. E., Rodríguez- Quijano, M.: Selection, training and validation pro- cess of a sensory panel for bread analysis: Influence of cultivar on the quality of breads made from com- mon wheat and spelt wheat. J. Cereal Sci., 2015 61, 55-62 DOI: 10.1016/ j.jcs.2014.09.008 [6] Frakolaki, G.; Giannou, V.; Topakas, E.; Tzia, C.: Chemical characterization and breadmaking poten- tial of spelt versus wheat flour. J. Cereal Sci., 2017 79, 50-56 DOI: 10.1016/j.jcs.2014.09.008 [7] Hidalgo, A., Brandolini, A.: Lipoxygenase ac- tivity in wholemeal flours from Triticum mono- coccum, Triticum turgidum and Triticum aes- tivum. Food Chem., 2012 131, 1499-1503 DOI: 10.1016/j.foodchem.2011.09.132 [8] Hetényi, K.; Németh, Á.; Sevella, A.: Examination of medium supplementation for lactic acid fermen- tation. Hung. J. Ind. Chem., 2008 36(1-2) 49-53 Hungarian Journal of Industry and Chemistry https://doi.org/10.1016/j.jnutbio.2017.09.001 https://doi.org/10.1016/j.jnutbio.2017.09.001 https://doi.org/10.1006/jcrs.1997.0139 https://doi.org/10.1016/ j.jcs.2014.09.008 https://doi.org/10.1016/j.jcs.2014.09.008 https://doi.org/10.1016/j.foodchem.2011.09.132 https://doi.org/10.1016/j.foodchem.2011.09.132 HUNGARIAN JOURNAL OF INDUSTRY AND CHEMISTRY Vol. 46(2) pp. 67–71 (2018) hjic.mk.uni-pannon.hu DOI: 10.1515/hjic-2018-0021 FORMATION OF GLYCIDYL ESTERS DURING THE DEODORIZATION OF VEGETABLE OILS ERZSÉBET BOGNÁR *1, GABRIELLA HELLNER2, ANDREA RADNÓTI2, LÁSZLÓ SOMOGYI1, AND ZSOLT KEMÉNY2 1Department of Grain and Industrial Plant Processing, Szent István University, Villányi út 29-43, Budapest, 1118, HUNGARY 2BEMEA Katalin Kővári R&D Centre, Illatos út 38, Budapest, 1097, HUNGARY Glycidyl esters are foodborne contaminants formed during the production of fats and oils, especially during the deodor- ization of palm oil. The hydrolyzed free form of glycidol has been categorized as probably carcinogenic to humans by the World Health Organization’s International Agency for Research on Cancer. The aim of this research was to study the formation of glycidyl esters during the lab-scale deodorization of the three most widely produced seed oils in the world (sunflower, rapeseed and soybean). The effects of two independent factors – temperature and residence time – were analyzed by a 32 full factorial experimental design and evaluated by response surface methodology. In accordance with findings in the literature, the greatest amount of glycidyl esters was formed in the soybean oil matrix. For all three oils, the effects of both residence time and temperature were significant, while the latter was more so. To reduce the formation of glycidyl esters, milder deodorization is required, which is limited because of the purposes sought by the thermal operation and removal of volatile minor components and contaminants. Keywords: glycidyl esters, deodorization, seed oils 1. Introduction Glycidyl esters (GEs) are foodborne contaminants formed in fat-containing food and food ingredients during high-temperature thermal treatment. According to previ- ous studies, glycidol is produced during digestion from the enzymatic hydrolysis of GEs [1,2]. The IARC (Inter- national Agency for Research on Cancer) has listed glyci- dol as a Group 2A or genotoxic carcinogen [3]. This year, the European Commission adopted the Commission Reg- ulation (EU) 2018/290 that stipulates the maximum level of glycidyl fatty acid esters permitted in vegetable oils and fats, infant formula, follow-on formula and foods for special medical purposes intended for infants and young children. The maximum concentration of glycidyl fatty acid esters is 1 mg/kg in vegetable oils and fats placed on the market for end consumers or for use as an ingre- dient in food, and 0.5 mg/kg for vegetable oils and fats destined for the production of baby food and processed cereal-based food for infants and young children [4]. GEs are formed in vegetable oils during the refining process in the deodorization step, which is conducted at high temperatures (200-275 ◦C) under vacuum (of less than 10 mbar residual pressure) [5, 6]. Deodorization is the last step of refining of conventional edible oils and is intended to remove undesirable substances in order to im- *Correspondence: zsofi.bognar@outlook.hu prove the taste, odor, color and oxidative stability of such oils [7]. According to data from the literature, high levels of GEs are primarily measured in refined palm oil and its fractions. Destaillats et al. [8] showed in their study that GEs are formed from di- and monoacylglycerols (DAGs and MAGs), but not from triacylglycerols (TAGs). Ac- cordingly, high levels of GE can be traced back to high levels of DAGs in crude palm oil [8]. The formation of GE starts at about 200 ◦C [8]. Analytical methods for the determination of GEs can be divided into two main groups: direct and indirect methods [9]. Individual GEs are determined by direct quantitation methods which are mainly based on liquid chromatography-mass spectrometry (LC-MS), requiring a significant number of reference compounds and internal standards [10, 11]. Indirect determination is based on the conversion of GEs into glycidol which is then isolated, derivatized, chromatographically separated and quanti- fied. The result is expressed as the amount of glycidol that can be released from GEs. These methods require only a small number of internal standards [9]. In our study, the quantity of GEs in seed oil during lab-scale deodorization was determined in order to exam- ine the effects of two independent factors – temperature and residence time – on the formation of GEs. mailto: zsofi.bognar@outlook.hu 68 BOGNÁR, HELLNER, RADNÓTI, SOMOGYI, AND KEMÉNY 2. Experimental 2.1 Samples and Measurements Bleached sunflower, rapeseed and soybean oils were sup- plied by Bunge Limited (Bunge Zrt. Hungary and Bunge Ibérica, S.A.U.). Diethyl ether, ethyl acetate, n-hexane and high-performance liquid chromatography (HPLC)- grade water were obtained from VWR International Kft. (Debrecen, Hungary). Toluene, isohexane, sodium bro- mide and phenylboronic acid were obtained from Merck Kft. (Budapest, Hungary). Methanol, sodium hydroxide and anhydrous sodium sulfate were purchased from Re- anal Laborvegyszer Kft. (Budapest, Hungary). The in- ternal standards glycidyl palmitate-d5 and 3-chloro-1,2- propanediol-d5 (3-MCPD-d5) were obtained from Lab- Standards (Budapest, Hungary). All reagents and chemi- cals were of analytical grade. Lab-scale deodorization trials were conducted in 150 g batches at temperatures between 220 and 260 ◦C. The bleached oils (sunflower, rapeseed or soybean) were heated to the target temperature (220, 230, 240, 250 or 260 ◦C) within 10–15 minutes. The process lasted 3 hours at a pressure of 3–4 mbar using nitrogen as a stripping gas. Without breaking the vacuum, sampling was con- ducted after 0, 15, 30, 45, 60, 90, 120 and 150 minutes had elapsed. The quantities of glycidyl esters were determined us- ing the American Oil Chemists’ Society (AOCS) Of- ficial Method Cd 29b-13, which is based on alkaline- catalyzed ester cleavage and transformation of the re- leased glycidol into monobromopropanediol (MBPD) and derived free diols using phenylboronic acid (PBA). These derivatives are measured by the Gas Chromatogra- phy/Mass Spectrometry (GC/MS) coupled system (Agi- lent 6890 coupled with 5973) in the selected ion monitor- ing (SIM) mode. Quantitative determination was based on the deuterated internal standard using characteristic ions for derivatised glycidol-d5 at m/z 150 and 245, and derivatised glycidol at m/z 147 and 240. 2.2 Experimental design and statistical anal- ysis The temperature and residence time were studied using response surface methodology (RSM). The results of the 32 full factorial experimental design (see Table 1) were evaluated by analysis of variance (ANOVA) models us- ing Statistica 13. The center point of the 32 full factorial design (mid temperature 240 ◦C) and mid time 90 min- utes) was repeated three times. Only the significant effects (of main effects and inter- actions) were taken into account in the response surface methodology. The generalized polynomial model for de- scribing the response of independent variables is given in y = β0 + β1X1 + β2X 2 1 + β3X2 + + β4X 2 2 + β5X1X2 + β6X1X 2 2 + + β7X 2 1X2 + β8X 2 1X 2 2 (1) Table 1: 32 full factorial experimental design Independent variables Levels -1 0 +1 X1 Temperature (◦C) 220 240 260 X2 Residence time (min) 0 90 180 Dependent Variables (Yi) Glycidyl esters (mg/kg) 3. Results and Evaluation 3.1 Experiments The results of the lab-scale investigation of GE forma- tion are shown in Fig. 1. In our experimental design, the greatest amount of GEs formed in soybean oil, in which the concentration of GEs reached 5.5 mg/kg at 260 ◦C af- ter 180 minutes (Fig. 1A). In the sunflower and rapeseed oils, the maximum concentrations of GEs reached were 1.6 and 1.5 mg/kg, respectively (Figs. 1B and 1C). The GE content of sunflower and rapeseed oils was kept un- der 1 mg/kg after 120 minutes of deodorization at a tem- perature of 250 ◦C or less, but for soybean oil this level was obtained at or below 230 ◦C. This demonstrates that the amounts of precursors in the oils strongly influence the formation of GE, and consequently the optimal de- odorization temperature. The threshold concentration of Figure 1: GEs of seed oils during deodorization: A) sun- flower oil, B) rapeseed oil, C) soybean oil Hungarian Journal of Industry and Chemistry FORMATION OF GLYCIDYL ESTERS DURING THE DEODORIZATION OF VEGETABLE OILS 69 Figure 2: Fitted surfaces for seed oils: A) sunflower oil, B) rapeseed oil, C) soybean oil 0.5 mg/kg permitted for infant food was complied with at 240, 230 and 220 ◦C for rapeseed, sunflower and soy- bean oils, respectively (after 120 minutes of deodoriza- tion). In the applied experimental setup, up to 0.3 mg/kg of GE formed after 10–15 minutes of heating. At lower deodorization temperatures, the effect of time becomes practically insignificant, especially at 220 and 230 ◦C. 3.2 Statistical analysis The application of RSM allowed the main effects and interactions to be determined simultaneously. ANOVA shows the significant effects, which can be used for build- Table 2: Regression coefficients for intercept (I), linear and quadratic factors, as well as interactions between fac- tors in the fitted models of seed oils Sunflower oil Rapeseed oil Soybean oil I 7.95 7.12 10.32 T −6.72× 10−2 −5.9×10−2 −9.02×10−2 T 2 1.45×10−4 1.23× 10−4 2× 10−4 t 1.17×10−1 2.16×10−1 1.14 t2 n.s. n.s. n.s. Tt −1.13× 10−3 −1.96×10−3 −1.01× 10−2 T 2t 3× 10−5 4× 10−5 2.2× 10−5 Tt2 n.s. n.s. −2.38× 10−8 n.s.: effect not significant ing the response surface model. The fitted surfaces for sunflower, rapeseed and soybean oils are presented in Figs. 2A-C, respectively. The shapes of the surfaces are very similar, the only difference is in their heights. The interactions between the independent variables can be ob- served from the fitted surfaces, because at lower tempera- tures the concentrations of GEs gradually increased over time, while at higher temperatures a more rapid increase occurred. For all three seed oils the temperature had the largest effect. The interaction between the independent variables and the effect of time were the second and third most sig- nificant, but the quadratic components and their interac- tions with the other factors were noticeable in most cases, as well. The regression coefficients are shown in Table 2 coefficients in the case of sunflower and rapeseed oils are very similar so the RSM diagrams of these oils fall within the same range of values (Figs. 2A and 2B). 4. Discussion According to the data from the literature, the oil that has been studied the most in this respect is palm oil along with its fractions [8, 12]. Cheng et al. [13] summarized the data from previous studies and according to this re- view the highest concentrations of GEs in seed oil were found in soybean oil when compared to rapeseed and sun- flower oils. This is in agreement with our observations. The higher concentrations of GEs that formed during de- odorization were due to the higher levels of DAGs and MAGs in the raw material. It was found that the critical temperature range is be- tween 220 and 240 ◦C, above which more than 0.5 mg/kg of GEs may form, depending on the quality of the raw material. This conclusion is similar to the results of pre- vious investigations. Craft et al. [12] concluded that be- tween 230 and 240 ◦C, the formation of GE is extensive, consequently this value should be considered as an upper limit for the deodorization process. De Kock et al. [14] suggested conducting deodorization for a longer period 46(2) pp. 67–71 (2018) 70 BOGNÁR, HELLNER, RADNÓTI, SOMOGYI, AND KEMÉNY of time at temperatures below 240 ◦C, which might also minimize the formation of trans fatty acids. 5. Conclusion The present investigation suggests that the formation of GEs in seed oils during deodorization is not negligible. The rate of formation can be traced back to the level of DAGs and MAGs [15] in the raw material. A simul- taneous increase in temperature and time could result in extremely high levels of GEs in oils. On an indus- trial scale, the formation of GEs can be controlled in the oils examined, meaning that the upper limit of GEs (1 mg/kg) in vegetable oils and fats placed on the market for general consumption can be achieved through preven- tive measures. The stricter limit imposed on oils destined for the production of food for infants and young children presents greater challenges, and thus requires a combina- tion of high quality raw materials as well as a controlled refining process. Acknowledgement Funding for this research was provided by the Doctoral School of Food Sciences at Szent István University (Bu- dapest) and by the BEMEA Katalin Kővári R&D Centre. The Project is supported by the European Union and co- financed by the European Social Fund (grant agreement no. EFOP-3.6.3-VEKOP-16-2017-00005). Symbols β0−8 Regression coefficients for intercept, linear and quadratic factors and interactions between factors X1, X2 Independent factors T Deodorization temperature t Deodorization time REFERENCES [1] Appel, K.E.; Abraham, K.; Berge-Preiss, E.; Hansen, T.; Apel, E.; Schuchardt, S.; Vogt, C.; Bakhiya, N.; Creutzenberg, O.; Lampen, A.: Rel- ative oral bioavailability of glycidol from glycidyl fatty acid esters in rats, Arch. Toxicol., 2013 87(9), 1649–1659 DOI: 10.1007/s00204-013-1061-1 [2] Frank, N.; Dubois, M.; Scholz, G.; Seefelder, W.; Chuat, J.-Y.; Schilter, B.: Application of gastroin- testinal modelling to the study of the digestion and transformation of dietary glycidyl esters, Food Addit. Contam. Part A, 2013 30(1), 69–79 DOI: 10.1016/j.foodchem.2010.08.036 [3] IARC (International Agency for Research on Can- cer): Glycidol, In: IARC Monographs Volume 77. On the evaluation of carcinogenic risks to humans (WHO Press, Lyon, France) 2000 pp. 469–486 ISBN: 9283212770 [4] Official Journal of the European Union: COMMIS- SION REGULATION (EU) 2018/290 of 26 Febru- ary 2018 amending Regulation (EC) No 1881/2006 as regards maximum levels of glycidyl fatty acid esters in vegetable oils and fats, infant formula, follow-on formula and foods for special medical purposes intended for infants and young children 2018 [5] Carlson, F.K.: Deodorization. In: Hui, Y. H. (ed.) Bailey’s industrial oil and fat products. Edible oil and fat products: Processing technology. 5th Edi- tion. Volume 4. (John Wiley & Sons Inc., New York, USA) 1996 pp. 411–449 ISBN: 9780471594284 [6] O’Brien, R.D.: Fats and oils formulating and pro- cessing for applications. Third Edition. (CRC Press Taylor & Francis Group, Boca Raton, Florida, USA) 2009 pp. 153–164 ISBN: 9781420061666 [7] Sipos, E.F.; Szuhaj, B.F.: Edible oil Processing. In: Hui, Y.H. (ed.) Bailey’s industrial oil and fat products. Edible oil and fat products: Oils and oilseeds. 5th Edition. Volume 2. (John Wiley & Sons Inc., New York, USA) 1996 pp. 497–602 ISBN: 9780471594260 [8] Destaillats, F.; Craft, B.D.; Dubois, M.; Nagy, K.: Glycidyl esters in refined palm (Elaeis guineensis) oil and related fractions. Part I: Formation mech- anism, Food Chem., 2012 131(4), 1391–1398 DOI: 10.1016/j.foodchem.2011.10.006 [9] Ermacora, A.; Hrncirik, K.: Indirect detection tech- niques for MCPD esters and glycidyl esters. In: MacMahon, S. (ed.) Processing contaminants in ed- ible oils MCPD and glycidyl esters (AOCS Press, Urbana, USA) 2014 pp. 57–90 ISBN: 9780988856509 [10] Thürer, A.; Granvogl, M.: Direct detection tech- niques for glycidyl esters. In: MacMahon, S. (ed.) Processing contaminants in edible oils MCPD and glycidyl esters (AOCS Press, Urbana, USA) 2014 pp. 91–120 ISBN: 9780988856509 [11] Blumhorst, M.R.; Venkitasubramanian, P.; Colli- son, M.W.: Direct determination of glycidyl es- ters of fatty acids in vegetable oils by LC–MS, J. Am. Oil Chem. Soc., 2011 88(9), 1275–1283 DOI: 10.1007/s11746-011-1873-1 [12] Craft, B.D.; Nagy, K.; Seefelder, W.; Dubois, M.; Destaillats, F.: Glycidyl esters in refined palm (Elaeis guineensis) oil and related fractions. Part II: Practical recommendations for effective mit- igation, Food Chem., 2012 132(1), 73–79 DOI: 10.1016/j.foodchem.2011.10.034 [13] Cheng, W.W.; Liu, G.Q.; Wang, L.Q.; Liu, Z.S.: Glycidyl Fatty Acid Esters in Refined Edible Oils: A review on formation, occurrence, analysis, and elimination methods, Compr. Rev. Food Sci. 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J. Ind. Chem., 1999 27(4), 293–295 46(2) pp. 67–71 (2018) HUNGARIAN JOURNAL OF INDUSTRY AND CHEMISTRY Vol. 46(2) pp. 73–77 (2018) hjic.mk.uni-pannon.hu DOI: 10.1515/hjic-2018-0022 EFFECT OF ALGAE TREATMENT ON STEVIA REBAUDIANA GROWTH RÉKA CZINKÓCZKY1 AND ÁRON NÉMETH *1 1Department of Applied Biotechnology and Food Science, Budapest University of Technology and Economics, Műegyetem rkp. 3, Budapest, 1111, HUNGARY Stevia rebaudiana Bertoni is a small, perennial and herbaceous shrub which originated in Paraguay (South America). Stevia rebaudiana is not native to Hungary but its cultivation and consumption may have many benefits, e.g. to reduce blood pressure and as a non-caloric sweetener. Steviol glycosides, mostly stevioside and rebaudioside A, located in the leaves are about 200–300 times sweeter than sucrose. S. rebaudina cultivation in Hungary would offer many opportu- nities in healthcare and the sweet industry. With the aim of achieving good green biomass yields, the effect of MACC4 autotrophic and heterotrophic algae strains was investigated by testing them as both leaf and soil fertilizers in the soil of Stevia rebaudiana seedlings and in its aqueous rooting experiments. In one of the later set up, the formation of roots was improved by combining the application of red light and algae treatment. Keywords: Stevia rebaudiana, Steviol glycosides, algae treatment, Chlorella vulgaris 1. Introduction Stevia rebaudiana Bertoni (Fig. 1) is a perennial shrub and a member of the Asteraceae family. Stevia originated in Brazil and Paraguay (South America). This plant is widely used by the Guaraní Indians of South America to sweeten tea [1, 2]. S. rebaudiana was botanically classi- fied in 1899 by Moisés Santiago Bertoni, who described it in more detail. Initially called Eupatorium rebaudianum, its name changed to S. rebaudiana (Bertoni) in 1905. The sweet principle was first isolated in 1909 and only in 1931 was the extract purified to produce stevioside, its chemical structure was established in 1952 as a diter- pene glycoside. Stevioside (Fig. 2) is described as a gly- coside comprised of three glucose molecules attached to an aglycone referred to as steviol moiety [3, 4]. S. re- baudiana also has other names like Sweet leaf, Sweet Herb of Paraguay, Sweet Honey Leaf and candyleaf. The sweetening components of the plant, i.e. steviol glyco- sides, were described in 1931 [5]. S. rebaudiana and its extracts have been used for a long time in Asia, South America and several countries in Europe. S. rebaudiana leaves and highly refined extracts are used as low-calorie sweeteners in Korea, Japan and Brazil [6]. Stevioside, one of the steviol glycosides, has been reported to lower the postprandial blood glucose concentration of Type II dia- betics and the blood pressure of mildly hypertensive pa- tients [7]. S. rebaudiana is used by diabetics as a diet ther- apy, and its extracts exhibit pharmacological effects such as anti-insulin resistance, the promotion of insulin secre- tion, as well as antihypertensive and anti-obesity proper- *Correspondence: naron@f-labor.mkt.bme.hu Figure 1: Stevia rebaudiana ties [8]. Nowadays, the utilization of alternative sweet- eners has become a viable option for producing low- or zero-calorie foods due to the development of the healthy food industry which intends to reduce the sucrose con- tent of food products by the total or partial replacement of sucrose with alternative sweeteners. Steviol glycosides are mainly produced in the leaves of the plant. The major components are steviol, stevioside and rebaudioside A. The typical proportions of the major components of the leaves are stevioside (5–10 % of the mailto:naron@f-labor.mkt.bme.hu 74 CZINKÓCZKY AND NÉMETH Figure 2: Structure of stevioside total dry weight of the leaves), Reb A (2–4 %), Reb C (1–2 %) and dulcoside A (0.4–0.7 %) [9]. The leaves ofS. rebaudiana are sessile, 3-4 cm in length, elongate-lanceolate or spatulate in shape with blunt-tipped laminae in addition to serrated margins from the middle to the tip and on the entire underside. The up- per surface of the leaves is slightly glandular-pubescent. The stem is weak-pubescent at its base and woody. The rhizome has slightly branching roots. Flowers are com- posite surrounded by an involucre of epicalyx. The capit- ula are in loose, irregular, sympodial cymes. The flowers (Fig. 3) are white and pentamerous [5]. This plant can grow up to 1 m tall if it is exposed to sufficient light and receives enough nutrients as well as water. Therefore, it is worth considering the examination of crop production due to its wide range of applications. Chlorella vulgaris is a eukaryotic unicellular green al- gae which is one of the fastest growing microalgae. This algae can be used in biodiesel processing following cell cultivation. The economic feasibility of algal biodiesel production highly depends on the biomass productivity and lipid yield [10]. Green algae (like Chlorella vulgaris) may produce phytohormones which can influence the growth of plants. Odgerel et al. used Chlorella vulgaris as a biofertilizer on barley and wheat. Faheed et al. used C. vulgaris as a biofertilizer on lettuce plants. These re- sults showed that algae treatment yields longer roots and shoots of wheat compared to control [11, 12]. The aim of our work was to test Chlorella vulgaris Figure 3: Stevia rebaudiana flowers Figure 4: Plant cells MACC4 autotrophic and heterotrophic cultures of mi- croalgae to enhance the roots, biomass and stems of S. rebaudiana. 2. Materials and methods In our work, the effects of hormones produced by algae on S. rebaudiana were tested. Phytohormones may im- prove its development. The plants were in a phytotron (25±1 ◦C) where they received 16 hours of light per day. Each plant was placed in a 4.5 cm × 5.0 cm planting cell (Fig. 4). In Table 1, the blue background denotes the root- growing experiments where seedlings were placed into water as a control and into an aqueous algal suspension for trials. Furthermore, the green background indicates the modeling of experiments in land: while seedlings in samples of commercial potting soil were sprinkled with water as a control and an algal suspension as to test changes in biomass, the growth of roots and stems was recorded in terms of weight and length, respectively. Cells were replicated three times for each setting. As algal suspensions, Chlorella vulgaris MACC4 het- erotrophic and autotrophic cultivated strains were used. The cell suspension was diluted by up to 300 times with water to achieve a concentration of 5 × 107 colony- forming units (CFU)/ml. From this solution, 2 ml was sprinkled onto each cell every 2 to 3 days. The duration of the experiments was about five weeks. At the end of the fifth week (Fig. 5), the mass of the total green biomass and the length of the stem and roots in both water and soil were measured. For the results a statistical evaluation was conducted with Minitab 17 statistical soft- ware. The statistical analysis consisted of a two-sample Table 1: Planting cells (H: heterotrophic, A: autotrophic, C: control, Green: seedlings in soil, Blue: seedlings in wa- ter, White: empty cells) Hungarian Journal of Industry and Chemistry EFFECT OF ALGAE TREATMENT ON STEVIA REBAUDIANA GROWTH 75 Figure 5: S. rebaudiana plants at the end of the experiment t-test where the algae-treatment samples were compared against the controls and each other. 3. Results and discussion The two-sample t-test in terms of the growth in biomass observed in the seedlings planted in soil is presented in Fig. 6. The p-value shows whether or not the treatment had an effect on biomass growth. The comparison between heterotrophic algae treat- ment and the control samples is presented in Fig. 6A. The p-value was 0.653, i.e. no significant difference exists be- tween the two groups of results that were examined. A Figure 6: Box plots of two-sample t-tests: biomass growth in soil (A: heterotrophic algae vs. control, B: heterotrophic vs. autotrophic algae, C: autotrophic algae vs. control). iiuv()luv comparison between the heterotrophic and autrotrophic algae cultures is presented in Fig. 6B. The p-value was 0.511, i.e. no significant difference exists between them. A contrast is made between the autotrophic algae treat- ment and the control samples in Fig. 6C. The p-value was 0.316, i.e. no significant difference exists between these groups either. From the results it can be seen that algae treatment does not have a positive effect on the growth of the green biomass of S. rebaudiana with regard to model experiments in soil. The two-sample t-tests in terms of stem growth are presented in Fig. 7. A comparison between the het- erotrophic algae treatment and the control samples is pre- sented in Fig. 7A. The p-value was 0.642, i.e. no sig- nificant difference exists between them. The results of heterotrophic versus autotrophic algae treatment cultures are shown in Fig. 7B. The p-value was 0.055, i.e. once more no significant difference exists between them. A contrast between autotrophic algae treatment and con- trol samples is presented in Fig. 7C. The p-value was 0.147, i.e. yet again no significant difference exists be- tween both groups. From these results it can be concluded that no significant improvements were observed in terms of the yield of plant biomass of algae treatments applied to seedlings planted in soil. However, the autotrophic al- Figure 7: Box plots of two-sample t-tests in terms of stem growth in soil: (A: heterotrophic algae vs. control, B: het- erotrophic vs. autotrophic algae, C: autotrophic algae vs. control) 46(2) pp. 73–77 (2018) 76 CZINKÓCZKY AND NÉMETH Figure 8: Box plots of two-sample t-tests in terms of root growth in land (A: heterotrophic algae vs. control, B: het- erotrophic vs. autotrophic algae, C: autotrophic algae vs. control) gae treatment seemed to be the most significant which suggests a weak positive effect in terms of the plant de- velopment of S. rebaudiana in soil may occur. The two-sample t-tests in terms of the root growth ob- served in soil are presented in Fig.8. A comparison be- tween heterotrophic algae treatment and the control sam- ples is presented in Fig. 8A. The p-value was 0.503, i.e. no significant difference exists between them. A contrast between the heterotrophic and autotrophic algae treat- ments is shown in Fig. 8B. The p-value was 0.357, i.e. no significant difference exists between them either. The difference between autotrophic algae treatment and the control samples is presented in Fig. 8C. The p-value was 0.811, i.e. once again no significant difference exists be- tween the examined two groups of results. These results suggest (without significance) that heterotrophic algae cultures maybe preferred for the root development of S. rebaudiana seedlings in soil. The two-sample t-tests in terms of the root growth in water are presented in Fig. 9. A comparison between heterotrophic algae treatment and the control samples is shown in Fig. 9A. The p-value was 0.012, i.e. a signif- icant difference exists between them and heterotrophic treatment is beneficial. A contrast between heterotrophic Figure 9: Box plots of two-sample t-tests in terms of root growth in water (A: heterotrophic algae vs. control, B: het- erotrophic vs. autotrophic algae, C: autotrophic algae vs. control) and autotrophic algae treatments is presented in Fig. 9B. The p-value was 0.003, i.e. a significant difference ex- ists between them and heterotrophic algae treatment is also beneficial. The difference between autotrophic algae treatment and the control samples is shown in Fig. 9C. The p-value was 0.128, i.e. no significant difference ex- ists between them. From these results it can be concluded that while heterotrophic algae treatment was found to be significantly advantageous for the root development of S. rebaudiana in water, the effect of autotrophic cultures did not significantly differ from that of the control samples. In soil a lateral-like root was formed, while in water the formation of a thicker root was observed. Just like when the root fibers were grown in land, not all the soil could be washed out without damaging the root. There- fore, a comparison between the biomass yield in water and soil was not conducted. 4. Conclusion The following conclusions can be drawn from the exper- iments with regard to the growth of S. rebaudiana. Nei- ther heterotrophic nor autotrophic algae treatments had any positive effect on the biomass growth in soil. By ex- amining the stem growth, the autotrophic culture seemed Hungarian Journal of Industry and Chemistry EFFECT OF ALGAE TREATMENT ON STEVIA REBAUDIANA GROWTH 77 to have a slightly positive effect but was not significant. In terms of root growth in soil, none of the treatments had any significant effect, but heterotrophic cultures seemed to have a slightly positive effect. Root growth in water supplemented regularly with heterotrophic algae cultures had a significant positive effect in comparison to the other treatments. Probably the positive effect of algae treatment in the case of the experiments on S. rebaudiana seedlings in water can be attributed to the fact that the applied al- gae provided complex nutrients unlike the pure tap water, while in the case of the experiments on seedlings in soil the additional nutrients provided by the algae treatment was practically negligible in comparison to those offered by the soil. Therefore, further studies will be done to separate the effect of algae as a provider of nutrients and as a source of plant hormones. Further studies would be necessary to prove whether changes in algae cell concentrations have an effect on the growth of Stevia rebaudiana or not, i.e. in soil, experi- ments on biomass growth should be applied differently in diluted algae suspensions with and without any addi- tional nitrogen sources. Moreover, different types of light, e.g. red, blue and white, will be tested. These additional plant studies will be implemented using larger numbers of samples. REFERENCES [1] Geuns, J. M. C.: Stevioside. Phytochemistry, 2003 64(5), 913–921 DOI: 10.1016/S0031-9422(03)00426-6 [2] Kaur, G.; Pandhair, V.; Cheema, G. S.: Extraction and characterization of steviol glycosides from Ste- via rebaudiana bertoni leaves. J. Med. Plants. Stud., 2014 2(5), 41–45 ISSN: 2320-3862 [3] Lemus-Mondaca, R.; Vega-Gálvez, A.; Zura-Bravo, L.; Kong, A. H.: Stevia rebaudiana Bertoni, source of a high-potency natural sweetener: A compre- hensive review on the biochemical, nutritional and functional aspects. Food Chem., 2012 132(3) 1121– 1132 DOI: 10.1016/j.foodchem.2011.11.140 [4] Barriocanal, L. A.; Palacios, M.; Benitez, G.; Ben- itez, S.; Jimenez, J. T.; Jimenez, N.; Rojas, V.: Ap- parent lack of pharmacological effect of steviol gly- cosides used as sweeteners in humans. A pilot study of repeated exposures in some normotensive and hypotensive individuals and in Type 1 and Type 2 diabetics. Regul. Toxicol. Pharmacol., 2008 51(1), 37–41 DOI: 10.1016/j.yrtph.2008.02.006 [5] Madan, S.; Ahmad, S.; Singh, G. N.; Kohli, K.; Kumar, Y.; Singh, R.; Garg, M.: Stevia rebaudiana (Bert.) Bertoni – A Review. Indian J. Nat. Prod. Resour., 2010 1(3), 267–286 ISBN: 3216321509, ISSN: 09760504 [6] Kinghorn, A. D. (ed.): Stevia - The genus Stevia in: Hardman, R. (ed.) Medicinal and aromatic plants – Industrial profiles series Vol. 19, CRC Press, Taylor & Francis, London UK, 2003. ISBN: 0-203-16594-2 [7] Gregersen, S.; Jeppesen, P. B.; Holst, J. J.; Her- mansen, K.: Antihyperglycemic effects of stevio- side in type 2 diabetic subjects. Metabolism, 2004 53(1), 73–76 DOI: 10.1016/j.metabol.2003.07.013 [8] Dyrskog, S. E. U.; Jeppesen, P. B.; Colombo, M.; Abudula, R.; Hermansen, K: Preventive ef- fects of a soy-based diet supplemented with ste- vioside on the development of the metabolic syn- drome and type 2 diabetes in Zucker diabetic fatty rats. Metabolism, 2005 54(9), 1181–1188 DOI: 10.1016/j.metabol.2005.03.026 [9] Puri, M.; Sharma, D.; Tiwari, A. K.: Downstream processing of stevioside and its potential applica- tions. Biotechnol. Adv., 2011 29(6), 781–791 DOI: 10.1016/j.biotechadv.2011.06.006 [10] Kim, J.; Lee, J-Y.: Growth kinetic study of Chlorella vulgaris (August 2016), pp. 2–7. 2009. ISBN: 9781615679140 [11] Odgerel, B.; Tserendulam, D.: Effect of Chlorella as a biofertilizer on germination of wheat and barley grains Proc. Mong. Acad. Sci., 2017 56(4) 26 DOI: 10.5564/pmas.v56i4.839 [12] Faheed, F. A.: Effect of Chlorella vulgaris as bio- fertilizer on growth parameters and metabolic as- pects of lettuce plant. J. Agri. Soc. Sci., 2008 4(4) 165-169 ISSN: 1813-2235 46(2) pp. 73–77 (2018) https://doi.org/10.1016/S0031-9422(03)00426-6 https://doi.org/10.1016/j.foodchem.2011.11.140 https://doi.org/10.1016/j.yrtph.2008.02.006 https://doi.org/10.1016/j.metabol.2003.07.013 https://doi.org/10.1016/j.metabol.2005.03.026 https://doi.org/10.1016/j.metabol.2005.03.026 https://doi.org/10.1016/j.biotechadv.2011.06.006 https://doi.org/10.1016/j.biotechadv.2011.06.006 https://doi.org/10.5564/pmas.v56i4.839 https://doi.org/10.5564/pmas.v56i4.839 HUNGARIAN JOURNAL OF INDUSTRY AND CHEMISTRY Vol. 46(2) pp. 79–84 (2018) hjic.mk.uni-pannon.hu DOI: 10.1515/hjic-2018-0023 COMPARISON OF PARTICLE SIZE DISTRIBUTION MODELS FOR POLYMER SWELLING ÁDÁM WIRNHARDT *1 AND TAMÁS VARGA1 1Department of Process Engineering, University of Pannonia, Egyetem u. 10, Veszprém H-8200, HUNGARY In polymer technologies, various particle shapes and size distributions can be found. One of these are heterodisperse polymer beads. The capabilities of polymer swelling can be used in industries, e.g in the production of ion-exchange resins, to intensify specific technological steps such as sulphonation in the manufacturing process of ion-exchange resins. According to the literature different approaches can be used to create models for describing the behavior of disperse systems, of which the simplest models are the particle size distribution models for a given state of the solid phase. The aim of our examination was to compare and evaluate these simple models in terms of modeling polymer swelling. Hence, most of these models examine how each of the investigated models can be applied to approximately describe growth in a heterodisperse polymer system and how the identified model parameters in each time step could be interpreted. All the models were fitted to generate particle size distributions based on a swelling rate constant. The swelling of a styrene divinylbenzene-based copolymer was chosen as the basis of our examination. A model is proposed that is capable of describing the changes in the size of beads over time in this system. Keywords: polymer swelling, particle size distribution, heterodisperse polymer beads, modeling, ion-exchange resin 1. Introduction Polymer beads are used as raw materials in a wide range of technologies, e.g. in the production of ion-exchange resins. Before the chemical modification of polymer beads, they are often swollen with different types of swelling agents such as dichloroethane, dichloromethane, toluene, etc. Monodisperse and heterodisperse types of beads are known in polymer technologies. The process of the swelling of monodisperse beads is easily measurable and easily predictable. The production of monodisperse poly- mers is a more expensive process than the production of heterodisperse beads, which makes heterodisperse poly- mer beads a more popular form. Heterodisperse polymer beads exhibit a closely nor- mal distribution in terms of particle size. The prediction of the swelling of these particle systems is more difficult because the different beads can swell at significantly dif- ferent rates due to the change in the specific area of each bead. The swelling of the polymer network system has al- ready been a subject of interest. Painter and Shenoy[1] considered the chemical properties of polymers. Schott [2] described the kinetics of polymer swelling. First or- der and second order kinetics were founded by him. A *Correspondence: wirnhardt.adam@fmt.uni-pannon.hu swelling model was formulated by Sweijen et al. [3] ac- cording to the diffusion properties of components in the polymer matrix. These models are capable of describing the swelling of polymer networks, but because of its com- plexity they are hard to apply in any kind of optimiza- tion process. Hence, the simplest particle size distribution (PSD) model, which can describe the swelling of poly- mers over time using the least number of parameters, can be of interest from a process intensification point of view. Bayat et al. collected PSD models from the last sev- enty years [4, 5]. Thirty-five models were listed. These models describe the cumulative mass fraction of poly- mers as a function of the diameter of polymer beads. The models contain one, two, three or four unknown parame- ters, which can be identified with a specific polymer frac- tion. A hyperbolic tangent distribution [6, 7] PSD model composed of four parameters was added to this list by us. This study is the first step in the process of devel- oping this model which focuses on the investigation of the swelling phenomena of the styrene divinylbenzene copolymer system. Therefore, our focus is on identifying a simple PSD model which is capable of describing the swelling of heterodisperse polymer beads. Hence, all the previously mentioned PSD models are investigated and compared. Our aim was not only to identify a PSD model which is capable of describing the distribution of the in- vestigated polymer system but to find a PSD model which mailto:wirnhardt.adam@fmt.uni-pannon.hu 80 WIRNHARDT AND VARGA exhibits a correlation between changes made to parame- ters and particle size. 2. Experimental For the modelling of heterodisperse polymer systems physical experiments with regard to swelling should be performed to obtain the data necessary to validate the model. In our case, with the lack of experiments, the data were generated from a model implemented and solved in MATLAB. A code was made in MATLAB for the gen- eration of these distributions. In the developed model, the swelling of polymer beads with a given theoretical rate of growth was calculated. The volume of each bead increased at the same rate. Hence, the diameter of the beads does not influence the rate of growth and the ten- sion caused by the swelling process of the polymer beads is neglected in this investigation. The following simplifi- cations were implemented in the model: 1. The shape of the polymer beads is a perfect sphere. 2. The particles swell until they reach a steady state. 3. The swelling rate of particles is constant until a steady state is achieved. 4. The number of particles is constant. 5. The initial PSD of the beads is close to normal. To generate the distributions after different durations of swelling an initial unswollen distribution is required. The initial distribution was calculated by MATLAB from a picture of heterodispersed particles. The Varion KS pre- form styrene divinylbenzene copolymer was used for the zero-time distribution. The polymer beads were identified by a circle detection algorithm and the size distribution of the detected particles was calculated using a reference particle. From the initial state, the size of the polymer particles starts to increase by applying a swelling agent to the sys- tem. The size of the particles increases until a steady state is achieved. The steady state in this case means that the size of the particles grows until a state when the amount of infiltration of the swelling agent is equal to the out- come amount. The size of the particles can increase until a maximum is reached because of the internal tension of the polymer. The data are generated using the parameters of the steady state. These parameters are the swelling rate (p [-]) and time required (t [sec]). PSDs were generated at different times during the swelling process. The next step was to examine the PSD models to determine if they were able to describe the dis- tribution in every instant. 2.1 PSD models In this study only PSD models that are capable of de- scribing cumulative mass fraction distribution were in- vestigated. Altogether five models with one parameter, twelve with two, two with three and four with four were examined. They are collected in Table 1. The cumulative mass fraction of particles is denoted by P (d), the maxima and minima of the particle size range are represented by dmax and dmin, respectively, and the particle diameter [mm] is denoted by d. The mod- els were fitted to all the distributions collected over time using extreme value problem solver algorithms in MAT- LAB. 2.2 Theoretical methodologies Two types of extreme value problem-solving methods were applied to fit the PSD models. One is a local ex- treme value problem solver known as the Nelder-Mead simplex algorithm and its function “fminsearch” to im- plement it in MATLAB. The other one is a global ex- treme value problem solver called “NOMAD” [8]. They are both components of the MATLAB toolkit. MATLAB 2011b was applied in all modelling steps. The minimum difference was sought between the gener- ated distribution data and calculated distributions based on each model. The parameters of PSD models were the results of this search. In every case, the goodness of fit was measured. For each model, every sample time was considered and the difference examined using the mean absolute difference. The average of the mean absolute difference of the percentage difference was calculated for every function. The extreme value problem solver at- tempted to find the minimum of the following equation Et = ∣∣P (d) ′ t − P (d)t ∣∣ nd (1) where the mean absolute difference between the gener- ated and calculated distribution is Et at instant t. The calculated distribution is denoted by P (d) ′ t and the gen- erated distribution by P (d)t at instant t. The number of items of data is represented by nd. 2.3 Model selection A selection could be made according to the average per- centage differences. The selection was carried out with a criterion. This criterion was an average percentage difference of five percent because under this value the difference is not considerable but over it an unaccept- able fit is shown. Three different models, namely the Rosin-Rammler, the Exponential-power_Pasikatan and the Logarithm-Zhuang models fitted to the generated data are shown in Fig. 1. The goodness of fit for these three models is 1 %, 5 % and 11 %, respectively. As can be seen the differences of 1 % and 5 % are negligible, and are only noticeable at diameters in excess of 0.7 mm. How- ever, a considerable difference can be observed between the models with fits of 5 % and 11 %. It can be seen that a goodness of fit of under 5 % is appropriate. Hungarian Journal of Industry and Chemistry COMPARISON OF PARTICLE SIZE DISTRIBUTION MODELS FOR POLYMER SWELLING 81 Table 1: The investigated PSD models Name Model 1 parameter (k1) 1 Gaudy-Meloy P (d) = 1− (1− d/dmax) k1 2 Nesbitt-Breytenbach P (d) = 10[(1/(k1 + 1)](d/2)k1+1 +[0.1− 1/(k1 + 1)](d/2)1/[1/(k1+1)−0.1] 3 Rosin-Rammler P (d) = 1− exp(−k1d) 4 Jaky P (d) = exp { − ( 1/k21 ) [ln(d/dmax)] 2 } 5 Schumann P (d) = (d/dmax) k1 2 parameters (k1, k2) 6 Power low- Paskikatan P (d) = [k1/(1− k2)]d1−k2 7 van Genuchten P (d) = [ 1 + (k1/d) k2 ]1/k2−1 8 Rosin-Rammler P (d) = 1− exp ( −k1dk2 ) 9 Fractal P (d) = exp {ln(k2))+[( 3k21 − 13k1 + 14 ) / ( k21 − 5k1 + 4 ) + 1 ] log(d) } 10 Power low - Gimenez P (d) = k1d k2 11 BEST P (d) = [ 1 + (k1/d) k2 ]2/k2−1 12 Bennet P (d) = k1k2d k1−1 exp ( −k2dk1 ) 13 Exponential power- Pasikatan P (d) = exp ( −k1dk2 ) 14 Logarithm-Zhuang P (d) = k1 ln(d) + k2 15 Log-exp-Kolev P (d) = k1 exp [k2 log(d)] 16 Weibull-2par P (d) = 1− exp [ −(d/k1)k2 ] 17 Lognormal- Zobeek P (d) = 1/ { k1(2π) 1/2 exp [ −(log(d)− k2)2/(2k21) ]} 3 parameters (k1, k2, k3) 18 S-Curve: Vipulanandan Ozgurel P (d) = 100 exp { −k1 [ k2 ln(d/0.001) d/k3 ]} 19 Weibull-3par P (d) = k1 − exp [ −(d/k2)k3 ] 4 parameters (k1, k2, k3, k4) 20 Gompertz P (d) = k1 + k2 exp {− exp [−k3(d− k4)]} 21 Weibull-4par P (d) = k3 + (1− k3) [ 1− exp ( −k1kk2 4 )] where k4 = (d− dmin)/(dmax − dmin) 22 Fredlund P (d) = { 1/ [ ln ( exp(1) + (k1/k2) k2 )]k3 }{ 1− [ln(1 + k4/d)/ ln(1 + k4/0.001)] 7} 23 Tanh if 0 E (z (T )) − z0, then the process has decreasing tendency in average. If 0 < E (z (T )) − z0, then an overflow can be expected over a large time interval. If 0 = E (z (T ))− z0, then the process is in equilibrium. To evaluate the process, the time the failure first occurred is required during the interval [0, Tmax], when the amount of material exceeded the capac- ity of the tank or was equal to zero. The time of failure is defined as the following function: TF (z0, zmax, Tmax) = { inf {T : 0 ≤ T ≤ Tmax : z(T ) ≤ 0 or zmax < z(T )} , if such a T value exists ∞, if for all 0 ≤ T ≤ Tmax 0 < z(T ) ≤ zmax (5) 46(2) pp. 91–100 (2018) 94 TARCSAY, MIHÁLYKÓ-ORBÁN, MIHÁLYKÓ This time point is a random variable too, its expecta- tion,E(TF (z0, zmax, Tmax)·1TF (z0,zmax,Tmax)<∞), will be denoted by E(TF ) and its standard deviation by D(TF ). They are finite, as 0 ≤ TF (z0, zmax, Tmax) · 1TF (z0,zmax,Tmax)<∞ ≤ Tmax is adhered to. By applying the renewal theory [8], it can be proven that Ψ satisfies the integral equations Ψ (z0, zmax, Tmax) = λl λl+λb  min ( z0 c ,Tmax )∫ 0 z0−ct1∫ 0 Ψ (z0 − ct1 − y1, zmax, Tmax − t1) · λle−λlt1gl(y1)dy1dt1 + e −λlTmax + + λb λl+λb  min ( z0 c ,Tmax )∫ 0 zmax−(z0−ct2)∫ 0 Ψ (z0−ct1+y2, zmax, Tmax−t2) · λbe −λbt2gb(y2)dy2dt2+e −λbTmax  , (6) if cTmax ≤ z0 and Ψ (z0, zmax, Tmax) = λl λl+λb  min ( z0 c ,Tmax )∫ 0 z0−ct1∫ 0 Ψ (z0−ct1−y1, zmax, Tmax−t1) · λle−λlt1gl (y1) dy1dt1 + + λb λl+λb  min ( z0 c ,Tmax )∫ 0 zmax−(z0−ct2)∫ 0 Ψ (z0−ct2+y2, zmax, Tmax−t2) · λbe−λbt2gb(y2)dy2dt2  (7) if z0 < cTmax. To design a buffer tank which is capable of operat- ing with a desired degree of reliability of 1 − α where α denotes the probability of malfunction during the time interval [0, Tmax], solutions to equation Ψ (z0, zmax, Tmax) = 1− α (8) must be found. 3. Parameter dependence of the reliability of the process and the expectation of failure time Since the integral equation proved to be exceedingly dif- ficult to handle analytically, a Monte Carlo simulation to approximate the probability values for different parame- ters was used. Monte Carlo simulations are more widely accepted tools in dealing with stochastic models [9, 10]. For the simulation environment, MATLAB R2015a [11] was used. Realization of the process when the pa- rameters Tmax = 50 h, λl = 0.3 h−1, λb = 0.4 h−1 and c = 5 kgh−1 were chosen is demonstrated in Fig. 2. The mean of the input suddenly increased in the function z(t), the withdrawals from the batch caused sudden decreases and continuous withdrawal resulted in a reduction in lin- ear parts. The amounts drained and fed were defined as ran- dom variables from the Gaussian distribution. The initial buffer capacity was 50 kg and continuous withdrawal re- sulted in a linear decrease in the amount of material. At T = 1 h, the tank was filled. The amount of material in the tank increased by 3 kg, then the continuous with- drawal resumed. A little bit later a sudden withdrawal occurred. Similar events were repeated at random time points with random quantities. At T = 7.8 h a large with- drawal took place and the material became exhausted, therefore, z(t) became negative. The time of failure, in this case the time a shortage was observed, was TF = 7.8 h. Although the process was investigated over an inter- val of time, it is sufficient to compute the values of z(t) only at those points where sudden changes occurred and at the endpoint of the interval. An overflow could only occur if an input was present. Both continuous and batch withdrawals can cause shortages. If the amount of mate- rial at the time points of batch inputs and outputs is com- Figure 2: The change in the mass of material in the buffer tank. Hungarian Journal of Industry and Chemistry OPTIMAL DESIGN AND OPERATION OF BUFFER TANKS UNDER STOCHASTIC CONDITIONS 95 Figure 3: The probability of a failure as a function of the initial buffer and tank capacities. puted, it can be determined whether or not the continuous withdrawal caused the shortage during the time interval bounded by the last two batch events. If it did, the time point of the shortage can also be computed by solving a linear equation. By applying a Monte Carlo simulation, the proba- bilities were approximated by relative frequencies and the expected failure times were estimated by the average times. 10, 000 simulations were conducted which yielded an accuracy 0.01. For example, Tmax = 50 h was fixed and the param- eters of the process were λl = 8 h−1, λb = 12 h−1 and c = 12 kg h−1. The amounts drained and fed were de- fined as random variables from the Gaussian distribution with a mean of 8 kg and a standard deviation of 2 kg. With the aforementioned parameters, the probability of malfunction was calculated and the following results ob- tained for the process under the indicated conditions (Fig. 3). Figure 4: The expected malfunction times as a function of initial buffer and tank capacities. Figure 5: A histogram of the malfunction times. In Fig. 3 it can be seen that when the tank capac- ity was fixed, the probability of failure increased as a function of the initial amount of material. This can be explained by the fact that although the likelihood of a shortage decreased, the amount of material in the tank tended to increase, therefore, the free volume of the tank decreased, hence the increase in the probability of over- flow. On the other hand, when the initial buffer capacity was fixed, the probability of a failure decreased as a func- tion of the tank capacity. This tendency can be explained by the fact that the probability of overflow decreased and stemmed from the fact that λb was greater than λl mean- ing that the average time intervals between feeds were smaller than those between drainings. This caused the process to be more prone to malfunction due to overflow. The times of failures (TF ) were investigated as well. Expected failure times are shown in Fig. 4 as a func- tion of the initial buffer and tank capacities. If no fail- ure occurred, then TF was equal to zero, therefore, the expected TF was close to zero as well. A histogram of the malfunction times is provided in Fig. 5 when z0 = 400 kg and zmax = 1500 kg. It demon- strates that no quick failures occurred due to a shortage of material resulting in an increase in the amount of ma- terial and the tank overflowing. The distribution of the malfunction time in this case is unimodal and the degree of dispersion is quite large. The dispersion of the mal- function time as a function of the initial buffer and tank capacities can be seen in Fig. 6 which demonstrates that when the tank is half full, large standard deviations with regard to the malfunction times were calculated. In the case of large or small capacities, the malfunction time can be accurately predicted as the degree of dispersion is small. 46(2) pp. 91–100 (2018) 96 TARCSAY, MIHÁLYKÓ-ORBÁN, MIHÁLYKÓ Figure 6: The standard deviation of the malfunction times. 4. Design of the tank and initial buffer ca- pacities for a given reliability level During previous research, only models that consisted of a batch feed and continuous drainage in the absence of batch drainage [5–7] were studied. In the papers that deal with these models, it has been published that the integral equation for the reliability of the unit could be solved analytically in special cases where the process over an infinite time interval as a function of one variable is ob- served. In these special cases the solutions to the equation were mainly exponential in form or the linear combina- tion of exponential functions [5, 6]. Consequently, when fitting a function to simulated data, a function was chosen which exhibits similar characteristics. By fixing Tmax, seeking Ψ is suggested as a function of the initial buffer capacity x and tank capacity y, in the form of equation H (x, y) = 1− ( 1− e(−Ax) )C( 1− e(−B(y−x)) )D , (9) where x < y; A, B, C, and D are positive parameters which have to be optimized. Numerical values of Ψ were computed by a Monte Carlo simulation for some values of z0 and zmax, and the parametersA–D were determined using the least squares method, by minimizing function S (A,B,C,D) = ∑ r ∑ s (Ψ (xr, ys)−H (xr, ys)) 2 (10) This function was minimized numerically. The approxi- mated function exhibited a fit to the original function of 95 % on average which was calculated using a Monte Carlo simulation. The error of the fitting was inversely proportional to the number of simulations used to model the system as well as the number of points with regard to the tank and initial buffer capacities investigated. Since the quality of the fit was high (95 % on average), it can be assumed that even if the minimum identified is a lo- Figure 7: The relationship between the tank and initial buffer capacities that correspond to different levels of re- liability 1− α. cal minimum, the approximation is sufficient for use in further computations. Using the fitted function, equation Ψ(x, y) ∼ H (x, y) = = 1− ( 1− e−Ax )C( 1− e−B(y−x) )D = 1− α. (11) was solved. Appropriate initial buffer and tank capacities for the process are provided by the solution to the equa- tion above with a reliability of 1−α over the time interval [0, Tmax]. A link between the values of x and y is provided by the solution to the equation, namely equation y = x− ln ( 1− ( 1− α (1− exp(−Ax))C )1/D ) B . (12) This relationship, using the parameter set presented in the previous section, is given in Fig. 7. The interval of the initial buffer capacity was [100, 500] kg and the step sizes applied were 100 kg. The interval of the tank capacity was [1000, 2500] kg and the step sizes applied were also 100 kg. To elimi- nate numerical inaccuracies, the values of the time inter- vals were transformed into the time intervals [0, 100]. By transforming the time intervals into a subset of [0, 100], A = 0.4966, B = 0.12, C = 0.9324, and D = 86.4875 were computed. After the computations, the results were transformed into the original time intervals. The required tank capacities as a function of the initial buffer capacity in the intermediate storage corresponding to the reliabil- ities 1 − α = 0.95, 0.975, . . . 0.99 can be seen in Fig. 7. It can be seen that with some initial values a reliabil- ity of 0.99 is infeasible since the likelihood of a short- age itself exceeds level α. The minimum initial amount Hungarian Journal of Industry and Chemistry OPTIMAL DESIGN AND OPERATION OF BUFFER TANKS UNDER STOCHASTIC CONDITIONS 97 Figure 8: The required initial buffer capacity correspond- ing to a fixed tank capacity of 1, 900 kg and reliability level of 0.8 as a function of the draining intensity (c) . of material in the intermediate storage with a reliability of 1− α can be expressed by − ln ( 1− (1− α) 1/C ) A < xmin (13) From Fig. 7 it can be seen that if the lower limit is used as the initial buffer capacity, the corresponding storage capacity is enormous. The reason for this is the fact that the likelihood of a shortage is equal to α and an over- flow is undesirable, therefore, the tank capacity must be very large. According to the results shown in Fig. 7, this value is approximately 150 kg. Moreover, if z0 exceeds a certain level, the function is by and large linear. It is shown by the linear part of the function that when the ini- tial buffer capacity exceeds 250 kg, the likelihood of a failure due to exhaustion of material is almost zero. The likelihood α of an overflow is provided by the difference between the tank and initial buffer capacities. Therefore, to calculate the required tank capacity over this time in- terval, the volume which can ensure that the likelihood of overflow will remain as α is simply added to the buffer capacity in the intermediate storage. Finally, the minimum tank capacity that corresponds to a given level of reliability can be determined by nu- merically minimizing function y = x− ln 1− ( 1− α (1− exp(−Ax)) C )1/D  B (14) For the reliability level 1− α = 0.95, the minimum tank capacity is approximately 1, 820 kg and the required ini- tial buffer capacity approximately 245 kg. By fixing the tank capacity and reliability level, the dependence of the required initial buffer capacity on the withdrawal rate was investigated. The values of the re- Figure 9: The required drainage intensity corresponding to a fixed tank capacity of 1, 900 kg and a reliability level of 0.8 as a function of the initial buffer capacity. quired initial buffer capacity were determined numeri- cally according to the secant method. The reliability level was 1−α = 0.8 and the tank capacity was 1, 900 kg. The results can be seen in Fig. 8. According to this result, by increasing the withdrawal rate, the required initial buffer capacity increases sharply which facilitates control of the process. Finally, the required drainage intensity corresponding to the reliability level of 1 − α = 0.8 and fixed tank ca- pacity zmax = 1, 900 kg as a function of the initial buffer capacity was provided (Fig. 9). It can be seen that it is also a monotonically increasing function, but the rate of increase is usually less than in the case of Fig. 8. 5. Economic investigations According to Fig. 7, if the minimum required amount of initial buffer capacity is supplied then the required level of reliability of the process can be achieved by an infinite number of combinations of tank and initial buffer capac- ities. To determine the optimal combination, economic evaluations of the design are recommended. It is assumed that following a possible failure, the process is restarted, however, such a restart is time-consuming and expensive. During the calculations both the income and expenditure associated with each parameter are taken into account. These include the costs of raw materials, the buffer tank, malfunctions and repairs as well as the income generated from sales of both the key component and raw product. To determine the income generated by the process at time T , equation Q (T ) = Gkey (T ) +Graw (T )−Kmat (T )− − Kshort (T )−Krep (T )−Ktank (15) was used. The symbols G and K represent the income and ex- penditure of the process in USD. The profitability of 46(2) pp. 91–100 (2018) 98 TARCSAY, MIHÁLYKÓ-ORBÁN, MIHÁLYKÓ the whole process, (Q) stems from the income gener- ated from the sales of the key component (Gkey) and raw product (Graw). The income is reduced by the various ex- penses of the process, namely the costs of raw materials (Kmat), restoring the buffer capacity of the tank in case of exhaustion (Kshort), repairs (Krep) and the buffer tank itself (Ktank). The method of calculating each source of income and expenditure is shown below. The main goal of the process is to produce the key component, which is isolated in the continuous subsys- tem. To calculate the profit that stems from this, equation Gkey (T ) = T − Nrep(T )∑ i=1 Trep  cβkey (16) was used. In this equation, βkey denotes the sale price of the key component (USD kg−1), T represents the dura- tion of the process throughout which the profit (h), the number of malfunctions (Nrep(T )), and the random time of repair (Trep) during each malfunction are examined. Additionally, the plant secures an income from the sales of the raw product as well as the remaining raw product at the end of the production process, which can be defined as shown in Graw (T ) = βraw δ z0 − T − Nrep(T )∑ i=1 Trep  c + + Nb(T )∑ i=1 yb i − Nl(T )∑ i=1 yl i + Nl(T )∑ i=1 yl i  (17) where βraw denotes the sale price of the raw product (USD kg−1) and δ is a factor which defines the price at which the remaining raw product can be sold following production. Among the expenses, it should be mentioned that the cost of raw materials used for the production of the raw product and the cost of the initial raw product in the tank are calculated according to equation Kmat(T ) = γmat Nb(t)∑ i=1 yb i + z0γmat (18) where γmat is the cost of the raw material (USD kg−1). In the event of its exhaustion, additional raw product is required to restore the initial buffer capacity of the tank and the cost of this is shown in Kshort(T ) = Nshort(T )z0γmat, (19) where Nshort(T ) denotes the number of malfunctions caused by exhaustion during time T . Finally, the cost of repairs and installing the interme- diate storage itself need to be considered. To determine the installation costs, the installation factor of the tank (f ) and the cost of the tank (γtank in USD) were taken Figure 10: Mean profit as a function of the initial buffer and tank capacities. into account. To determine the expense of repairs, the parameter γrep was used to represent the cost of repairs (USD h−1) which was calculated according to equations Krep(t) = Nrep(t)∑ i=1 Trepγrep (20) and Ktank = f z0.6 max γtank. (21) The cost of installing the buffer tank was calculated ac- cording to references found in the literature [12]. The mean of the profit was investigated according to the reliability level of 0.95 ≤ 1 − α using a Monte Carlo simulation and its optimum was calculated using the grid method. It is shown by the results that if the re- liability of the system is high, then the costs of repairs and malfunctions in general are negligible compared to the cost of storage. As a result, the maximum profit was achieved close to the minimum storage capacity which is shown in Fig. 10. This value roughly corresponds to the minimum of the investigated boundary, using a reli- ability of 0.95. To generate this figure the following pa- rameters were used: βkey = 120 USD kg−1, δ = 0.3, γmat = 80 USD kg−1, βraw = 100 USD kg−1, f = 100 USD kg−0.6, γtank = 12, 000 USD, mtrep = 0.5 h, and σtrep = 0.29 h, where repair times were independent ran- dom variables of the uniform distribution during the time interval [0, 1]. The maximum profit according to these calculations is 4.76 · 104 USD, which can be achieved by tank and initial buffer capacities of 2, 101 kg and 389 kg, respectively. 6. Conclusion In this paper, a stochastic storage model was investigated. Random batches as inputs and outputs, as well as contin- uous withdrawal were allowed. A Monte Carlo simula- tion was used for the investigation. An analytic function Hungarian Journal of Industry and Chemistry OPTIMAL DESIGN AND OPERATION OF BUFFER TANKS UNDER STOCHASTIC CONDITIONS 99 was fitted to the simulated data, which provided a link between the initial buffer and tank capacities that corre- spond to a given level of reliability. The results agree with engineering practice. Although the data for the research did not stem from authentic sources, by utilizing data from the industry, the distribu- tion of the random variables present during the process could be determined using standard statistical methods. Therefore, the method can be a useful supplement during the design phase of a chemical plant and also be utilized to help simplify the overall control of a chemical process. Symbols Small letters c draining intensity (kg h−1) f installation factor of a tank (kg−0.6) g probability density function (h−1) m expectation x fixed initial buffer capacity (kg) y fixed tank capacity (kg) yb mass of batch fed into the tank (kg) yl mass of batch drained from the tank (kg) z mass of material (kg) Capital letters A,B,C,D fixed parameters of the approximated failure probability function G income (USD) E expectation H approximated failure probability function K expenses (USD) N number of events during time interval [0, Tmax] P probability Q net income (USD) T time (h) TF time of failure (h) Greek letters α probability of malfunction β sale price (USD kg−1) γ cost (USD kg−1) δ ratio of decrease in material value λ parameter of exponential distribution (h−1) σ standard deviation ψ function describing the probability of reliable operation during time interval [0, Tmax] Indices 0 initial b feed i index of event (i = 1, 2, · · · ) rep repair short material exhaustion l draining mat reactant max maximum min minimum r the number of mesh points of the initial buffer capacity s the number of mesh points of the tank capacity t time raw raw material tank tank key key component REFERENCES [1] Towler, G., Sinnott, R. 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