ЗВІТ З НДР 29-81 ЗА 2007 – 2009 Р Food and Environment Safety - Journal of Faculty of Food Engineering, Ştefan cel MareUniversity - Suceava Volume X, Issue 4 - 2011 49 MODELING OF THE THERMO-PHYSICAL PROPERTIES OF AQUEOUS SUCROSE SOLUTIONS II. BOILING PO IN T, S PECIFIC HEAT CA PA CITY AN D TH ERMA L CON DUC TIV ITY Andrei I. SIMION1, Cristina G. GRIGORAŞ1, Lăcrămioara RUSU 1, *Adriana DABIJA2 1“Vasile Alecsandri” University of Bacău, Department of Chemical and Food Engineering, Mărăşeşti no 157, Bacău 600115, Romania 2“Ştefan cel Mare” University of Suceava, Faculty of Food Engineering, Universităţii no 13, Suceava 720229, Romania *Corresponding author Received 10 September 2011, accepted 25 October 2011 Abstract: The aim of this study was to establish mathematical relations between temperature or pressure and sucrose concentration with boiling point, specific heat capacity and thermal conductivity of aqueous sucrose solutions. In order to assess and select a suitable mathematical model the known data were fitted in different equations. Two equations were generated for each thermo-physical properties, taking in consideration the level of precision and simplicity of formulation. For boiling point of aqueous sucrose solutions two equations with an average of relative errors of 0.22% and regression coefficients greater than 0.999 were generated, for ranges of 5 – 90% in sucrose concentration and pressure of 0.123.105 – 1.105 Pa. For specific heat capacity two equations were formulated with average relative errors of 0.002% and R2 = 0.9994 for intervals of temperature of 0 to 100 °C and sucrose concentration of 0 to 90% and for thermal conductivity were generated two equation with average relative errors of 0.004% and R2 = 0.9992 for a range of temperature of 0 to 80 °C and sucrose concentration between 0 and 60%. The obtained equations can be loaded in computer software available both for industrial and academic users and so facilitating the sizing and optimization calculations of various technological equipment and processes. Keywords: sucrose, aqueous solutions, mathematical models 1. Introduction Aqueous solutions of carbohydrates have been studied for many years due to their both scientific and practical importance (molecular biology and biochemistry, food chemistry and technology, sugar industry etc.). Due to the common availability of sucrose and the ease of its purification, the system sucrose - water was the subject of many physicochemical studies. The fact that dilute sucrose solutions could be used as a model system to demonstrate the validity of fundamental laws of physical chemistry and chemical thermodynamics additionally stimulated the popularity of these studies [1]. The increasing practical interest in sucrose solutions caused a great demand for predictive methods of determining its physical properties such as boiling point, heat capacity and thermal conductivity. The boiling point can be directly correlated to the chemical structure of the molecule and reflects the strength of the intermolecular forces (among other forces Food and Environment Safety - Journal of Faculty of Food Engineering, Ştefan cel MareUniversity - Suceava Volume X, Issue 4 - 2011 50 present) that hold the sucrose molecules together. The stronger the intermolecular forces, the more tightly the atoms will be held together and, therefore, the boiling point is higher [2]. Heat capacity and thermal conductivity are two of the most fundamental thermodynamic properties of liquid substances and they are closely related to their other physical and chemical properties. They are intimately related to the temperature dependence of fundamental thermodynamic functions [3]. These properties may be relatively easily determined in the laboratory with great accuracy; and they are of key importance for linking thermodynamics with microscopic fluid structure and dynamics but having predictive models can be a useful adjunct. The accumulated data have led to the development of both empirical and phenomenological correlations, and many such correlations have been incorporated into design and analysis methods [4]. Most correlations, however, are applicable to only a relatively narrow range of conditions. The purpose of this study is, therefore, to develop correlations by critically evaluating and regressing various types of experimental data available from the literature. 2. Experimental Tabular data (Table 1, 2 and 3) concerning the variation of aqueous sucrose solutions boiling point, thermal conductivity and specific heat capacity with sucrose concentration and temperature were used as primary data for the regression analysis. Microsoft Excel™ 2007 spreadsheets, CurveExpert® and TableCurve 3D® v.4 software were used to establish the equations. The tabular data were plotted in Temperature – Thermo-physical property, sucrose content – Thermo-physical property coordinates and different regression techniques, involving the method of least squares were used to reveal the best-fit equation. Table 1 Boiling point Bp [°C] of aqueous sucrose solutions as a function of the mass fraction X [%] pressure p [Pa] Boiling point, Bp [°C] Sucrose concentration, X w [%] Pressure p.105, Pa 0.123 0.199 0.311 0.473 0.7 1 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 50.05 50.12 50.17 50.26 50.39 50.52 50.69 50.80 51.01 51.32 51.70 52.30 52.80 53.65 55.05 56.80 - - 60.05 60.10 60.18 60.27 60.40 60.54 60.71 60.85 61.10 61.40 61.82 62.45 63.00 63.90 65.40 67.30 70.00 - 70.05 70.11 70.18 70.28 70.42 70.55 70.73 70.90 71.18 71.52 71.94 72.60 73.20 74.18 75.80 77.85 80.75 86.00 80.06 80.11 80.19 80.28 80.43 80.57 80.76 80.95 81.25 81.61 82.06 82.75 83.40 84.46 86.20 88.35 91.50 97.20 90.06 90.12 90.19 90.29 90.44 90.58 90.78 91.00 91.32 91.72 92.18 92.90 93.60 94.75 96.60 98.90 102.25 108.40 100.06 100.12 100.20 100.30 100.45 100.60 100.80 101.05 101.40 101.80 102.30 103.05 103.80 105.05 107.00 109.40 113.00 119.60 Food and Environment Safety - Journal of Faculty of Food Engineering, Ştefan cel MareUniversity - Suceava Volume X, Issue 4 - 2011 51 Table 2 Thermal conductivity [W/(m . K)] of aqueous sucrose solutions as a function of the mass fraction X [%] and temperature t, [°C][5, 6] Sucrose concentration, X w [%] Thermal conductivity, [W/(m . K)] at temperatures t, [°C] 0 10 20 30 40 50 60 70 80 0 10 20 30 40 50 60 0.565 0.544 0.505 0.473 0.443 0.413 0.383 0.583 0.551 0.52 0.488 0.457 0.391 0.384 0.599 0.566 0.535 0.501 0.47 0.437 0.405 0.614 0.581 0.548 0.514 0.48 0.449 0.415 0.628 0.594 0.56 0.526 0.492 0.458 0.419 0.641 0.607 0.572 0.536 0.502 0.467 0.432 0.652 0.617 0.588 0.547 0.512 0.477 0.441 0.663 0.628 0.592 0.555 0.519 0.484 0.449 0.672 0.636 0.6 0.563 0.526 0.491 0.455 Table 3 Specific heat capacity Cp [J/(kg . K)] of aqueous sucrose solutions as a function of the mass fraction X [%] and temperature t, [°C][7] Temperature, t [°C] Specific heat capacity Cp [J/(kg . K)] at sucrose concentration, X [%] 0 10 20 30 40 50 60 70 80 90 0 10 20 30 40 50 60 70 80 90 100 3936 3936 3936 3977 3977 3977 3977 3977 3977 4019 4016 3684 3684 3726 3726 3726 3726 3726 3810 3810 3810 3852 3433 3475 3475 3517 3517 3559 3559 3601 3601 3643 3643 3182 3224 3224 3266 3308 3349 3349 3391 3433 3475 3475 2931 2973 3014 3056 3098 3140 3140 3182 3224 3266 3308 2680 2721 2763 2805 2847 2889 2973 3014 3056 3098 3140 2428 2470 2554 2596 2638 2680 2763 2805 2847 2889 2973 2177 2219 2303 2345 2428 2470 2554 2596 2680 2721 2763 1926 2010 2052 2135 2219 2261 2345 2386 2470 2554 2596 3936 3936 3936 3977 3977 3977 3977 3977 3977 4019 4016 3. Results and Discussion 3.1 Boiling point Using Microsoft Excel™ 2007 spreadsheets and CurveExpert® software, a Modified Hoerl Model correlation between pressure p and boiling point, at constant aqueous sucrose concentration X, [%] has been established:   Cpp pBAB /1  (1) For ranges of sucrose concentration between 5 and 85%, the coefficients of the Modified Hoerl Model equations A, B and C are presented in Table 4. The regression coefficients R2 are greater than 0.99, thus indicating a good correlation of variables. Table 4 Coefficients for equation (1) Sucrose conc., X [%] A B C R 2 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 101.596 101.644 101.728 101.973 101.973 102.308 102.112 102.562 102.917 103.313 103.791 104.521 105.264 106.475 108.405 110.793 114.586 121.375 0.98196 0.98211 0.98204 0.98214 0.98214 0.98236 0.98226 0.98234 0.98231 0.98251 0.98273 0.98304 0.98320 0.98373 0.98422 0.98466 0.98295 0.98210 0.26788 0.26803 0.26762 0.26712 0.26712 0.26670 0.26697 0.26675 0.26629 0.26609 0.26558 0.26462 0.26411 0.26404 0.26228 0.25944 0.25192 0.24535 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 Food and Environment Safety - Journal of Faculty of Food Engineering, Ştefan cel MareUniversity - Suceava Volume X, Issue 4 - 2011 52 In order to correlate A, B and C coefficients with sucrose mass concentration, more models were used in CurveExpert® software (1st, 2nd and 3rd degree polynomial equations, “vapor pressure” model, “heat capacity” model etc.). The best fit model is a 3rd degree polynomial equation for the A coefficient and quadratic equations for the B and C coefficients (Table 5). 32 dTcTbTatCoefficien A  (2) 2, cTbTatsCoefficien CB  Table 5 Coefficients for equation (2) Coeff. A B C a 101 0.9823 0.2672 b 0.1128961704 -3.00E-05 6.00E-05 c -3.820845E-03 7.004E-07 -2.00E-06 d 4.88158E-05 - - R2 0.994 0.970 0.932 Combining the equations (1) and (2) and replacing the coefficients with numeric values, the final form of proposed equation model (Eq. 3) is:   )3( )9823.0053077( )1011128961704.0 038208452.30588158.4( )2672.0056062( /12 23 2      EXE p p p XEXE X XEXEB To quantify the deviation of calculated densities from tabular data, the relative error equation was use and its values are presented in Table 6: [%]100   tabular calculatedtabular    (4) The average of the induced relative errors for the proposed models is 0.22% for the proposed mathematical model. By plotting the tabular data for aqueous sucrose solutions boiling point in TableCurve 3D® v.4 software (Fig. 1) an equation for the response function was generated, chosen due to the relative simplicity of formulation and regression coefficient (Eq. 5). The coefficients of the fitted polynomial equation are presented in Table 7. Table 6 The induced relative errors for the proposed model (3) for boiling point of aqueous sucrose solutions Relative errors, ε [%] Sucrose concentration, X w [%] Pressure p.105, Pa 0.123 0.199 0.311 0.473 0.7 1 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 0.00422 0.06781 0.10495 0.03253 0.11270 0.21509 0.31780 0.18847 0.10589 0.03310 0.12519 0.11667 0.59176 0.72748 0.21195 0.50231 - - 0.24345 0.40210 0.42817 0.39174 0.27933 0.17721 0.08829 0.14724 0.15940 0.25959 0.36936 0.38017 0.79412 0.95659 0.52791 0.10705 1.44869 - 0.03757 0.21822 0.29134 0.26487 0.16100 0.08711 0.00604 0.00229 0.02143 0.02919 0.16137 0.18842 0.55981 0.70410 0.31942 0.24715 1.45175 4.84629 0.12326 0.09753 0.17967 0.18448 0.08590 0.00734 0.08982 0.10788 0.14693 0.10964 0.00217 0.04117 0.38047 0.51124 0.16027 0.29716 1.45218 4.71030 0.17590 0.05329 0.16393 0.17006 0.08578 0.01369 0.08762 0.13819 0.19018 0.18603 0.06926 0.02193 0.29154 0.40029 0.08526 0.33774 1.40415 4.55567 0.02649 0.21966 0.33292 0.34955 0.27582 0.19789 0.10193 0.0239 0.04984 0.03455 0.05520 0.10741 0.39870 0.47823 0.19893 0.15364 1.19791 4.26999 Food and Environment Safety - Journal of Faculty of Food Engineering, Ştefan cel MareUniversity - Suceava Volume X, Issue 4 - 2011 53 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Pre ssu re, [ 10^ 5 P a] 01 02 03 04 05 06 070 80 Sucrose concentration, [%] 50 50 60 60 70 70 80 80 90 90 100 100 110 110 120 120 B oi lin g P oi nt , [ [° C ] B oi lin g P oi nt , [ [° C ] Boiling Point Rank 31 Eqn 157010504 lnz=a+blnx+c/x0.5+dy2+ey2lny+fy2.5+gy3 r2=0.99958643 DF Adj r2=0.99955659 FitStdErr=0.38092776 Fstat=39477.482 a=4.7356452 b=0.20791255 c=-0.1303382 d=-0.00037254489 e=0.00044369357 f=-0.00026010431 g=9.6176697e-06 Figure 1. Aqueous sucrose solutions boiling point values plotted in TableCurve 3D and fitted polynomial equation (5) with residuals. )5( lnlnln 35.2 225.0 gXfX XeXdXpcpbaBp   Table 7 Coefficients for equation (5) Coeff. Value Coeff. Value a b c d 4.7356452 0.20791255 -0.1303382 -0.0003725448 e f g 0.00044369357 -0.00026010431 9.6176697E-06 The equation (5) is a polynomial equation, Rank 31, Eqn. 157010504 in TableCurve 3D® v.4 library with R2 = 0.99958643, R2adj = 0.9995565, FitSdErr = 0.0003725 and Fstat. = 39477.482. 3.2 Specific Heat Capacity Using Microsoft Excel™ 2007 spreadsheets linear correlation between temperature T, [K] and specific heat capacity, at constant aqueous sucrose concentration X, [%] has been established: bTaC p  (6) For ranges of temperature between 273 and 373 K, the values of the A and B coefficients and regression coefficients, R2 of each linear equation are presented in Table 8. In order to correlate A and B coefficients with sucrose concentration, more models were used in Microsoft Excel™ 2007. The best fit model is also a linear equation. bXatsCoefficien BA , (7) Table 8 Coefficients for equation (6) Sucrose conc., X [%] A B R2 10 20 30 40 50 60 70 80 90 3722.12 3234.75 2869.25 2339.64 1952.12 1371.81 984.973 511.335 93.2872 0.777273 1.603636 2.100000 3.079091 3.619091 4.755455 5.293636 6.088182 6.734545 0.813 0.864 0.975 0.985 0.991 0.995 0.994 0.996 0.997 Table 9 Coefficients for equation (7) Coeff. a b A B 4182.8620454545 0.0045707071 -45.7032772727 0.0755772727 Combining the equations (6) and (7) and replacing the coefficients with numeric values, the final form of proposed equation model (Eq. 8) is: T XC p X)075577.000457070.0( )70327.4586.4182(   (8) To quantify the deviation of calculated densities from tabular data, the relative error equation was use and its values are presented in Table 10. The average of the induced relative errors for the proposed models is 0.002% for the proposed mathematical model. By plotting the tabular data for aqueous sucrose solutions specific heat capacity in TableCurve 3D® v.4 software (Fig. 2) an equation for the response function was generated (Eq. 9). Food and Environment Safety - Journal of Faculty of Food Engineering, Ştefan cel MareUniversity - Suceava Volume X, Issue 4 - 2011 54 Table 10 The induced relative errors for the proposed model (8) for specific heat capacity of aqueous sucrose solutions Temperature, T [K] Relative errors, ε [%] Sucrose concentration, X [%] 0 10 20 30 40 50 60 70 80 90 273 283 293 303 313 323 333 343 353 363 373 0.066 0.127 0.320 0.523 0.331 0.140 0.051 0.242 0.433 0.427 0.163 0.035 0.376 0.348 0.058 0.465 0.872 1.279 0.556 0.158 0.240 0.459 0.029 0.584 0.070 0.479 0.167 0.377 0.261 0.277 0.354 0.180 0.444 0.023 0.386 0.553 0.187 0.170 0.488 0.416 0.065 0.277 0.611 0.260 0.014 0.154 0.257 0.390 0.519 0.645 0.560 0.422 0.287 0.156 0.028 0.005 0.157 0.277 0.394 0.507 0.617 0.699 0.544 0.425 0.310 0.198 0.048 0.490 0.742 0.308 0.112 0.519 0.584 0.185 0.202 0.578 0.482 0.067 0.900 0.153 0.639 0.309 0.445 0.489 0.231 0.652 0.074 0.743 0.091 0.706 0.579 0.143 0.856 0.313 0.378 0.763 0.092 0.535 0.478 0.066 0.127 0.320 0.523 0.331 0.140 0.051 0.242 0.433 0.427 0.163 The equation (9) is a polynomial equation, Rank 50, Eqn. 302 in TableCurve 3D® v.4 library with R2 = 0.99944977, R2adj = 0.9994138, FitSdErr = 13.701972, Fstat. = 33785.237. 27028 029030 031032 033034 035036 0370 Temperature, [K] 90 80 70 60 50 40 30 20 Sucro se co ncen tratio n, [% ] 1500 1500 2000 2000 2500 2500 3000 3000 3500 3500 4000 4000 4500 4500 H ea t C ap ac ity , [ J/ kg K ] H ea t C ap ac ity , [ J/ kg K ] Heat Capacity Rank 50 Eqn 302 z=a+blnx+cy+d(lnx)^2+ey^2+fylnx r 2̂=0.99944977 DF Adj r 2̂=0.99941388 FitStdErr=13.701972 Fstat=33785.237 a=25132.56 b=-7267.3551 c=-161.21331 d=630.05763 e=-0.0010015742 f=24.255336 Figure 2. Aqueous sucrose solutions specific heat capacity values plotted in TableCurve 3D and fitted polynomial equation (9) with residuals. TfX eXTdcXTbaC p ln )(lnln 22   (9) The coefficients of the fitted polynomial equation are presented in Table 11. Table 11 Coefficients for equation (5) Coeff. Value Coeff. Value a b c 25132.56 -7267.3551 -161.21331 d e f 630.05763 -0.0010015742 24.255336 3.3 Thermal Conductivity Using Microsoft Excel™ 2007 spreadsheets linear correlation between aqueous sucrose concentration X, [%] and specific heat capacity, at constant temperature T, [K] has been established: BXAC p  (10) The A and B values for the fitted linear equation are presented in Table 12. bTatsCoefficien BA , (11) Table 12 Coefficients for equation (10) Temperature, T [K] A B R 2 273 283 293 303 313 323 333 343 353 0.568357 0.584857 0.598821 0.613964 0.628893 0.641393 0.653679 0.663179 0.672036 0.00311 0.00330 0.00323 0.00332 0.00345 0.00349 0.00353 0.00358 0.00363 0.997 0.998 0.999 0.999 0.999 1.000 0.999 0.999 1.000 In order to correlate A and B coefficients with temperature, more models were used in Microsoft Excel™ 2007. The best fit model is also a linear equation (Table 13). Food and Environment Safety - Journal of Faculty of Food Engineering, Ştefan cel MareUniversity - Suceava Volume X, Issue 4 - 2011 55 Table 13 Coefficients for equation (11) Coeff. a b A B 0.2145613296 -0.0014797877 0.0013113690 -0.0000061488 Combining the equations (10) and (11) and replacing the coefficients with numeric values, the final form of proposed equation model (Eq. 12) is: )12(06T)6.1488E70.00147978( 90.00131136960.21456132( X T   To quantify the deviation of calculated densities from tabular data, the relative error equation was use and its values are presented in Table 15. The average of the induced relative errors for the proposed models is 0.004% for the proposed mathematical model. 60 50 40 30 20 10Sucrose concentration, [%] 270 280 290 300 310 320 330 340 350 Temp eratu re, [K ] 0.35 0.35 0.4 0.4 0.45 0.45 0.5 0.5 0.55 0.55 0.6 0.6 0.65 0.65 0.7 0.7 T he rm al C on du ct iv ity , [ w /m K ] T he rm al C on du ct iv ity , [ w /m K ] Thermal Conductivity Rank 17 Eqn 316 z=a+bx+c/y+dx^2+e/y^2+fx/y+gx^3+h/y^3+ix/y^2+jx^2/y r 2̂=0.99940883 DF Adj r 2̂=0.99929515 FitStdErr=0.0019651459 Fstat=9955.5537 a=-0.84385948 b=-0.0051670655 c=1602.2814 d=2.3609905e-06 e=-528571.74 f=0.45271455 g=3.7037037e-08 h=53598501 i=42.375474 j=-0.0020785223 Figure 3. Aqueous sucrose solutions thermal conductivity values plotted in TableCurve 3D and fitted polynomial equation (13) with residuals. By plotting the tabular data for aqueous sucrose solutions thermal conductivity in TableCurve 3D® v.4 software (Fig. 3) an equation for the response function was generated chosen due to the best regression coefficient (Eq. 13). TjXTiXThTfX TedXTcbXa //// // 223 22   (13) The coefficients of the fitted polynomial equation are presented in Table 14. Table 14 Coefficients for equation (13) Coeff. Value Coeff. Value a b c d e -0.84385948 -0.0051670655 1602.2814 2.3609905E-06 -528571.74 f g h i j 0.45271455 3.7037037E-08 53598501 42.375474 -0.0020785223 The equation (13) is a polynomial equation, Rank 17, Eqn. 316 in TableCurve 3D® v.4 library with R2 = 0.999440883, R2adj = 0.999295, FitSdErr = 0.00196514, Fstat. = 9955.553. 4. Conclusions Two equations were generated for each thermo-physical properties, taking in consideration the level of precision and simplicity of formulation. Table 15 The induced relative errors for the proposed model (12) for thermal conductivity of aqueous sucrose solutions Temperature, T [K] Relative errors, ε [%] Sucrose concentration, X [%] 0 10 20 30 40 50 60 273 283 293 303 313 323 333 343 353 1.339 0.459 0.035 0.341 0.475 0.447 0.115 0.205 0.815 0.555 0.450 0.004 0.434 0.509 0.581 0.166 0.075 0.782 0.871 0.246 0.343 0.539 0.548 0.557 1.241 0.099 0.745 1.017 0.222 0.130 0.463 0.591 0.344 0.288 0.306 0.882 0.729 0.026 0.524 0.377 0.641 0.498 0.361 0.348 1.038 0.398 0.875 0.521 0.944 0.698 0.462 0.444 0.190 0.806 0.016 2.210 0.763 0.883 0.420 0.421 0.316 0.007 0.760 Food and Environment Safety - Journal of Faculty of Food Engineering, Ştefan cel MareUniversity - Suceava Volume X, Issue 4 - 2011 56 For boiling point of aqueous sucrose solutions two equations with an average of relative errors of 0.22% and regression coefficients greater than 0.999 were generated, for ranges of 5 – 90% in sucrose concentration and pressure of 0.123.105 – 1.105 Pa. For specific heat capacity two equations were formulated with average relative errors of 0.002% and R2 = 0.9994 for intervals of temperature of 0 to 100 °C and sucrose concentration of 0 to 90% and for thermal conductivity were generated two equation with average relative errors of 0.004% and R2 = 0.9992 for a range of temperature of 0 to 80 °C and sucrose concentration between 0 and 60%. 5. References 1. STARZAK, M., MATHLOUTHI, M., Temperature dependence of water activity in aqueous solutions of sucrose, Food Chemistry, 96 (3), 346-370, (2006) 2. LI, Q., CHEN, X., HU, Z., Quantitative structure–property relationship studies for estimating boiling points of alcohols using calculated molecular descriptors with radial basis function neural networks, Chemometrics and Intelligent Laboratory Systems, 72 (1), 93-100, (2004) 3. WILHELM, E., Heat Capacities: Introduction, Concepts and Selected Applications in: Heat Capacities Liquids, Solutions and Vapours (Editors: Wilhelm, E., Letcher, T.M.), The Royal Society of Chemistry, England, 1-27, (2010) 4. BUBNÍK, Z., HENKE, S., KADLEC, P., HINKOVÁ, A., POUR, V., Database of the properties of sucrose, sucrose solution and food, Journal of Food Engineering, 77 (3), 399-405, (2006) 5. ILIESCU G., VASILE C., Caracteristici termofizice ale produselor alimentare, Ed. Tehnica, Bucuresti, 109-103 p (1982) 6. MACOVEI V.M., Culegere de caracteristici termofizice pentru biotehnologie şi industrie alimentară, Ed. Alma, Galaţi, 199-200 p, (2000) 7. MATHLOUTHI M., REISER P., Sucrose, Properties and Applications, Chapman & Hall, London, 208 p, (1995) 8. SIMION, A.I., DOBROVICI, P.E., RUSU, L., GAVRILĂ, L., Modeling of the thermophysical properties of grapes juice I. Thermal conductivity and thermal diffusivity, Annals of Food Science and Technology, ISSN 20652828, X (2), 363-368, (2009) 9. SIMION, A.I., GRIGORAŞ, C., RUSU, L., GAVRILĂ, L., Modeling of the thermophysical properties of grapes juice II. Boiling point and density, Studii şi cercetări ştiinţifice: Chimie şi inginerie chimică – Biotehnologii Industrie alimentară, ISSN 1582540X, X (4), 365-374, (2009) 10. SIMION A.I., DOBROVICI P.E., GRIGORAS C.G., RUSU L., Modeling of the thermo-physical Properties of aqueous sucrose solutions I. Density and dynamic and kinematic viscosity, Annals of Food Science and Technology, ISSN 20652828, in press, (2011)