HUNGARIAN JOURNAL
OF INDUSTRIAL CHEMISTRY
VESZPREM
Vol. 30. pp. 95 - 101 (2002)
VARYING POROSITY KINETIC MODEL FOR DIRECT AND REACTIVE
SOLID-LIQUID EXTRACTION
I. SEIKOV A and A. MINTCHEV
(Department of Chemical Engineering, University of Chemical Technology and Metallurgy, blvd. Kilment Ohridski 8,
1756 Sofia, BULGARIA)
Received: Apri123, 2001
A mathematical model is presented accounting for the effects of porosity increase during extraction from vegetable
materials. The relation between the porosity and the total extract release is derived from the solid phase volume balance.
The model will be used to interpret the experimental data for alkaloid recovery from leaves and radix of the medicinal
plant Atropa Belladonna. The extractability has been determined by dissolution of alkaloidic salts in polar solvent (direct
extraction) and by alkaline transformation of salts to bases in non-polar solvent (reactive extraction). Supporting
experiments were performed in order to estimate the kinetics of solvent penetration. For inert conditions, the estimated
effective diffusivities are nearly equal to those obtained under reaction conditions. The resorted differences in the
diffusivity as a result of the porosity changes remain lower in respect to the strong influence of the different initial pore
structure of the two raw materials.
Keywords: solid-liquid extraction, vegetable alkaloid recovery, chemical reaction, porous medium, liquid penetration
Introduction
Solid-liquid extraction coupled by chemical or
biochemical reaction occurs frequently during
valorisation of natural materials [1-2]. Generally the
kinetics of the process is represented by macroscopic
mass balance on the overall solid phase with volume
reaction models:
aC2 _ z
i)t-D~JJV C2 +Rv (1)
where Rv is the rate of chemical reaction per unit
volume and C2(t,r) represents the concentration of the
diffusing reaction product. This equation allows a
constant effective diffusivity Dt!JJ to be estimated
assuming that the initial structure of the porous solid is
maintained while the extraction proceeds.
In many cases during the treatment of the vegetable
material several additional processes, as co-solutes
migration, solvent adsorption, hydration or other
reactions occur simultaneously with valuable
component mass transfer. The structure of the solid can
be readily affected and this is accompanied generally by
a porosity increase. Varying porosity causes an increase
in the diffusivity with the course of the extraction.
Theoretical studies have revealed that the ratio of
effective diffusivity to molecular diffusivity varies
proportionally by c/3"3 depending on the adopted
geometric description of the pore structure [3-6].
Initial experiments with the considered plant
indicated sizeable amounts of dissolved co-solutes. In
parallel an increase of the volume of solvent penetrating
in the solid was resorted that differed for the various
solvents that were used [7]. Then, the measurement and
evaluation of the porosity effect are important for the
accurate prediction of the values of D ~if under reactive
or inert conditions.
In the present paper a dynamic model is proposed to
describe the diffusive-reactive phenomena when the
porosity increases with the course of the extraction. To
predict the porosity changes a simplified model is
adopted that relates the kinetics of solvent penetration to
the kinetics of release of the total extract. The presented
model will be used to interpret the experimental data of
kinetics of alkaloid recovery by direct and reactive
extraction from different parts of the medicinal plant
Atropa belladonna in a batch system.
Mathematical model
The overall process of extraction with simultaneous
chemical reaction involves consideration of the
following phenomena:
96
(a) chemical conversion of insoluble compound that is
initially adsorbed or chemically bounded in a solid
to soluble reaction product, prior to its diffusion
through the pore space;
(b) parallel release of all-soluble compounds initially
present accompanied by additional solvent
penetration and porosity increase.
The approximate model is derived under the
following assumptions:
- the solid represents one monodispersed phase of
spherical particles with mean radius Rs and initial
porosity £p.o; the particles retain their shape and
dimension during reaction and extraction, although
the porosity increases;
- the extractable compounds are uniformly distributed
in the porous solid particles;
- the solid-solvent phases ratio f3 is high, so that the
solutions are always dilute and density variations
and multicomponent effects on the diffusion are
negligible;
- the analysis is restricted to first-order irreversible
reaction that takes place all over the solid volume
without participation of the pores, according to the
rate equation:
dCs (t) = -k C (1- £ )
dt r s P
(2)
where kr=fipH, T) is the effective reaction rate
constant.
Under varying porosity condition the transient
diffusion of the soluble reaction product within the
particle obeys the following reiationship [8]:
iJ(e.PCP) 1 0 ( 2(iJCP) ) (3) -a-t-=7 or D~g(e.P)r a;- -Cpvr +k,C,(l-ep)
The solvent radial velocity Vr in the pores can be
related to the porosity increase from the continuity
equation:
a£p +_!_i_~zv )=0
at r 2 dr r (4)
After integration of the continuity equation and
substituting this in Eq.( 3) the conservation equation
takes the form:
The associated boundary conditions are:
.(acp) =O
ur t=O
{6}
-D • ..-(
0J; L. +<•·,c,>, •••. ~kJc,1, •• , -C,(t>) (7)
In the last step of the process~ the solute is
transported from the pores opening on the contact
surface to the bulk liquid phase at concentration Clt):
dCl (t) = ]_k f3(C 1- - C (t)) (8)
d R
m p r-R, 1
t s
Solid phase volume balance may be used as
theoretical possibility to correlate the changes in a pore
volume with the amount of compounds released [9]. It is
known that solvent penetration in the pore space is the
initial stage of the extraction. It is assumed that an
initial porous volume £p.o Vs is immediately filled with
solvent. With the disappearance of extractable
compounds from the solid the free space volume inside
the particles increases and the solvent penetration
continues during the whole stage of the extraction.
The solid phase apparent volume Vs consists of inert
solid matter Vin• pore volume filled with solvent ~it)
and extractable compounds Vexlt):
(9)
The solvent volume impregnated the solid is
represented by the varying porosity:
(10)
The decrease in the volume of the extractable
compounds Ve.xlt) may be expressed through the amount
extracted for the timet. Generally, the extract increases
in time mexr=f(t), it can be described by sufficient
accuracy by equation of the type:
(11)
where A, B and H are empirical coefficients. Then the
unextracted fraction in the solid phase '}{ t) is defined
from the total balance:
y(t) = 1- mext(t)
Xomo
(12)
where the initial mass fraction X0 is established
experimentally after multiple treatment with fresh
solvent. The particular volumes can be expressed as
follow:
X 0 m0 - me.xr(t)
P~xt
(13)
(14)
Introducing Eqs.(JO), (13) and (14) into Eq.(9)
gives:
Vs = ~o (1-=_Xo + Y_!o)
1 BP Pm P~xt
(15)
When the changes in the dimension of the solid
particles are negligible. solvent penetration equals the
volume of the disappearance of extractable compounds.
The porosity changes in a function of time is given by
the foUowing relationships:
1- X 0 y(t)X 0 --+---
E (t)=l-(1-E ) An Pext (16)
P p,o 1-X X __ o+_o_
Pin Pext
The porosity changes would affect the solute
diffusivity. An exponential increase in the effective
diffusivity in respect to the extracted fraction (1-'0 is
assumed and it is defined by the following empirical
function:
D = D expa(l-y)
eff eff,O (17)
where a is a numerical constant and D eff,O is the
effective diffusivity evaluated for the initial conditions.
The system of Eqs. (2-17) can be rearranged to a
dimensionless form:
de* (r)
2
*
-·-=-Th C dr (18)
dd;r) =3Bif3(c;l~=1 -c;) (20)
I.e. c; (O) = 1 , c; co,cp) = o, c; co)= o (21)
B.C.
ac* a; 11'=0 =O
* a c* I cp dE l *I *) - D __ I' m=l +--P- = Bi\C "'=1 - C
Olp -r 3 d'f p "1' I
with the following dimensionless parameters:
* c c =--,
Cs,O
D
* _ D eff _ a(l-y)
----exp
Deff,O
f3=i,
l
D
eff,O t r=y,
$
(22)
(23)
(24)
where Th is called Thiele-type modulus for the porous
particle that brings out the relative significance of the
reaction rate [10,11].
Numerical treatment
The coupled system of second order,. partial and
ordinary differential equations of the presented model is
solved numerically. Four-order Runge-Kutta method
was utilized for the ordinary differential equations. The
97
A
·~ 0.8
0.2 0.4 0.6 0.8
Fig.l Reaction rate constant influence on the averaged
concentration in the solid phase (computed for Bi=400, kr=
0.8 s"\ 0.8 10"2 s"1 and 0.8 10"4s"1)
approach for the parabolic partial differential equations
is based on Crank-Nikolson finite difference scheme.
For the resolution of the resulting systems of algebraic
equations forward-backward Thomas' algorithm was
used.
From the dimensionless mass balance of the solid
particle Eq. ( 19) it is clear that Thiele modulus, the
magnitude of variation in porosity Ep and effective
diffusivity D* will control the process. The integration
of this equation around the overall solid particle volume
yields the evolution of the averaged concentration
in the particle:
. (25)
d • a [I . ) { . ac,) (ile,) 1 a r~· . ) .. -< C >=- B C = D - • - -- -C +Th C
dt • ar v. r , a~ "'" ih 1'2 a~ 3 , '
The values of this term can be positive or negative
depending on the relative magnitude of the rate of
diffusion and chemical reaction. Fig. I shows the plots
=f(t) computed for specific ranges of Thiele
modulus. The curves are compared with the prediction
provided from a pure diffusional model. In the usual
situation for large Biot numbers there can be
distinguished three different kinetic regimes:
- diffusion-controlling regime (Th> > 1 ): in case of
instantaneous or very fast chemical reaction the
conversion takes place before the solute can diffuse
into the interior of the particle; the effect of reaction
rate is negligible and the disappearance of the solute
is a continuously decreasing function;
- reaction-diffusion regime (Th> 1): the diffusion of
solute is not fast enough to compensate for its
appearance by reaction and the evolution of the
concentration passes through a maximum
before the reactant is completely converted;
- reaction rate-controlling regime (Th40) the prediction approaches an
asymptotic curve controlled purely by pore diffusion.
Physically, for given particle size and reaction rate
constant, the parameter Th increases as the effective
diffusivity D~"ifis decreased:
using porous solid of very small pore size;
using porous solid having a small porosity or high
tortuosity factor.
The effect of the varying porosity under reaction or
non~reaction conditions is explained by these
considerations. In Fig.3 are presented the computed
values of dimensionless concentration in the liquid
phase cl "( 1:) for both diffusion-controlling and reaction-
diffusion regime with porosity as parameter. The kinetic
behavior is simulated for three cases: constant porosity
(Ep=0.4). moderate (£p=0.4+0.55) and very marked
porosity change (Ep=0.4-f().7).
As expected. under diffusion-controJiing regime the
higher the porosity the faster the overall extraction
process. However. under reaction-diffusion regime a
delay in the process is predicted as the porosity is
increased. The increasing values of the porosity Ep and
the effective diffusivity D(ff lead to a decrease in the
values of Til. When the rate of reaction is decreased in
respect to the diffusion rate~ the concentration gradient
at the sofid"liquid interface declines rapidly and this
effect is not completely compensated by the increasing
D~ti
Fig.4 Steps of alkaloid recovery from Atropa Belladonna
plant: a) Direct solid-liquid extraction; b) Reactive solid-liquid
extraction
As a result from the contradictory effect of the
varying porosity erroneous results can be obtained using
a model with constant porosity, namely an apparent
decrease in D eff when the reaction is carried out in a
reaction-diffusion regime.
Experimental
Exemplary vegetable alkaloid recovery by direct or
reactive extraction has been studied. Small quantities of
tropan alkaloids are found in leaves, seeds and radix of
the medicinal plant Atropa Belladonna. These are
predominantly in alkaloidic salt form and dissolved in
the cellular liquid. The known methods for alkaloid
extraction are based on their different solubility
according to solvent polarity. The polar organic solvents
are appropriate solvents for alkaloid salts. When using
non-polar solvent, alkaloid bases dissolve. The co-
solutes are also selectively removed. Unvaluable
substances, as polysaccharides, mineral salts, tanins,
flavanoids dissolve in ethanol. Chloroform extracts
contain non-polar substances: chlorofils, ac~ds, fatty
oils, pigments. The overall process consists of the
following stages (Fig.4):
1. Solid-liquid extraction by direct dissolution of salts
in polar solvent (direct extraction) or by prior
alkaline transformation of salts to bases in non-polar
solvent (reactive extraction).
2. Extract purification from associated co-solutes by
acidic treatment with aqueous solution.
3. Crude-alkaloids recovery from the cleaned-up
extract by alkaline transformation in alkaloid bases.
In the experimental study the solvent was methanol
for direct extraction, and chloroform under reaction
conditions. Adjustment of pH alkaline of the solution
was made by means of 25% NH3• For acidification of
the aqueous solutions 8% HCI was used. Alkaloids were
extracted from dried and fractionated samples, provided
from two different parts of the plant, namely radix and
leaves. The structure of the porous solid was
investigated by nitrogen adsorption at 77.4 K by the
simplified single-point BET procedure. The results
show that the pore spaces of the epigeous and
subterraneous tissues strongly differ in their structural
parameters:
-fit for direct extraction
~experimental -fit for reactive extraction
oq,----~----~----~-----r----~----~
0 600 1200 1800
time, sec
2400 3000 3600
Fig.S Course of extraction C1=f(t) from radix samples
o experimental
<> experimental
300 600 900
time{sec)
-fit for physical extraction
-fit for reactive extraction
1200 1500 1800
Fig.6 Course of extraction C1=f(t) from leaves samples
leaves: specific area 1.7 m2 g-1, free volume 0.6 cm3
g-1, mean pore radius 11 nm.
radix: specific area 0.4 m2, g-1, free volume 0.15 cm3
g-1, mean pore radius 16 nm.
The initial content of alkaloids was obtained after
continuous extraction in a Soxhlet apparatus: 0.3% of
the dried mass for leaves and 0.6% for radix. The
experimental procedure has been divided in two groups.
The first one analyses the recovery of the alkaloids in
the cleaned-up extracts to provide the kinetic curves
Cz=J(t). For this aim the solutions were analysed for
alkaloids by spectrophotometric measurement at
wavelength A=430 nm [12-13].
The second group investigates the kinetics of total
extract removal and solvent penetration. The
observations include simply measuring the changes in
weight: when the pores are filled with a solvent (msz).
and after removing the impregnated solvent by drying at
40 oc for about 12 hours (mss)· From this experimental
values the kinetics of total extract release mexi=J( t) and
the volume of solvent penetrating into the porous
material V~.s=J(t) can be determined by noting that:
msl (t)- mss (t)
pl
(26)
(27)
0.15
0.125
;g
~ 0.1
~
g 0,075
~
"'" 0.05
2
0.025
99
•
reactive extraction with CHCr;
0 +-----r-----.------r-----r-----r-----+ 0.6
300 600 900
time(sec)
1200 1500 1800
Fig.7 Experimental and predicted total extract and solvent
penetration increase during direct and reactive extraction of
radix samples
0.15,----------------------.. 1.7
0.125
§'
g 0.1
~ I 0,075
'd 0.05
2
0.025
• •
-........----o------1:>-------4 1.6 i
direct extraction with CH 3 OH 1.5 ~ ;g
--l..,_.,o.-o-----c:r-----o-------0 ~ '0
1.4 i i
e'""'
i!
1.3 8.
+----.----r---.---~--..,.----+ 1.2
300 600 900 1200 1500 lSOO
time (sec)
Fig.8 Experimental and predicted total extract and solvent
penetration increase during direct and reactive extraction of
leaves samples
Results and Discussions
Kinetic experiments were carried out in a stirred batch
reactor, at 25 °C, under the following conditions:
hyrdomodulus 1]=0.09 m3 kg"1, particles mean size
R;=0.5 10-3 m, extraction time tma.x===:3600 s for radix
samples and tmax= 1800 s for leaves. Rotation speed of 4
revolutions s"1 assures internal diffusion-controlling
process under inert conditions. Figs.5 and 6 show the
course of direct and reactive extraction of alkaloid
Ct=:f(t) obtained respectively from radix and from
leaves. The symbols are the experimental points, the
curves represent the best-fit simulation results.
It is evident that the extraction from leaves samples
is achieved more easily: the time of equilibration is 2
time smaller and the drawing out alkaloids is more
complete: 87% degree of recovery with 72% from the
radix. The effect of chemical reaction depicts an
identical trend for the two raw materials: shift to
sigmoidal extraction~time behaviour characterized by
decline of the extraction rate in the early stage of the
process, followed by steep increase. The total amount of
crude alkaloids gained with chemical reaction is slightly
increased. The facts prove that some alkaloids are not
originally in salt form, and these bounded in other forms
are extracted by chemical reaction.
For the different methods of extraction the amounts
of the total extract may be varying because of the
different dissolving activities. The experimental data for
the total extract per unit mass of solid m*exr=fit) thus
100
Table I Fitted values for model parameters in case of constant or varying porosity
Plant radix samples Plant leaves samples
reactive extraction direct extraction reactive extraction direct extraction
eu-f(rJ En-canst ep-{(y)
kn I02 s"1 1.89 1.16
Deff,lOiomzs-1 1.32 0.78 1.45
a(Eq.l7) 2.6 2.3
Th 4.6-3.6 4.72
obtained is shown by the points in Figs.7 and 8. The
following empirical relationships were deduced:
m;xt == 0.148 -0.139exp-o.006SSt (28)
(from radix with methanol)
m * = 0.0669- 0.0586exp -o.o07251 (29) ....
(from radix with chloroform)
* 0 1 06 94 --O.OOSJt m.x~ = . -0. exp
(from leaves with methanol)
m:x~ = 0.0764-0.0631exp-o.oos441
(from leaves with chloroform)
(30)
(31)
A steep increase in the amount of total extract is
recorded in the early stage of the process. The same
figures represent the comparison between measured (by
points) and predicted values (continuous lines) of the
volume of the solvent impregnated the solid. The
experimental observations confirm that the solvent
continuously penetrates in the solid during extraction.
The higher the initial porosity, the great~r the initially
penetrated solvent volume, but its relative increase
during extraction is lower. For direct extraction from
radix~ the methanol penetrated in the solid increases
from 0.767 to 0.901 mllg solid that represents porosity
increases between 0.4-0.56. With the increasing
penetrated volume from 1.52 to 1.64 m1/g solid for
leaves. the porosity is increased only from 0.6 to 0.65.
Lower porosity variation was recorded during treatment
with chloroform: in the range £p=0.39-0.47 for radix and
Ep =0.6~0.63 for leaves.
The experimental data for the kinetics of solvent
penetration is very near to the predicted from the
particle volume balance. Thust although the
experimental data is not sufficiently detailed, it seems
that the presented approach is able to determine
approximately the range of the porosity increase.
The above experimental procedure forms the basis
for the estimation of the kinetic parameters (Table 1 }.
To highlight the possible effects of porosity increase.
the values of the adjustable parameters, obtained by the
varying porosity model reported here (Ep =:f(f))~ are
compared with the values obtained in constant porosity
model (£p=Ep. 0). The following conclusions can be
made:
?p-const ?p=f(y) Ev=const ev=fiy) ?p=const
1.46 1.76
2.89 8.46 7.15 8.62 9.22
0.9 1.1
1.3-1.2 1.43
- The values of the reaction rate constant kr are almost
identical and remain independent from the solid
phase structure. During extraction from radix, or
from leaves, the transition from diffusional to mixed
diffusion-reaction regime is registered.
- For the same raw material the values of Deff for
reacting system were predicted to be smaller than
those for inert system using constant porosity model.
In order to predict the same rate of extraction at a
lower porosity, in diffusion-controlling regime an
increased D eff has to be used in the constant porosity
model. In contrast, in a mixed diffusion-reaction
regime, an apparently lower Deff will be calculated.
When the varying porosity model is used, identified
diffusion coefficients using polar or non-polar
solvent are similar. This result seems to be more
realistic, since the two solvents have approximately
the same viscosity and the solute concentrations are ·
in the same order of magnitude.
- In case of direct, or reactive extraction, the
diffusivity D 4f in the porous particles from leaves
are higher than those from radix - the factor between
the coefficients is in the range 7-8. The larger Deff
suggests lower tortuousity factor and more regular
pore structure of the leaves samples.
The identified values of the adjustable numerical
constant a in Eq.( 17) show much larger increase in Deff
in case of lower initial porosity. It is obvious that liquid
penetration affects also the interconnectivity of the
pores and the tortuosity factor is decreased. Appreciable
differences in the effective diffusivity were obtained,
considering or not porosity increase, for the kinetic
behavior of radix samples where porosity increase is
greater than 20%. The major deviation of about 200% in
the effective diffusivity was obtained for direct
extraction from radix when the total extract remove
reached 15%.
For the examined solid-liquid system dimension
increase and swelling of the porous particles is not
observed and the penetrated solvent volume remains
relatively low. The resorted differences in D~ffas a result
of the porosity increase remain lower in respect to the
strong influence of the initial pore structure.
Conclusion
A dynamic model with variable transport properties is
presented to predict the kint:dc behaviour during direct
or reactive extraction from vegetable material. Starting
point is the experimentally recorded kinetics of solvent
penetration and total extract release. The variation of the
porosity with the total extract release is taken into
account. An exponential increase in the effective
diffusivity with the evolution of the fraction extracted is
considered.
To exploit the model suitability, the extractibility of
alkaloids from the medicinal plant Atropa belladonna
has been reported. Different kinetics of extraction of
alkaloids was obtained for the different parts of the
plant using different method for valuable compound
liberation. Using chemical reaction the equilibration
delays about 2 times in re3pect to the direct dissolution,
without sensible increase in the recovery degree. Using
ethanol, or chloroform as solvent under direct or
reactive reaction the estimated values for the effective
diffusivities are independent of the method of
dissolution, but they depend very strongly on the initial
structure of the pore space. The values of effective
diffusion calculated at 25 oc varies in the range
1.32 10-10 m2 s-1 for radix to 8.62 10-10 m2 s-1 for leaves.
The resorted differences in the kinetic behaviour
show that it may be advantageous to characterize porous
media changes directly by measuring the kinetics of
solvent penetration. While the commonly used
techniques of pore space determination, as mercury
porosimetry or B .E. T. gas adsorption allows
investigation only of dry material, the experimental
kinetics of liquid impregnation provides direct
information about swelling properties of the solvent and
eventual structural changes with advancement of the
extraction. The presented approach can be extended to
include the particle dimension changes when
considerable swelling is observed and the resorted
effects are more obvious.
C*
Deff
DeJJ.o
D*
SYMBOLS
specific external area, m2 m-3
Biot number (=kmR/ DeJJ,o)
solute concentration in bulk liquid phase,
kgm-3
solute concentration in pores of particle,
kgm-3
volume-averaged concentration in solid phase,
kgm-3
transformable compound concentration in solid
phase, kg m-3
dimensionless concentrations
effective diffusivity. m2 s·1
effective diffusivity at initial porosity, m2 s-1
factor for effective diffusivity increase ( =Deff I
Deff,O)
chemical reaction rate constant, s-1
external mass transfer coefficient, m s·1
initial mass of solid phase. kg
mass of inert compounds in the solid phase, kg
mass of extracted compounds, kg
mass of extracted compounds per unit of dried
solid, kg kg-1
101
mst common mass of solid phase, impregnated with
solvent, kg
mss mass of solid phase after removing solvent
excess, kg
r radial coordinate, m
Rv volume reaction rate, kg m-3 s-1
Rs particle radius, m
Th Thiele-type modulus ( ==Rs "vf 1-Ep)k/D eff)
Xo initial mass fraction of extractable compounds,
kg kg"1
Vexr extractable compounds volume, m3
· Vin inert compounds volume, m3
v[ liquid phase volume, m3
V,s solvent volume in the solid phase pores, m3
Vs solid phase apparent volume, m3
vr solvent radial velocity in the pores, m s-1
Greek Letters
a empirical constant defined by Eq.( 17)
f3 phase ratio ( = V /Vz)
r fraction of unextracted compounds
Ep porosity of the particle
Ep,o initial porosity of the particle
tp relative coordinate
A. wavelenght, nm
1] hydromodulus (=Vz/m0 ), m
3 kg-1
r dimensionless time(= Deff,otiR/)
REFERENCES
1. MINKOV S., MINTCHEV A. and PAEV K.: J. of Food
Engineering, 1996,29, 107-113
2. GOTO M., SMITH J. M. and MCCOY B. J.: Chern.
Eng. Sci., 1990, 45 (2), 443-448
3. RAMACHANDRAN P. A. and SMITH J. M.: Chern.
Eng. J., 1977, 14, 137-146
4. FAN L. S., MIYANAMI K. and FAN L. T.: Chern.
Eng. J., 1977, 11, 13-20
5. HPOLLEWAND M. P. and GLADDEN L. F: Chern.
Eng. Sci., 1992,47 (7), 1761-1770
6. MARMUR A. and COHEN R.: J. of Colloid and
Interface science, 1997, 189,299-304
7. SEIKOVA I., GUIRAUD P. and MINTCHEV A.:
Comptes rendues de l' Academie Bulgare des
Sciences, 2000, 53(3), 55-58
8. TRIDAY J. and SMITH J.. M.: AICh J., 1988, 34 (4),
658--668
9. HINZ Th. and EGGERS R.: Nabrung, 1996, 40 (3),
116-124
10. SATIERFIED C. N.: Heterogeneous Catalysis in
Practice, McGraw-Hall, New York, p.87~119, 1980
11. McGREAVY C., ANDRADE J. S. and RAJAGOPAL K.:
Chern. Eng. Sci. 1992, 47 (9·11), 2751.-2756
12. SOKOLOV A. V. and POPOV D. M.: Farmatsiya
{Moscow), 1989, 38 (6); 62-65
13. GRJSHINA M.S., DYUKOVA V. V .• KOVALENKO L.
I. and POPOV D. M.: Khim.·Farmatsiya Zh.
(Moscow), 1985, 19 (9) .1102wll05
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