МАТЕМАТИЧНА МОДЕЛЬ ДИНАМІКИ ДВОХКАМЕРНОГО ЕЛЕКТРОЛІЗЕРА ДЛЯ ВИВЧЕННЯВЛАСТИВОСТЕЙ ІОНООБМІННИХ МЕМБРАН НА ОСНОВІ ПРОТОННИХ ІОННИХ РІДИН
A mathematical model of mass transfer processes in the electrolysis of one-component solutions of 1,1 symmetric strong electrolytes NaOH and NaCl in a two-chamber electrochemical reactor with mesh electrodes based on platinum titanium is formulated. Experimental modeling of processes is performed wa...
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| Дата: | 2022 |
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| Мова: | Англійська |
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V.I.Vernadsky Institute of General and Inorganic Chemistry
2022
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Репозитарії
Ukrainian Chemistry Journal| _version_ | 1871465800824520704 |
|---|---|
| author | Koshel, Mykola Koshel, Serhii Polishchuk, Yulia |
| author_facet | Koshel, Mykola Koshel, Serhii Polishchuk, Yulia |
| author_institution_txt_mv | [
{
"author": "Mykola Koshel",
"institution": "Ukrainian State University of Chemical Technology"
},
{
"author": "Serhii Koshel",
"institution": "Ukrainian State University of Chemical Technology"
},
{
"author": "Yulia Polishchuk",
"institution": "Ukrainian State University of Chemical Technology"
}
] |
| author_sort | Koshel, Mykola |
| baseUrl_str | https://ucj.org.ua/index.php/journal/oai |
| collection | OJS |
| datestamp_date | 2026-07-22T08:23:48Z |
| description | A mathematical model of mass transfer processes in the electrolysis of one-component solutions of 1,1 symmetric strong electrolytes NaOH and NaCl in a two-chamber electrochemical reactor with mesh electrodes based on platinum titanium is formulated. Experimental modeling of processes is performed was carried out under conditions of continuous precise monitoring of the system (NaOH concentration and volume of solution in the chambers).The electrolysis system was designed to balance the flow of components through the membrane to study its properties and to determine five unknown parameters of mathematical modeling of the process. The mathematical model is a system of equations, which includes the unknown transfer numbers of counterions through the membrane, the electrolyte diffusion coefficient, the electroosmotic flux constant, and the empirical parameters of the approximating expressions. |
| doi_str_mv | 10.33609/2708-129X.88.02.2022.131-137 |
| first_indexed | 2025-09-24T17:43:43Z |
| format | Article |
| fulltext |
Фізична хімія
ISSN 2708-129X. УКР. ХІМ. ЖУРН., 2022, т. 88, No 2 131
UDC 519.6/544.6 +665.9 doi: https://doi.org/10.33609/2708-129X.88.02.2022.131-137
MATHEMATICAL MODEL OF TWO-CHAMBER ELECTROLYSER DYNAMICS FOR
STUDYING PROPERTIES OF ION EXCHANGE MEMBRANES BASED ON PROTON
IONIC LIQUIDS
M.D. Koshel
1*
, S.A. Koshel
1
, Y.V. Polishchuk
1
1
Ukrainian State University of Chemical Technology, Haharina Ave, 8, Dnipro, Ukraine, 49000
*email: kkknd@ua.fm
A mathematical model of mass transfer processes in the electrolysis of one-component solutions
of 1,1 symmetric strong electrolytes NaOH and NaCl in a two-chamber electrochemical reactor
with mesh electrodes based on platinum titanium is formulated. Experimental modeling of
processes is performed was carried out under conditions of continuous precise monitoring of the
system (NaOH concentration and volume of solution in the chambers).The electrolysis system
was designed to balance the flow of components through the membrane to study its properties
and to determine five unknown parameters of mathematical modeling of the process. The
mathematical model is a system of equations, which includes the unknown transfer numbers of
counterions through the membrane, the electrolyte diffusion coefficient, the electroosmotic flux
constant, and the empirical parameters of the approximating expressions.
Keywords: electrolysis, mathematical model, ion exchange membrane, transfer number,
electroosmosis, diffusion.
INTRODUCTION. Ionic liquids are
organic substances, mainly salts, which exist in
liquid-phase form over a wide range of
temperatures. Their characteristic properties are
ionic electrical conductivity and low melting
point, which in most cases does not exceed
100
o
C. We studied some Proton Ionic Liquids
(PIL) based on ammonium oligoesters -
chemical compounds with organic cations and
inorganic anions (residues of sulfuric,
orthophosphate and acetic acids), which were
synthesized by neutralization of organic acids
and inorganic bases[1]. The high interest in
ionic liquids for ion exchange is due to the fact,
that they have a clear ability to serve as
effective cation exchange membranes with high
selectivity.Due to such properties, the aim of
many experiments with water-soluble ionic
liquids has always been to measure their
individual physicochemical properties (specific
conductivity (), concentration of protons (pH),
and their dependence on concentration and
temperature).Thus, using the known laws of
physicochemical processes (theory of electrical
conductivity and electrolytic dissociation) it is
possible to establish the parameters of the
charge transfer process and the role of
individual ions in the mechanism of electrical
conductivity. The analysis of the revealed
regularities made it possible to reveal
correlations between the possible structure of
ionic liquids and the physicochemical properties
of their aqueous solutions.
Another way to study ion-exchange
properties of electrochemical systems with PIL
membranes is mathematical modeling.In [1] the
method of computerresistometry [2] was used.
The probability of the existence of dynamic
processes far from equilibrium was also
experimentally assessed. On the basis of
mailto:kkknd@ua.fm
Mathematical model of two-chamber electrolyser dynamics…
132 ISSN 2708-129X. УКР. ХІМ. ЖУРН., 2022, т. 88, No 2
Fig.1. Principled scheme of the cathode chamber (a), two-chamberelectrolyzer-reactor (b) work, and a photo
of there actor.
complex measurement results, correlations were
established between the physicochemical
properties of the studied aqueous-organic
mixtures and the estimated possible parameters
of the structure of organic components.
The aim of this study was to build a
mathematical model of processes in a two-
chamber reactor-electrolyzer using in
experiments known types of industrial cation
exchange (МФ-4СК, МА-40) membranes and
anion exchange membrane MA-40.
EXPERIMENT AND DISCUSSION
OF THE RESULTS. The experiment was
performed in a two-chamber electrolyzer-
reactor for electrolysis of theNaOH solutions
with initial concentration of 0,004 mol/dm
3
(fig.
1).Heterogeneous membranes of the MK and
MA-40 series were used in the experiment.The
calculations base on the following items.
The migratory flux of ОН
–
ions gOH
M
and
the molar flux of Na
+
ions equal to it are
proportional to the charge flow I (Аmin) and
the number of n
+
cation transfers according to
equation:
1
( ) .
26,8
Mg
OH
n = I (1)
Diffusion flow is carried out through the
membrane according:
, D
NaOH
dC
dx
g = -D (2)
D –the effective diffusion coefficient of NaOH,
– the membrane thickness, dC/dx = dC/δ – the
gradient of NaOH concentration in the
membrane. The concentration of C in (2) has a
dimension of mol / cm
3
.
The water is consumed in the electrochemical
reaction at the cathode chamber (Fig. 1 a, b),
and the speed of this process can be accurately
calculated according to Faraday's law.
2 0,891 , R
H O g = I (3)
0,891 - water flow rate, g/minute (respectively
0,0495 mol/minute).
In parallel, a rather significant
electroosmotic flow of water molecules
(according to [3] to 5.1 molecules of water per
mobile cation) is carried out through the
membrane according to the equation:
1
42
281 8,12 10
.
4 3,14 8,9 10
OSM
H Og
dE I
dx
(4)
M.D. Koshel, S.A. Koshel, Y.V. Polishchuk
ISSN 2708-129X. УКР. ХІМ. ЖУРН., 2022, т. 88, No 2 133
= 818,1210
–12
- dielectric constant of water;
– zeta-potential, B; – dynamic viscosity of
the electrolyte, Pa·s; dE/dx= (I/(δ)- potential
gradient in the electrolyte, V/cm; I– current,
Ahm;-specific electrical conductivity of the
electrolyte, ℧*cm; δ– membrane thickness, cm.
The equation (4) is inconvenient for use in
a mathematical model because it contains an
inaccurate value of the zeta potential (). In
addition, the value of δ in the denominator
means that as the membrane thickness increases,
the electroosmotic flux must decrease. In
reality, the rate of electroosmotic flux is a
constant value that is proportional to the current
and does not depend on the thickness of the
membrane. Therefore, the mathematical model
uses a more reliable and simpler equation,
which includes only one unknown parameter
k
OSM
current values (mol/(Ahm·min) - the flow
of gН2О
ОSМ
at a current value of 1 A):
.
2
OSMOSMg k I
H O
= (5)
The water plays a unique role in all
physicochemical processes that take place in the
environment and especially in the biosphere [4],
so in this study, the features of its movement
through membranes, especially electroosmosis,
are decisive. Electroosmotic water flow is an
individual sensitive characteristic of membranes
used in various technologies: on composite
membranes in the purification of glycerol [5], in
the purification by a combination of
electrodialysis and ion exchange of electroplates
from nickel [6] and etc. It can be assumed that
even without the action of an electric field in the
filtration process, the effects of water transfer
due to osmotic phenomena (on organo-inorganic
membranes [7]) may occur.
The summary mass flow of ions
(gSUM)across the membrane of all components
depends on the electrolysis conditions, so it is
an unknown parameter to be determined.
Thus, the mathematical model of the
process of electrolysis of NaOH solution is a
system of 5 equations with specified values of
the mode parameters (current, initial NaOH
concentration, membrane thickness, initial
conductivity parameters) and five unknown
parameters. The mathematical model uses
equations that approximate the concentration
dependences of the electrolyte in the region C>>
0.02 mol/dm
3
parabolas of the 2nd and 3rd
degree. One exponential equation was used to
approximate nonlinear concentration
dependences of electrical conductivity f(C)in
the region up to 1mol/dm
3
:
0 0 1 ,( )MAX
E
C
exp
F
(6)
FE is the characteristic parameter of the function
f(C) at the points with the initial and
maximum values of the concentration in the
interval of the experiment duration of 30
minutes.
Formally, the mathematical model can be
visualized in matrix form Z = X Y
2
2
0
M
OH
D
NaOH
R
H O
OSM
H O
MAX
E
g
g
g
g
F
=
/ 26,8
/
0,871
1
1
1
OSM
I n
D dC dx
I
k I
2
2
M
NaOH
R
H O
DIF
NaOH
OSM
H O
SUM
g
g
g
g
g
However, the matrix form of the mathematical
model is inconvenient for practical use, because
the third column has a structure that the number
of elements and their physical content does not
agree with the first two columns. Therefore, the
main results of data processing of the
experiment (column 3) were recorded in the
form of table 1.
Mathematical model of two-chamber electrolyser dynamics…
134 ISSN 2708-129X. УКР. ХІМ. ЖУРН., 2022, т. 88, No 2
Table 1
Calculated unknown parameters of the experiment performed on the example of the membrane МF-4SКin
the electrolyte NaOH (mol/min)
gNaOH
М
gH2O
R
gNaOH
DIF
gH2O
OSM
gSUM
0,000274 0,008259 -2,5810
–8
0,004230 0,012763
Other conditions for which the experiment was
performed are listed below in tables 2 and 3.
Processing of experimental data (tables 2 and 3)
on the mathematical model was carried out by
numerical iterative method. The numerical
values of the unknowns were successively
changed (Table 1) and the accuracy of the result
was controlled by the least squares algorithm at
each step. The procedure was performed until
the values of the randomly selected unknowns
thus did not coincide with the specified
accuracy with their values obtained in the
experiment (table 1).
The graphs in Figures 2,3 - illustrate the
dynamics of the time change of the electrolyte
concentration with the initial value shown in
table 2.
Table 2
Arbitrarily set process parameters in the cell at the
beginning of the experiment. Membrane МФ-4СК,
electrolyte –NaOH
I, Ahm , ℧*cm δ, сm C, mol/dm
3
0,0091764 0,0017 0,02 0,0038
Table 3
Intermediate (calculated) process parameters in the
electrolyzer
n+ FE, сm W1 W2
0,8 15 0,00002 125
**W1,W2 are parameters dimensionless for
adjustment
Visually, the degree of accuracy can be seen by
reconciling the calculated (approximated)
graphs with the experimental data in Figures 2
and 3.
Fig. 2. 1 –experiment, 2– approximation along the
trend line (parabola of the 2nd order,), 3 –
construction (according to the approximation
formula) of the parabola at points with an interval of
1 minute
Fig. 3. 1- experimental data for the membrane МF-
4SК in NaOH solution, 2 –approximation of the
graph of the total mass flow of all components of
g
SUM
(equation 1÷ 5)
The common result of the experiment is
the dependence С=f() in the interval of 30
minutes. All other parameters (R, Co…) are the
primary intermediate data from which the final
Mathematical model of two-chamber electrolyser dynamics…
ISSN 2708-129X. УКР. ХІМ. ЖУРН., 2022, т. 88, No 2 135
result is formed. In fig. 2 and 3 show the results
of the experiment on the membrane МФ-4СКin
NaOH solution with an initial concentration of
0,004 mol/dm
3
.
Forms of graphs in Fig. 2 and 3 do not
exactly coincide with each other, because only 5
unknown parameters are used in the
calculations, shown in Table 1. If we introduce
additional elements into the mathematical
model, it would be possible to achieve greater
consistency in the form of graphs. But this is not
necessary, because for comparison only the
qualitative similarity of the form of graphs in
Figures 2 and 3, built on the same scale (here
0.006 mol / dm
3
× 30 minutes) is important. This
similarity is the basis for concluding that the
values of the unknown parameters of the studied
membrane (table 1) are determined correctly.
Modification of membranes in different
ways [8] allows changing their individual
properties in a wide range. This is the main
purpose of the modification, and a mathematical
model is only a convenient tool for identifying
and analyzing these changes.
From table 1 you can see what role in the
mass balance play for given conditions, the
different mechanisms of transfer of components.
In this case, the migratory and diffusion flows
of NaOH have little effect on the total balance
(0,000274 -2,5810
–8
)/ 0,012763, which is about
2%. At the same time, the water flow rate in the
reaction (0,008259) and the electroosmotic flux
(0,004230) mol / minute are proportional to the
total flow (0,012763) mol / minute.
Thus, choosing the desired conditions, the
mathematical model shows the appropriate
package of balance flows for comparative
analysis.
Note that studies in NaCl solutions are
possible only on membranes resistant to
dissolved chlorine, even at low current
densities. Heterogeneous membranes of the MK
and MA-40 series satisfy this condition.
Also note that the function С() represents
the effect of changing the electrolyte
concentration in the cathode chamber for a
particular membrane (fig 4, eq.7).
0
2 1 .
C C
n
C
(7)
Fig.4. Time change of the anion transfer number
calculated by equation 7. 1-primary experimental
data, 2- calculation taking into account
electroosmosis. NaCl electrolyte, MA-40 membrane.
During the experiment, all changes in the
state of the system accumulate in the solution.
Therefore, the numbers of transfer calculated by
eq. (7), which gives the value of the resultas a
constant, always decreases overtime (fig. 4, eq.
8).
0
1 1 ,
(( ) / 26,8)
C C V
n
It
0
2 1 .
C C
n
C
(8)
The powerful factor is the electroosmosis of
water from the chamber (-) to the chamber (+).
The rate of electroosmotic water transfer was
found on the MA-40 membrane by the value of
the change in the volume V of the chambers (-)
and (+).
In general, formula (7) does not take into
account the volume of the chambers and is
unsuitable for taking into account the transfer of
water by electroosmosis. But due to the fact that
Mathematical model of two-chamber electrolyser dynamics…
136 ISSN 2708-129X. УКР. ХІМ. ЖУРН., 2022, т. 88, No 2
the water transfer effect still exists (regardless
of the formula), a formal approach was used to
take it into account. According to the results of
the experiment, 6 cm
3
were transferred in 90
minutes with a constant current drop from 18 to
3 mA, and the charge lasted only 0,012 Ahm h.
Hence the electroosmotic effect can be
estimated as:
=0,006 dm
3
/0,012 Ahm h= 0,5 дм
3
/ Ahm h.
It is clear that the obtained number is
random, because in each measurement it
strongly depends on the specific conditions of
the experiment, such as the history of membrane
swelling, as well as parameters that change
continuously during the experiment (electrolyte
concentration, current, instantaneous values of
effective electrolyte diffusion coefficient, and
etc.). Equation 9 was formed on the basis of the
data of the exact experiment with the MA-40
membrane.
V= Vo-*(I) (9)
This is generally a formal expression for
the volume of the cathode chamber at some
point in time , where (I ) is a continuously
increasing amount of missed charge.
Equation (9) was used to calculate the
number of anion transfer across the MA-40
membrane (Fig. 4). From the result it can be
seen that the consideration of electroosmosis
gives a significant refinement of the calculation.
The calculated average value of the number of
chloride ion transfer increased from 0.76 to
0.96. But some slight slope (Figure 2) still
exists. This means that in the process of
electrolysis with the MA-40 membrane, the
action of unknown factors not taken into
account by the mathematical model is observed.
CONCLUSIONS. A mathematical model
of processes in a two-chamber electrolyzer
reactor for electrolysis of solutions of pure one-
component electrolytes NaOH and NaCl has
been created. The mathematical model contains
a system of mass balance equations with five
unknown parameters to be determined and
reflect the dynamics of changes in instantaneous
values of unknown mass flows of components.
Experimental studies of the transfer
processes of system components (mass balance)
in a two-chamber electrolyzer with platinum-
plated titanium electrodes have illustrated the
high accuracy and reproducibility of the results
of measuring the transfer numbers in ion
exchange membranes.
The complete correspondence between the
experimental data and the result of their
mathematical modeling is shown.
Data processing of a simple experiment in
a two-chamber electrolyzer with the use of a
mathematical model makes it possible to
accurately determine the properties of
membranes. It is a convenient tool for studying
and comparing water-soluble ion exchangers in
order to optimize their technologies.
ACKNOWLEDGEMENT. The work was
done under the state support according to the
theme "Polymer nanocomposites based on
organo-modified layered silicates and polymer
matrices of different nature", № state
registration 0121U109623, 2021-2022.
МАТЕМАТИЧНА МОДЕЛЬ ДИНАМІКИ
ДВОКАМЕРНОГО ЕЛЕКТРОЛІЗЕРА
ДЛЯ ВИВЧЕННЯ ВЛАСТИВОСТЕЙ
ІОНООБМІННИХ МЕМБРАН НА
ОСНОВІ ПРОТОННИХ ІОННИХ РІДИН
М. Д. Кошель
1
, С. А. Кошель
1
, Ю. В.
Поліщук
1
1
Український державний хіміко-
технологічний університет, м. Дніпро, просп.
Гагаріна, 8, Україна, 49000
*email: kkknd@ua.fm
https://uk.wikipedia.org/wiki/%D0%94%D0%BD%D1%96%D0%BF%D1%80%D0%BE_(%D0%BC%D1%96%D1%81%D1%82%D0%BE)
https://uk.wikipedia.org/wiki/%D0%9F%D1%80%D0%BE%D1%81%D0%BF%D0%B5%D0%BA%D1%82_%D0%93%D0%B0%D0%B3%D0%B0%D1%80%D1%96%D0%BD%D0%B0_(%D0%94%D0%BD%D1%96%D0%BF%D1%80%D0%BE)
https://uk.wikipedia.org/wiki/%D0%9F%D1%80%D0%BE%D1%81%D0%BF%D0%B5%D0%BA%D1%82_%D0%93%D0%B0%D0%B3%D0%B0%D1%80%D1%96%D0%BD%D0%B0_(%D0%94%D0%BD%D1%96%D0%BF%D1%80%D0%BE)
https://uk.wikipedia.org/wiki/%D0%9F%D1%80%D0%BE%D1%81%D0%BF%D0%B5%D0%BA%D1%82_%D0%93%D0%B0%D0%B3%D0%B0%D1%80%D1%96%D0%BD%D0%B0_(%D0%94%D0%BD%D1%96%D0%BF%D1%80%D0%BE)
https://uk.wikipedia.org/wiki/%D0%9F%D1%80%D0%BE%D1%81%D0%BF%D0%B5%D0%BA%D1%82_%D0%93%D0%B0%D0%B3%D0%B0%D1%80%D1%96%D0%BD%D0%B0_(%D0%94%D0%BD%D1%96%D0%BF%D1%80%D0%BE)
https://uk.wikipedia.org/wiki/%D0%9F%D1%80%D0%BE%D1%81%D0%BF%D0%B5%D0%BA%D1%82_%D0%93%D0%B0%D0%B3%D0%B0%D1%80%D1%96%D0%BD%D0%B0_(%D0%94%D0%BD%D1%96%D0%BF%D1%80%D0%BE)
https://uk.wikipedia.org/wiki/%D0%9F%D1%80%D0%BE%D1%81%D0%BF%D0%B5%D0%BA%D1%82_%D0%93%D0%B0%D0%B3%D0%B0%D1%80%D1%96%D0%BD%D0%B0_(%D0%94%D0%BD%D1%96%D0%BF%D1%80%D0%BE)
mailto:kkknd@ua.fm
M.D. Koshel, S.A. Koshel, Y.V. Polishchuk
ISSN 2708-129X. УКР. ХІМ. ЖУРН., 2022, т. 88, No 2 137
Сформульовано математичну модель
процесів масообміну в процесі електролізу
однокомпонентних розчинів простих
сильних електролітів NaOH та NaCl у
двокамерному електрохімічному реакторі з
сітчастими електродами на основі
платинованого титану. Виконано
експериментальне моделювання процесів.
Електроліз здійснюється за умов
безперервного точного контролю стану
системи (концентрації NaOH та об′єму
розчину в камерах). Систему електролізу
призначено для встановлення балансу
потоків перенесення компонентів через
мембрану, властивості якої вивчають, і
визначенням 5 невідомих параметрів
математичного моделювання процесу.
Математична модель є системою рівнянь, до
якої входять невідоме число перенесення
протиіону у мембрані, коефіцієнт дифузії
електроліту, константа електроосмотичного
потоку та емпіричні параметри
апроксимуючих виразів.
Ключові слова: електроліз, математична
модель, іонообмінна мембрана, число
перенесення, електроосмос, дифузія.
REFERENCES
1. Koshel N.D., Koshel S.A.,
Sverdlikovskaya O.S., Chervakov O.V.
Equilibrium States in Aqueous Solutions of
Some Ionic Liquids. Surface Engineering and
Applied Electrochemistry. 2021. 57(1): 88–100.
2. KoshelN.D., SmyrnovaO.V.,
KostyryaM.V. The study of ion exchange
kinetics on the anionite in weak electric fields .
8-th internfcional conference on Materials
Science & Condensed Matter Physics.
September 12 - 16, 2016 - Chisinau, Moldova.
Abtracts p.133
3. OsetrovaN.V., SkundinA.M.Heat-
resistant membranes for fuel cells.
Electrochemical energy. 2007. 7(1): 3–16 (in
Russian)
4. GoncharukV., ArkhipchukV.
Demineralized water and vital activity of
organisms.Vestnik NAN Ukrainy. 2002. 9. 45–
48. (in Russian)
5. Dzyazko Y.S., Rozhdestvenska L.M.,
Vasilyuk S.L., Kudelko K.O., Belyakov V.N.
Composite membranes containing nanoparticles
of inorganic ion exchangers for electrodialytic
desalination of glycerol. Nanoscale research
letters. 2017. 12(1): 1–9.
6. Dzyazko Yu. S. Purification of a diluted
nickel solution containing nickel by a process
combining ion exchange and electrodialysis.
Desalination. 2004. 162: 179–189.
7. Myronchuk V.G., Dzyazko Y.S.,
Zmievskii Y.G., Ukrainets A.I., Bildukevich
A.V. Organic-inorganic membranes for
filtration of corn distillery. Acta periodica
technologica. 2016. 47: 153–165.
8. DzyazkoY., RozhdestveskayaL.,
ZmievskiiY., VolfkovichY., SosenkinV.
Heterogeneous membranes modified with
nanoparticles of inorganic ion-exchangers for
whey demineralization. Materials Today:
Proceedings. 2015. 2(6): 3864–3873.
Стаття надійшла 15.02.2022
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| id | oai:ojs2.1444248.nisspano.web.hosting-test.net:article-409 |
| institution | Ukrainian Chemistry Journal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-07-23T01:07:48Z |
| publishDate | 2022 |
| publisher | V.I.Vernadsky Institute of General and Inorganic Chemistry |
| record_format | ojs |
| resource_txt_mv | ucjorgua/a4/a8fa8a279b2eea650e3812ee13834da4.pdf |
| spelling | oai:ojs2.1444248.nisspano.web.hosting-test.net:article-4092026-07-22T08:23:48Z MATHEMATICAL MODEL OF TWO-CHAMBER ELECTROLYSER DYNAMICS FOR STUDYING PROPERTIES OF ION EXCHANGE MEMBRANES BASED ON PROTON IONIC LIQUIDS МАТЕМАТИЧНА МОДЕЛЬ ДИНАМІКИ ДВОХКАМЕРНОГО ЕЛЕКТРОЛІЗЕРА ДЛЯ ВИВЧЕННЯВЛАСТИВОСТЕЙ ІОНООБМІННИХ МЕМБРАН НА ОСНОВІ ПРОТОННИХ ІОННИХ РІДИН Koshel, Mykola Koshel, Serhii Polishchuk, Yulia electrolysis, mathematical model, ion exchange membrane, transfer number, electroosmosis, diffusion. A mathematical model of mass transfer processes in the electrolysis of one-component solutions of 1,1 symmetric strong electrolytes NaOH and NaCl in a two-chamber electrochemical reactor with mesh electrodes based on platinum titanium is formulated. Experimental modeling of processes is performed was carried out under conditions of continuous precise monitoring of the system (NaOH concentration and volume of solution in the chambers).The electrolysis system was designed to balance the flow of components through the membrane to study its properties and to determine five unknown parameters of mathematical modeling of the process. The mathematical model is a system of equations, which includes the unknown transfer numbers of counterions through the membrane, the electrolyte diffusion coefficient, the electroosmotic flux constant, and the empirical parameters of the approximating expressions. V.I.Vernadsky Institute of General and Inorganic Chemistry 2022-03-25 Article Article Physical chemistry Физическая xимия Фізична xімія application/pdf https://ucj.org.ua/index.php/journal/article/view/409 10.33609/2708-129X.88.02.2022.131-137 Ukrainian Chemistry Journal; Vol. 88 No. 2 (2022): Ukrainian Chemistry Journal; 131-137 Украинский химический журнал; ##issue.vol## 88 ##issue.no## 2 (2022): Ukrainian Chemistry Journal; 131-137 Український хімічний журнал; Том 88 № 2 (2022): Український хімічний журнал; 131-137 2708-129X 2708-1281 en https://ucj.org.ua/index.php/journal/article/view/409/215 Copyright (c) 2022 Mykola Koshel, Serhii Koshel, Yulia Polishchuk https://creativecommons.org/licenses/by-nc/4.0 |
| spellingShingle | Koshel, Mykola Koshel, Serhii Polishchuk, Yulia МАТЕМАТИЧНА МОДЕЛЬ ДИНАМІКИ ДВОХКАМЕРНОГО ЕЛЕКТРОЛІЗЕРА ДЛЯ ВИВЧЕННЯВЛАСТИВОСТЕЙ ІОНООБМІННИХ МЕМБРАН НА ОСНОВІ ПРОТОННИХ ІОННИХ РІДИН |
| title | МАТЕМАТИЧНА МОДЕЛЬ ДИНАМІКИ ДВОХКАМЕРНОГО ЕЛЕКТРОЛІЗЕРА ДЛЯ ВИВЧЕННЯВЛАСТИВОСТЕЙ ІОНООБМІННИХ МЕМБРАН НА ОСНОВІ ПРОТОННИХ ІОННИХ РІДИН |
| title_alt | MATHEMATICAL MODEL OF TWO-CHAMBER ELECTROLYSER DYNAMICS FOR STUDYING PROPERTIES OF ION EXCHANGE MEMBRANES BASED ON PROTON IONIC LIQUIDS |
| title_full | МАТЕМАТИЧНА МОДЕЛЬ ДИНАМІКИ ДВОХКАМЕРНОГО ЕЛЕКТРОЛІЗЕРА ДЛЯ ВИВЧЕННЯВЛАСТИВОСТЕЙ ІОНООБМІННИХ МЕМБРАН НА ОСНОВІ ПРОТОННИХ ІОННИХ РІДИН |
| title_fullStr | МАТЕМАТИЧНА МОДЕЛЬ ДИНАМІКИ ДВОХКАМЕРНОГО ЕЛЕКТРОЛІЗЕРА ДЛЯ ВИВЧЕННЯВЛАСТИВОСТЕЙ ІОНООБМІННИХ МЕМБРАН НА ОСНОВІ ПРОТОННИХ ІОННИХ РІДИН |
| title_full_unstemmed | МАТЕМАТИЧНА МОДЕЛЬ ДИНАМІКИ ДВОХКАМЕРНОГО ЕЛЕКТРОЛІЗЕРА ДЛЯ ВИВЧЕННЯВЛАСТИВОСТЕЙ ІОНООБМІННИХ МЕМБРАН НА ОСНОВІ ПРОТОННИХ ІОННИХ РІДИН |
| title_short | МАТЕМАТИЧНА МОДЕЛЬ ДИНАМІКИ ДВОХКАМЕРНОГО ЕЛЕКТРОЛІЗЕРА ДЛЯ ВИВЧЕННЯВЛАСТИВОСТЕЙ ІОНООБМІННИХ МЕМБРАН НА ОСНОВІ ПРОТОННИХ ІОННИХ РІДИН |
| title_sort | математична модель динаміки двохкамерного електролізера для вивченнявластивостей іонообмінних мембран на основі протонних іонних рідин |
| topic_facet | electrolysis mathematical model ion exchange membrane transfer number electroosmosis diffusion. |
| url | https://ucj.org.ua/index.php/journal/article/view/409 |
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