Name
Pismenskiy Alexander Vladimirovich
Scholastic degree
•
Academic rank
associated professor
Honorary rank
—
Organization, job position
Kuban State University
Web site url
—
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Articles count: 6
There is a 2D mathematical model of ion transport
binary salt with the main conjugate effects of
concentration polarization in the overlimiting current
mode: the bulk charge and the dissociation/
recombination of water, gravity and electroconvection
and Joule heating the solution in the form of a
boundary value problem for systems of differential
equations with partial derivatives in the article. This
system is presented in a form convenient for numerical
solution. We describe the necessary boundary
conditions. This article presents a theoretical study of
the interaction of forced, gravitational and
electroconvection, the dissociation / recombination of
water molecules, and Joule heating of the solution and
heat transport through membranes. We have
constructed a mathematical model of two-dimensional
non-stationary ion transport binary salt in a smooth
rectangular channel desalting electrodialysis device
using equations Nernst-Planck-Poisson, heat
conduction and Navier-Stokes equations and the
natural boundary conditions. For numerical solution
we use the finite element method, with the splitting of
task at each new time layer into three subtasks:
electrochemical, thermal conductivity, hydrodynamic.
Such approach to the development of numerical
methods is the original and can solve arising in
modeling boundary-value problems for a nonlinear system of partial differential equations
An analysis of the experimental data obtained by the
authors, as well as reference books, allowed to
hypothesize about the essential role of gravitational
convection in electromembrane systems with
ampholytes even in underlimiting current regimes. The
article is devoted to the development of the
mathematical model of ion transport in a flow
elecrtomembrane system during electrodialysis of
ampholyte-containing solutions with taking into
account a possible appearance of gravitational
convection, in particular, due to nonisothermal
protonation–deprotonation reactions of ampholytes.
The article presents the boundary value problem that is
the new mathematical model for diffusion, convection
and electromigration of four components of the
solution (ions of sodium, dihydrogen phosphate and
hydrogen, as well as molecules of orthophosphoric
acid) in a half of an electrodialysis desalination
channel, adjacent to an anion-exchange membrane. The membrane is considered as ideally selective and
homogeneous. The system of partial differential
equations, that is the base of the model, also includes
equations of Navier-Stokes, material balance,
convective heat conduction and the electroneutrality
condition. The system of equations is supplemented by
a number of natural and original boundary conditions.
A distinctive feature of this study is the absence of
assumptions about the equilibrium of chemical
reactions in a diffusion layer. The results of the study
can be used for the development of environmentally
rational and resource saving membrane technologies
for a processing of products of agro-industrial complex
This article is devoted to the asymptotic analysis of
boundary value problem for a system of equations of
Nernst-Planck and Poisson for a singularly perturbed
system of ordinary differential equations [1], based on
two parameters. This boundary value problem
simulates electrodiffusion of four kinds of ions at the
same time in the diffusion layer in electro-membrane
systems with perfectly selective membrane, taling into
consideration the reaction of recombination of two
ions. Meanwhile the other two ions represent ions of a
binary salt. As a simple example, we consider the
transport of ions sodium, chlorine, hydrogen and
hydroxide, moreover, hydrogen and hydroxyl ions
recombine in the diffusion layer. A more complex case
is the transfer of the products of dissociation of the
dihydrogen phosphate of sodium, namely, ions of
sodium and dihydrogen phosphate, the latter dissociate at the interface, in turn, hydrogen ions and hydrogen
phosphate. Thus, in the solution can simultaneously
store three different types of ions: sodium, hydrogen,
phosphate. During the transfer, hydrogen ions and ions
of hydrogen phosphate recombine to produce
phosphoric acid. The article has revealed the structure
of the Nernst diffusion layer at currents above
Harkatsa current. It is shown, that in the diffusion
layer, there are two types of boundary layers: the inner
(reaction) boundary layer and boundary layer at the
interface solution / membrane
The influence of dissociation / recombination of water
molecules is important for understanding
electroconvection processes, as some authors believe
that the emergence of new carriers + H and − OH , and
can lead to a reduction in the space-charge and,
consequently, to electroconvection disappearance.
However, as shown in [5], the dissociation of water
molecules, although it reduces the space charge and
increases the threshold fall potential jump at which
begins electroconvection, yet it persists and effectively
mixes the solution. This article is devoted to
mathematical modeling of electrodiffusion of four
types of ions at the same time (two salt ions as well as
+ H and − OH ions) in the diffusion layer in electromembrane
systems with perfectly selective membrane
under the joint influence of violation of electrical neutrality, and the reaction of dissociation /
recombination of water molecules, development of
mathematical models of these processes, building
efficient algorithms asymptotic and numerical analysis
for different types of electrolytes. The work proposes a
new mathematical model of the process of transfer of
salt ions in view of the space charge and the
dissociation / recombination of water in the form of a
boundary value problem for a system of ordinary
differential equations. This system is reduced to a form
convenient for numerical solution. We have calculated
the required additional boundary conditions for the
electric field. Numerical and asymptotic solution of the
boundary value problem and physico-chemical
analysis of the influence of dissociation /
recombination on the transfer of salt ions is expected
to devote the next part of the work
This article is a continuation of the previous works of
the authors [The influence of reaction dissociation /
recombination of molecules of water on transportation
of electrolyte 1:1 in the membrane systems in the
diffusion layer. Part 1. Mathematical model //
Scientific journal of Kuban State Agrarian University,
2016. No. 07(121) and The influence of the reaction of
dissociation / recombination of molecules of water on
transportation of electrolyte 1: 1 in membrane systems
in the diffusion layer. Part 2. Asymptotic analysis //
Scientific journal of Kuban State Agrarian University,
2016. – №08(122)] and devoted to assessing the
possibility of gravitational convection due to the
recombination of hydrogen and hydroxyl ions. The
article presents the solution of a boundary-value
problem, which is a mathematical model of
electrodiffusion for the four types of ions at the same
time (two ions of salts and hydrogen and hydroxyl
ions) in the diffusion layer in electro-membrane
systems with ideal selective membrane, with the heat
transfer equation and the Navier-Stokes equation. The
article shows the possibility of the emergence of
gravitational convection due to the exothermic reaction
of recombination of water molecules in the depth of
the solution. The article considered the reaction of
recombination of hydrogen ions and hydroxyl,
although the main results can be applied, after appropriate modifications, and to amfolit-containing
solutions, such as wine, juices, dairy products,
microbiological processing of biomass (amino acids,
anions of polybasic carboxylic acids), municipal
effluent (anions of phosphoric acid), etc.
In the article, we have suggested a general mathematical model of non-stationary and non-isothermal process of a binary electrolyte transfer in dilute solutions in an electro-membrane system (EMS), taking into account the joint action of gravitational convection, forced convection and electro convection in potential dynamic mode. This model is a boundary problem for a system of two-dimensional quasi-linear Navier-Stokes equation and Nernst-Planck-Poisson in partial derivatives equation. We have developed a theory of similarity of the process of heat and mass transfer in electro-membrane systems, specifically, in a desalting channel of electro dialysis apparatus, taking into account joint actions of concentration polarization, space charge, gravity convection, forced convection and electro convection. It is shown that the criterion of electro convection does not directly depend on the initial concentration, and, therefore, electro convection occurs at any initial concentration. At the same time, the criterion of concentration convection linearly dependents on the initial concentration, and, therefore, at high concentrations, concentration convection prevails, while at lower concentrations, the role of gravitational convection begins to fall whereas the role of electro convection increases. The theory of similarity of the process of heat and mass transfer in the desalting channel of electro dialysis apparatus built in this work taking into account the joint action of concentration polarization, space charge, gravity convection, forced convection and electro convection is important for engineering calculations, for scaling the results of experiments in an electro-membrane cell for industrial electro dialysis water desalting apparatus