Name
Urtenov Makhamet Khuseyevich
Scholastic degree
•
Academic rank
professor
Honorary rank
—
Organization, job position
Kuban State University
Web site url
—
Articles count: 43
We propose a mathematical model of ion transport binary salt in electroosmotic flow in a capillary. The capillary is open on one side and immersed in a vessel of large volume, in which the concentration of the solution is maintained constant, and the other side closed ion exchange membrane. The walls are considered wettable, i.e. the solution adheres to the walls. This means that the mathematical modeling used to rate the condition of sticking. We study the boundary value problem for a coupled system of equations Nernst, Planck, Poisson and Navier-Stokes equations. Used boundary conditions of general form. The mathematical model is based on the general laws of transport and contains no adjustable parameters. Using this model, the basic laws of ion transport salt solution liquid flow, the emergence and development electroconvection, distribution of concentration of salt ions in the capillary with a small change in time, ie, in the initial (transitional) regime. We have identified the presence of ion-exchange membrane surface electroconvective vortices and their influence on the mechanisms of ion transport of salt and fluid movement in different areas of the capillary. A feature of the capillary transport is to the right of the vortex region stagnant areas with a higher concentration of ions
In the article we have derived mathematical models of non-stationary transport binary electrolyte in EMS (electromembrane systems: electrodialysis apparatus, electromembrane cell, etc.) for the galvanostatic mode. To be specific, as EMS viewed channel of desalting of EDA (electrodialysis apparatus) and EMS with RMD (rotating membrane disk). We present a formula expressing the intensity of the electric field through the current density and concentration. Also, we have received the differential equation for the current density. The fundamental point here is derived new equation for the unknown vector function of current density of the initial system of equations of Nernst-Planck. In addition, the article shows the output equation for the current density in three dimensions; we have proposed various methods for solving the equation of the current density and the boundary conditions for the current density. The proposed mathematical models of transport binary electrolyte are easy to be generalized to an arbitrary electrolyte. However, the corresponding equations are cumbersome. It should be also noted that the boundary conditions can be varied and depend on the purpose of a particular study in this regard, in this work are just the equation having the general form
Micro and nanofluidics are the new multidisciplinary
sciences. One of the tasks of which is creation and
management of flow of fluid in the thin channels size
of a few nano- or micrometer which exposed the
external electric field, where the walls are the ion
exchange membrane. Electroosmosis
(electroconvection) plays an important role in these
tasks. A large number of articless were devoted to
electroosmosis. One of the first, Dukhin S.S.,
Mishchuk N.A. and Rubinstein I. gave a theoretical
explanation of the overlimiting current by
electroosmosis. They used two-dimensional Stokes
equation to calculate the flow of the electrolyte, and
one-dimensional equations of Nernst-Planck and
Poisson to calculate the electric power. These
researches have multiple limitations because of the
computational complexity the mathematical
simulation. Thus, there is an actual problem of the
asymptotic solution of boundary value problems for
the two-dimensional systems of equations of NernstPlanck
and Poisson without these restrictions. These
researches we derived in simplified models of
electroosmosis in galvanic dynamical mode using the
decomposition method. We have created a hierarchical
system of two-dimensional mathematical models of
ion transport of salt and electroosmosis in micro- and
nanochannels formed by selective ion-exchange
membranes
This article describes a mathematical model of transport
of salt ions in a cell with a rotating disk cation exchange
membrane at transcendent current regimes, taking into
account electroconvection. Based on this model, we had
a theoretically study of the process of transfer of salt
ions and the dependence of the thickness of the
diffusion layer from the fall of potential. This article is
a continuation of [8] and [9], it conducted a numerical
analysis of boundary value problem for a system of
equations Nernst-Planck-Poisson and Navier-Stokes
equations, modeling the transport of salt ions in a
cylindrical cell with a rotating disc cation exchange
membrane based on electroconvection. It is shown there
is an electroconvection vortex in the center of the
membrane disc. The solution flows around this vortex
and forms a stagnation zone in front of it. With the
increase in the size of the fall of potential, the
electroconvective vortex decreases and at some value,
the electroconvective vortex disappears. The study was
conducted in the 1000 s when the angular velocity of 30 turns in a minute and change of the potential difference
of 0.2V to 1.4V with a step 0.1. As a result, in this
study it is shown that the thickness of the diffusion
layer is practically linearly dependent on the fall of
potential. The linear dependence of the thickness of
diffusion layer from the fall of potential, in the first
approximation, is disturbed by a slight deflection curve,
the causes of which are needed to be found by means of
extra experiments
This work presents a new approach to the countries’
credit rating definition, based on the advanced mathematical
models, such as neural network model, multiple
regression, cluster analysis and discriminant analysis.
A range of the analyses such as discriminant, cluster,
multiple regression models and a neural network
were performed on the following economic figures:
GDP per capita, GDP value, annual growth rate of
GDP, FDI - foreign investment, rate of unemployment,
consumer price inflation index, the size of government
debt in percentage of GDP. The results, obtained for
each model were combined in the countries’ credit
rating estimation system called "7M"
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 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
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.
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
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