Name
Urtenov Makhamet Khuseyevich
Scholastic degree
•
Academic rank
professor
Honorary rank
—
Organization, job position
Kuban State University
Web site url
—
Articles count: 43
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
This article is a continuation of the works [1,2], which were devoted to the study of hydrodynamics and transport of salt ions in the experimental electrochemical cell with a rotating disk with a cation exchange membrane of exact current modes, when the condition of local electroneutrality. This article presents a mathematical model of transport of salt ions in a cell with a rotating disk with a cation exchange membrane exorbitant current regimes, taking into account electroconvection. Under these conditions, fluid dynamics depends on the ion transport process salt and described by the system of Navier-Stokes equations in cylindrical coordinate system with the electric forces
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 article analyzes the boundary problem model of transport of binary electrolyte membrane systems in the approximation of Ohm's law. Different methods of solution are proposed
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.
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
In this article authors propose the asymptotic solution of the boundary value problem modeling the transport of salt ions in the cell electrodialysis desalination unit. The domain of the camera desalting broken into two subdomains: electroneutrality and space charge. Subdomains has own asymptotic expansion.
The subdomain of the space charge has unique solvability of the current approach used by the solvability condition of the next approximation
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"
This article is a continuation of [1, 2] and is devoted to the description of a program complex "Region-Credit" for the assessment of financial stability, economic development, credit, socio-economic status and investment attractiveness of Russian regions. The article is an example of a comprehensive credit
analysis, socio-economic status and investment attractiveness of Krasnodar Region for the period from 2008 to 2014 with the help of a program complex "Region-Credit", whose results are compared with peer review rating agency AK&M