Scientific Journal of KubSAU

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

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

This article focuses on the mathematical modeling of evaluation of financial and economic activities of a company and on definition (based on this model) of such balance settings (line F1 and F2) which would make financial-economic indicators of the activities of the organization optimal, and the total cumulative score was the maximum. The knowledge and the use of the optimal parameters of the balance will allow the managers to plan strategy for the future development of the company. The article analyzes the dependencies of each of the 15 basic indicators (profitability, turnover, financial stability, liquidity and solvency) of financial and economic activity of the organization on the balance parameters. The optimal values of the parameters of the balance and the main indicators of financial and economic activities of the organization have been found. We have also built a mathematical model of optimal control of financial and economic indicators in the form of a problem of mathematical programming. For example, for the company called "Nika" it is shown the possibility of improving estimation of financial and economic condition of the organization. Knowledge of the optimal parameters of the balance will allow the managers to plan strategy for the future development of the organization. To solve this problem we have used the method of generalized reduced gradient implemented in Excel, with which there was found a maximum of the objective function for the article restrictions. The article describes the analysis algorithm of the optimization problem. A common assessment was carried out in stages, based on the calculation algorithm of sequentially improved target functions

For effective management of economic and financial activity of a modern enterprise it is required to have information – software supply for its separate components: branches, divisions, services. Automation of the account allows accelerating significantly the process of granting, processing and the analysis of information necessary for the purposes of management. An important aspect on introduction of a program complex is the concept on its realization, i.e. the head of the company should define the way of development of automation of business - processes, what type of introduction is more preferable to the enterprise, what documents will formalize each of the stages. The article generalizes the data obtained by practical consideration on the basis of the realized projects on introduction of the automated systems in the companies from various fields of activity. The main stages of the design direction in the sphere of automation of business – processes are presented in this work, as well as the features of the subject and the characteristics of each stage, documentary objects for realization of each of them. Also on the basis of the carried-out analysis, the authors described a number of the existing shortcomings on realization of the design direction. In view of the data specified in article, the companies will be able to begin the project on automation of their own business effectively and quickly

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

The aim of this work is to carry out numerical analysis of time behavior of electroconvection in membrane systems, such as a desalting channel of electrodialysis apparatus. The current-voltage curve and the solution flaw were analyzed theoretically using mathematical models of ions transfer taking into account electroconvection in smooth desalting channel consisting of ideally selective anion- and cation-exchange membranes. The Hurst numbers for different parts of the current-voltage curve were calculated in order to determine whether the parts were persistent. The Fourier-analysis of the oscillating term of the current-voltage curve was carried out for the first time so as to determine predominant frequencies in the signal. Frequencies of passing of complexes of vortexes through the cross-section of the desalting channel were calculated. Frequencies of oscillations of concentration profiles were determined. It was found that the frequencies of oscillations of the concentration profiles coincide with the frequencies of passing of complexes of vortexes through the cross-section of the desalting channel. The oscillations of the current-voltage curve were physically interpreted. Namely, it was shown that the main frequency of oscillations of the current-voltage curve corresponds to the frequency of oscillations of the concentration profiles. The oscillations of the concentration profiles, produced by the passing of complexes of vortexes, cause oscillations of conductivity and, consequently, cause oscillations of resistance and of the current density. It was shown that the main frequency of the signal corresponds to the frequency of passing of complexes of vortexes through the cross-section of the desalting channel

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

The article presents a mathematical model of the effect on ion transport electro convection salt in non-smooth camera channel desalting electro dialysis apparatus in the presence of forced convection. The basic rules of process of electro convection are revealed

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

The article presents a new approach to 2D modeling of transport of salt ions in EMC (electro systems: electrodialysis devices, electro-cells, etc.) under the condition of electrical neutrality with limiting and overlimiting current density. For definiteness as seen half of EMS channel EDA desalting (electrodialysis apparatus), the right border, which serves as a CEM (cation exchange membrane). The new approach in the use of partial differential equations of the first order, instead of equations of convective diffusion. A common method of transport modeling binary electrolyte in the EMS under the condition of electrical neutrality, is to use the equation of convective diffusion (partial differential equations of the second order). The article presents a new approach to modeling 2D transfer binary electrolyte in EMS under the same conditions, using partial differential equation of the first order for the decision, which does not require a boundary condition for concentration on the membrane surface. This allows you to simulate the transport of salt ions, as in prelimit and exorbitant current density and to determine the boundaries of the field of electrical neutrality