Scientific Journal of KubSAU

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

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

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

This article continues the works [1,2], devoted to the theoretical study of the basic laws of electroconvection caused by natural or artificial inhomogeneous conductivity of ion-exchange membranes in a smooth rectangular channel electrodialysis desalination unit. For this purpose, a mathematical model was created for a binary electrolyte electroconvection at overlimiting current modes in the form of a boundary value problem for a coupled system of the Nernst-Planck-Poisson and Navier-Stokes equations. We have studied the influence of heterogeneity on the ion-exchange membranes and ion transport electroconvection salt, calculated currentvoltage characteristic. The possibility of intensification of mass transfer due to the surface modification of ion exchange membranes was also shown

The phenomenon of electro convection in membrane systems is of considerable interest, because it is, according to many authors, the main mechanism of overlimiting mass transfer. A great number of theoretical and experimental works, in which, as a rule, dimensional values were used, are devoted to electro convection study. Because of that, in actual fact, there is investigated the influence of individual factors on the transfer process. For example, the influence of voltage jumps, the average speed of a forced stream of the solution, the geometric characteristics of the channel, the initial concentration, etc. However, the influence of these factors appears not separately, at the same time. Thus, there is the problem of introducing dimensionless complexes of dimensional values that have a physical meaning and that allow to evaluate the inner links of the process. As it is known, for solving that problem, there is applied a theory of similarity, based on the transition towards dimensionless parameters in equations and formulas describing the process, and using values, typical of the system under study. This work is devoted to the determining of physical meaning of similarity criteria of salt ions processes, taking into account electro convection in the desalting channel of electro dialysis apparatus. The channel is bounded with perfectly selective, homogeneous anion-exchange and cation-exchange membranes. The introduced similarity criteria are used so as to conduct the theoretical study of the effect of a number of parameters of a desalting process on electro convection

This work is a continuation of [1], which was devoted to the investigation of the hydrodynamics of the experimental electrochemical cell with rotating disk cation exchange membrane. This article focuses on the transport of salt ions in a closed cell at different initial experimentation with modes of exact current regimes. The main regularities of transport of salt ions and membrane equal accessible surface were set

This article investigates hydrodynamic of experimental electrochemical cell with rotating disk in the cation exchange membrane. We have also investigated the flow in open, with the free surface of the solution and in hermetically closed cells. The main regularities of the hydrodynamics of the experimental cell at its real size were set