This article considers a theoretical analysis of the influence of the main coupled effects and spacers on the transfer of salt ions in electromembrane systems (EMS) using a 2D mathematical model of the transfer process in a desalting channel with spacers based on boundary value problems for the coupled system of Nernst–Planck–Poisson and Navier–Stokes equations. The basic patterns of salt ion transport have been established, taking into account diffusion, electromigration, forced convection, electroconvection, dissociation/recombination reactions of water molecules, as well as spacers located inside the desalting channel. It has been shown that spacers and taking into account the dissociation/recombination reaction of water molecules significantly change both the formation and development of electroconvection. This article confirms the fact of the exaltation of the limiting current studied by Harkatz, where it is shown that the current (flux) of salt ions increases when the dissociation reaction begins by a certain value called the exaltation current, which is proportional to the flow of water dissociation products. A significant combined effect of electroconvection and dissociation/recombination reactions as well as the spacer system in the desalting channel on the transport of salt ions are shown. The complex, nonlinear, and non-stationary interaction of all the main effects of concentration polarization and spacers in the desalting channel are also considered in the work.

Magnetic fluid (MF) is a colloidal system consisting of ferromagnetic particles (magnetite) with a diameter of ~10 nm suspended in a dispersion medium of a carrier fluid (for example, kerosene). A distinctive feature of magnetic fluid is the fact that when an electric field is applied to it using two electrodes, thin layers consisting of close-packed particles of the dispersed phase are formed in the regions near the surface of both electrodes. These layers significantly affect the macroscopic properties of the colloidal system. In this work, the interpretation of the near-electrode layer is for the first time given as a new type of liquid membrane, in which the particles of the dispersed phase become charged with the opposite sign. On the basis of experimental studies, we propose a physicochemical mechanism of the autowave process in a cell with a magnetic fluid. It is based on the idea of oppositely recharging colloidal particles of magnetite in a liquid membrane. A mathematical model of an autowave process, which is described by a system of coupled partial differential equations of Nernst–Planck–Poisson and Navier–Stokes with appropriate boundary conditions, is proposed for the first time. One-dimensional, two-dimensional, and three-dimensional versions of the model are considered. The dependence of the frequency of concentration fluctuations on the stationary voltage between the electrodes was obtained, and the time of formation of a liquid membrane was estimated. Qualitative agreement between theoretical and experimental results has been established.

This article proposes various new approximate analytical solutions of the boundary value problem for the non-stationary system of Nernst–Planck–Poisson (NPP) equations in the diffusion layer of an ideally selective ion-exchange membrane at overlimiting current densities. As is known, the diffusion layer in the general case consists of a space charge region and a region of local electroneutrality. The proposed analytical solutions of the boundary value problems for the non-stationary system of Nernst–Planck–Poisson equations are based on the derivation of a new singularly perturbed nonlinear partial differential equation for the potential in the space charge region (SCR). This equation can be reduced to a singularly perturbed inhomogeneous Burgers equation, which, by the Hopf–Cole transformation, is reduced to an inhomogeneous singularly perturbed linear equation of parabolic type. Inside the extended SCR, there is a sufficiently accurate analytical approximation to the solution of the original boundary value problem. The electroneutrality region has a curvilinear boundary with the SCR, and with an unknown boundary condition on it. The article proposes a solution to this problem. The new analytical solution methods developed in the article can be used to study non-stationary boundary value problems of salt ion transfer in membrane systems. The new analytical solution methods developed in the article can be used to study non-stationary boundary value problems of salt ion transport in membrane systems.

The electrical conduction of a magnetic fluid (MF) on kerosene, stabilized by oleic acid, is investigated in an external magnetic field. The analysis of th

A ferrocolloid is a suspension of nanometer-sized ferromagnetic particles (magnetite) in a carrier liquid (kerosene). A unique feature of a ferrocolloid is the fact that layers consisting of densely packed particles are formed near the electrode surface under the influence of an external electric field. Each layer is a liquid membrane, and its formation significantly affects the various properties of the system. For example, the development of a unique phenomenon in a ferrocolloid is self-organization (self-oscillations and autowaves). The applied external periodic force leads to a change (capture) of the frequency of the autowave process-forced synchronization of autowaves. The experimentally obtained synchronization was investigated by the method of electrically controlled interference. After multiple experiments and theoretical studies, a physical mechanism for the synchronization of the autowave process in a cell with a ferrocolloid was proposed for the first time. A mathematical model of forced synchronization of autowaves, which is described by a system of nonlinear differential equations, was proposed for the first time as well. Adding an external periodic force into the model led to a change in the frequency of autowaves; synchronization by an external force was confirmed by computational experiments.

The article proposes various new approximate analytical solutions of the boundary value prob-lem for the non-stationary system of Nernst-Planck-Poisson (NPP) equations in the diffusion layer of an ideally selective ion-exchange membrane at overlimiting current densities. As is known, the diffusion layer in the general case consists of a space charge region and a region of local electroneutrality. The proposed analytical solutions of the boundary value problems for the non-stationary system of Nernst-Planck-Poisson equations are based on the derivation of a new singularly perturbed nonlinear partial differential equation for the potential in the space charge region (SCR). This equation can be reduced to a singularly perturbed inhomogeneous Burgers equation, which, by the Hopf-Cole transformation, is reduced to an inhomogeneous singularly perturbed linear equation of parabolic type. Inside the extended SCR, there is a suffi-ciently accurate analytical approximation to the solution of the original boundary value prob-lem. The electroneutrality region has a curvilinear boundary with the SCR, and with an un-known boundary condition on it. The article proposes a solution to this problem. The new ana-lytical solution methods developed in the article can be used to study non-stationary boundary value problems of salt ion transfer in membrane systems.