канд. физ.-мат. наук, доц. кафедры прикладной математики Кубанского государственного университета
канд. экон. наук, доц. кафедры прикладной математики Кубанского государственного университета
д-р физ.-мат. наук, проф., зав. кафедрой прикладной математики Кубанского государственного университета
We formulated the sufficiently general 2D mathematical model of time-dependent non-isothermal transport process of binary electrolyte in electromembrane system (EMS) in coaction of forced, gravitational and electroconvection in potentiostatic mode. For definiteness, we consider desalination channel of electrodialysis apparatus (EDA) as EMS. The model is a boundary value problem for a system of quasilinear partial differential equations. The initial system of equations describing time-dependent transfer of binary electrolyte ions in an electric field consists of the hydrodynamic equations and the equations of the Nernst-Planck-Poisson. For the density of the solution the Boussinesq approximation is used. The density of buoyancy forces in this paper is supposed to be conditioned just by a concentration polarization of the solution. A detailed description of the initial and boundary conditions is given. Computational experiments are made with varying the initial concentration of the solution from 100 mol/m3 down to 1 mol/m3 using the Comsol Multiphysics software. It is shown that at the beginning of the desalination process of the pumping solution with a concentration of 10 mol/m3 or more, the gravitational convection is a dominating process, while the role of electroconvection is negligible. However, when the time goes by and the concentration decreases in the desalting process, the role of gravitational convection declines, while the role of electroconvection increases. For sufficiently diluted solutions, with a concentration of less than 1 mol/m3, the role of gravitational convection is negligible, and the electroconvection dominates from the beginning of the desalination process.
В данной работе сформулирована математическая модель нестационарного неизотермического процесса переноса в электромембранной системе (ЭМС) для бинарного электролита с учетом вынужденной, гравитационной и электроконвекции в потенциостатическом режиме. Для определенности в качестве ЭМС рассматривается канал обессоливания электродиализного аппарата (ЭДА). Теоретически изучено взаимодействие вынужденной, гравитационной и электроконвекции.