Generalization of 2D conversion system of equations Nernst-Planck-Poisson and hierarchical system of models on the 3D case

Abstract

The purpose of this article is to summarize the conversion Kovalenko A.V. and Urtenova M.H. of two-dimensional system of equations Nernst-Planck-Poisson hierarchical system of mathematical transport models on the 3D case in a dimensionless form. This article discusses two cases: the transport of a binary electrolyte channel electrodialysis desalting device and membrane system with a rotating membrane disk. To achieve this goal was held dimensionless system of equations Nernst-Planck-Poisson in the case of 3D. Thus, in the case of a system with a rotating membrane disc as a characteristic width acted diffusion layer thickness calculated by Levich formula, and as the characteristic velocity - the speed of the feed solution to its depth the surface of the membrane disc. Further assessment was made of the dimensionless variables: Pecle number and the parameter on the basis of this assessment was made to simplify the decomposition equations Nernst-Planck-Poisson derived a mathematical model of transport in the approximation of a generalization of Ohm's law (LOM) in a cartesian coordinate system in the case of 3D. Then, the resulting model was transferred to LOM cylindrical coordinate system, taking into account the axial symmetry, thereby transferring model was obtained with a rotating disc membrane approximation generalizations Ohm's law.