Estimates to the weak solution of the electro-hydrodynamical boundary value problem for the unit cell of cation-exchange membrane

TL;DR

This paper analyzes a model of fluid filtration through a porous layer with charged cells, deriving estimates for flow parameters and proving boundedness of key physical quantities.

Contribution

It provides new a priori estimates for flow characteristics in a charged porous medium with finite Debye radius, advancing understanding of electro-hydrodynamical behavior.

Findings

Velocity, pressure, electric potential, and ion flux densities are bounded.

Dependence of flow parameters on Debye radius is characterized.

Finite Debye radius case analyzed in detail.

Abstract

We study a model problem on the filtration of a conducting fluid through a porous layer. A porous medium is presented as an assemblage of identical spherical cells. Each cell consists of a porous core and liquid shell. We show the dependence of each flow parameter on the Debye radius which characterizes how far the influence of a charge extends in electrolyte. The common case of finite Debye radius in comparison to the cell radius is analyzed. We derive apriori estimates for flow characteristics which show the specific behavior of the fluid. The boundedness of velocity field, pressure, electric potential and ion flux densities was proved.