A consistent description of the kinetic processes of electrolyte ion transport in a dynamic porous medium

TL;DR

This paper develops a unified theoretical framework combining kinetic and hydrodynamic models to describe ion transport in porous media, introducing fractional calculus to model subdiffusive behavior.

Contribution

It presents a novel set of equations for ion transport, incorporating fractional derivatives to accurately model subdiffusion in porous structures.

Findings

Derived a generalized diffusion equation of Cattaneo type with fractional derivatives.

Provided a consistent description of ion transport processes in porous media.

Demonstrated the applicability of fractional calculus to subdiffusive phenomena.

Abstract

The consistent description of kinetic and hydrodynamic processes is applied to the study of ion transport processes in the ionic solution-porous medium system. A system of equations is obtained for the nonequilibrium single-ion distribution function, the nonequilibrium average value of the energy density of the interaction of solution ions, and the nonequilibrium average value of the number density of particles in a porous medium. Using the fractional calculus technique, a generalized diffusion equation of the Cattaneo type in fractional derivatives is obtained to describe the processes of subdiffusion of particles in a porous medium.