Asymptotic Analysis of Three-Scale Model of pH-Dependent Flows in 1:1 Clays with Danckwerts’ Boundary Conditions

Abstract

The electroremediation process is an efficient method for removing pollutants from clayey soils. We model this process in kaolinite clays considering three scales—nano, micro and macro—under the assumption of a stratified geometry in conjunction with more realistic Danckwerts' boundary conditions imposed at the electrodes. The resulting multiscale model is a coupled system of nonlinear partial differential equations. We derive analytical solutions of the macroscopic equations considering the asymptotic behavior of strongly convective and diffusive regimes. We perform numerical simulations of different scenarios for the electroremediation using the Galerkin finite element method together with a staggered algorithm and the Newton–Raphson method. We validate the accuracy of the proposed algorithm by comparing the discrete solutions to the analytical ones. Finally, we explore and discuss optimal scenarios for the electroremediation process depending on the input values of pH, electrical current, and mass inflow using dimensionless numbers defined from the analytical solutions.

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