# AMaSiS 2021 - Abstract

**Allaire, Grégoire**

*Homogenization of electrokinetic equations*

Ecole Polytechnique, France

In this talk I will review some results on the homogenization (or upscaling) of a system of partial differential equations describing the ideal or non-ideal transport of a N-component electrolyte in a dilute Newtonian solvent through a rigid porous medium. This system describes electrokinetic effects which are important in various applications, including nuclear waste storage or Li-ion batteries. Our approach is based on a linearization argument, first proposed by O'Brien, around an equilibrium solution in the absence of external forces. Assuming that the motion is governed by a small static electric field and a small hydrodynamic force allows us to linearize the model and then to proceed to its homogenization. In particular, we prove that the effective tensor satisfies Onsager properties, namely it is symmetric positive definite. I will explain the differences with some other approaches in the homogenization of such electrokinetic equations. Eventually some numerical computations of homogenized coefficients will be discussed.

This is a joint work with R. Brizzi, J.-F. Dufrěche, A. Mikelic and A. Piatnitski.