Homogenization of the linearized ionic transport equations in random porous media

In this paper we obtain the homogenization results for a system of partial differential equations describing the transport of a N-component electrolyte in a dilute Newtonian solvent through a rigid random disperse porous medium. We present a study of the nonlinear Poisson-Boltzmann equation in a random medium, establish convergence of the stochastic homogenization procedure and prove well-posedness of the two-scale homogenized equations. In addition, after separating scales, we prove that the effective tensor satisfies the so-called Onsager properties, that is the tensor is symmetric and positive definite. This result shows that the Onsager theory applies to random porous media. The strong convergence of the fluxes is also established. In the periodic case homogenization results for the mentioned system have been obtained in Allaire et al (2010 J. Math. Phys. 51 123103).

Automated summary

In this paper, we study the homogenization of a system of partial differential equations in a random porous medium for the transport of an electrolyte in a solvent. We establish the convergence of the stochastic homogenization procedure and prove the well-posedness of the two-scale homogenized equations. We also demonstrate the validity of the Onsager theory for random porous media and establish the strong convergence of the fluxes.