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In this paper we extend the homogenization results obtained in (G. Allaire,A. Mikeli\'c, A. Piatnitski, J. Math. Phys. 51 (2010), 123103) for a system ofpartial differential equations describing the transport of a N-componentelectrolyte in a dilute Newtonian solvent through a rigid periodic porousmedium, to the case of random disperse porous media. We present a study of thenonlinear Poisson-Boltzmann equation in a random medium, establish convergenceof the stochastic homogenization procedure and prove well-posedness of thetwo-scale homogenized equations. In addition, after separating scales, we provethat the effective tensor satisfies the so-called Onsager properties, that isthe tensor is symmetric and positive definite. This result shows that theOnsager theory applies to random porous media. The strong convergence of thefluxes is also established.

Homogenization of the linearized ionic transport equations in random porous media