  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 of
partial differential equations describing the transport of a N-component
electrolyte in a dilute Newtonian solvent through a rigid periodic porous
medium, to the case of random disperse porous media. 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.
