Generalized Onsager relations for electrokinetic effects in anisotropic and heterogeneous geometries

We lay down a general formalism to describe the linear electrohydrodynamic response of systems of arbitrary topology, symmetry and heterogeneity, and through an explicit proof, we demonstrate a set of general Onsager relations between the corresponding electrokinetic coefficients. This generalizes a classical result of Mazur and Overbeek [P. Mazur and J.T.G. Overbeek, Recl. Trav. Chim. Pays-Bas. 70, 83 (1951)] to situations that may become of practical relevance in particular in the field of microfluidic devices. Technically, our proof of the symmetry of the generalized conductance matrix relies on an adaptation of the reciprocal theorem of low-Reynolds-number hydrodynamics.