Summary: We propose and analyze a novel membrane-based fractionation process that combines conventional countercurrent dialysis with a phenomenon of “pseudo-sedimentation”. An elliptic transmission problem is formulated to describe the steady-state concentration field of a given chemical species. Matching of spectral expansions at the transmission boundary yields an infinite system of linear algebraic equations for the eigenfunction expansion coefficients of the solution. Existence and uniqueness of the solution, framed in terms of a Fredholm alternative, are proven within a subset of the parameter space, along with regularity at the transmission boundary. The paper also develops a perturbation solution in order to interpret the theory in physical terms. Finally, numerically generated concentration profiles indicate the degree of selectivity that could be achieved with a separation apparatus based upon our physical concept.