Dynamics of osmosis in a porous medium

Abstract

We derive from kinetic theory, fluid mechanics and thermodynamics the minimal continuum-level equations governing the flow of a binary, non-electrolytic mixture in an isotropic porous medium with osmotic effects. For dilute mixtures, these equations are linear and in this limit provide a theoretical basis for the widely used semi-empirical relations of Kedem & Katchalsky (Kedem & Katchalsky 1958Biochim. Biophys. Acta27, 229–246 (doi:10.1016/0006-3002(58)90330-5)), which have hitherto been validated experimentally but not theoretically.