title: 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 1958 Biochim. Biophys. Acta 27, 229-246 (doi:10.1016/0006-3002(58)90330-5), which have hitherto been validated experimentally but not theoretically. The above linearity between the fluxes and the driving forces breaks down for concentrated or non-ideal mixtures, for which our equations go beyond the Kedem-Katchalsky formulation. We show that the heretofore empirical solute permeability coefficient reflects the momentum transfer between the solute molecules that are rejected at a pore entrance and the solvent molecules entering the pore space; it can be related to the inefficiency of a Maxwellian demi-demon.
authors.affiliation: Department of Chemical Engineering and Biotechnology , University of Cambridge , Cambridge CB2 3RA, UK.
authors.forename: Silvana S S
authors.initials: SS
authors.lastname: Cardoso
authors.affiliation: Instituto Andaluz de Ciencias de la Tierra , CSIC-Universidad de Granada , Campus Fuentenueva, 18071 Granada, Spain.
authors.forename: Julyan H E
authors.identifier: 0000-0001-7392-0957
authors.initials: JH
authors.lastname: Cartwright
keywords: Maxwell's demon; osmosis; porous medium; semipermeable membrane