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Dynamics of osmosis in a porous medium.



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Cardoso, Silvana SS 
Cartwright, Julyan HE  ORCID logo


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.



Maxwell's demon, osmosis, porous medium, semipermeable membrane

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R Soc Open Sci

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The Royal Society
J.C. acknowledges the financial support of Spanish MICINN grant no. FIS2013-48444-C2-2-P, and thanks Pembroke College, Cambridge, for a visiting fellowship. This work was performed within the framework of the NASA Astrobiological Institute focus group on thermodynamics, disequilibrium and evolution (TDE).