Journal
ROYAL SOCIETY OPEN SCIENCE
Volume 1, Issue 3, Pages -Publisher
ROYAL SOC
DOI: 10.1098/rsos.140352
Keywords
osmosis; porous medium; semipermeable membrane; Maxwell's demon
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Funding
- Spanish MICINN [FIS2013-48444-C2-2-P]
- Pembroke College, Cambridge
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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.
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