Hydrodynamic models for diffusion in microporous membranes.

The hydrodynamic theory of diffusion is extended to describe osmotic flow of binary solutions in microporous membranes. It is shown that the one-dimensional microscopic rate equations of irreversible thermodynamics are completely consistent with creeping flow hydrodynamic analyses. It is further shown how one may determine the one-dimensional coefficients from the results of hydrodynamic analysis and how one may obtain macroscopic descriptions by integrating the microscopic equations over the diffusion path. In this way a complete and self-consistent means is developed for interpreting macroscopic behavior in terms of a molecular model. By way of example, a scheme is presented and implemented for estimation of reflection coefficients, , from the hydrodynamic analysis of P. M. Bungay and H. Brenner ( 1973, 60, 81). The resulting ’s are sensitive to the solute radial probability density; for a uniform distribution the present values are larger than those reported recently by other workers.