Hydrodynamic models for diffusion in microporous membranes

Abstract

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 onedimensional 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, σ, from the hydrodynamic analysis of P. M. Bungay and H. Brenner (Journal of Fluid Mechanics 1973, 60, 81). The resulting σ'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.