Diffusion and convection across heteroporous membranes: a simple macroscopic equation

Here the problem of identifying a set of macroscopic parameters which describe the transport of a neutral solute across a heteroporous membrane by convection and diffusion is considered. An approximate equation for the solute flux is developed in terms of the membrane boundary conditions and the macroscopic parameters Lp (hydraulic conductivity), sigma s (reflection coefficient), Ps (permeability), and qs (index parameter). The unique feature of this model is that the four macroscopic parameters are (1) expressed in terms of the set of single-pore parameters [Lpi, sigma si, Psi] and the pore-size distribution only, (2) invariant to conditions which alter the volume (Jv) and solute (Js) fluxes, and (3) consistent with simultaneous measurements of Jv and Js. The four-parameter equation for Js is shown to be in good agreement with the exact solution for the extreme case of a membrane composed of two distinct sets of pores which differ greatly in radii.