Mechanism of osmotic flow in porous membranes

A model for osmotic flow in porous membranes is developed from classical transport and thermodynamic relations. Mathematical expressions for the reflection coefficient as a function of solute dimension and shape, and more generally pore/bulk distribution coefficient, are derived for long cylindrical pores of circular cross section. For a rigid, spherical macromolecule the osmotic reflection coefficient equals (1 - Phi)(2), where Phi is the solute distribution coefficient; this result differs significantly from expressions found in the literature. The effect of weak solute adsorption to (or repulsion from) the pore wall can also be accounted for in the derivation. The driving force for osmotic flow arises from solute-pore wall interactions which cause radial variations in concentration and concomitant gradients in pressure normal to the wall. Implications of this three-dimensionality of osmotic phenomena are discussed with particular reference to the adequacy of one-dimensional treatments in relating reflection coefficient to membrane and solute properties.