Transport across homoporous and heteroporous membranes in nonideal, nondilute solutions. II. Inequality of phenomenological and tracer solute permeabilities

The phenomenological solute permeability (omega p) of a membrane measures the flux of solute across it when the concentrations of the solutions on the two sides of the membrane differ. The relationship between omega p and the the conventionally measured tracer permeability (omega T) is examined for homoporous and heteroporous (parallel path) membranes in nonideal, nondilute solutions and in the presence of boundary layers. In general, omega p and omega T are not equal; therefore, predictions of transmembrane solute flux based on omega T are always subject to error. For a homoporous membrane, the two permeabilities become equal as the solutions become ideal and dilute. For heteroporous membranes, omega p is always greater than omega T. An upper bound on omega p- omega T is derived to provide an estimate of the maximum error in predicted solute flux. This bound is also used to show that the difference between omega P and omega T demonstrated earlier for the sucrose-Cuprophan system can be explained if the membrane is heteroporous. The expressions for omega P developed here support the use of a modified osmotic driving force to describe membrane transport in nonideal, nondilute solutions.