Transport across homoporous and heteroporous membranes in nonideal, nondilute solutions. I. Inequality of reflection coefficients for volume flow and solute flow.

The Kirkwood formulation of the Stefan-Maxwell equations is used to develop the transport equations for a membrane bounded by nonideal, nondilute solutions. The reflection coefficients for volume flow and solute flow are not equal but are related by a simple expression that depends on the concentration of the bounding solutions. The ratio of the two coefficients is independent of heteroporous membrane structure and the thickness of adjacent boundary layers. Experimental measurements of these reflection coefficients for sucrose transport across Cuprophan verify this relationship; this indicates that the Onsager reciprocal relation, which is assumed by the theory, holds for nonideal, nondilute solutions. The two reflection coefficients may be made operationally identical by a simple redefination of the osmotic driving force.