Dilute solution approximation and generalization of the reflection coefficient method of describing volume and solute flows

Abstract

Kedem and Katchalsky introduced an approximation for dilute solutions which requires that the quantity (Deltapi/Deltapi(i))ø(i) be much less than one. Zelman attempted to generalize the reflection coefficient concept to apply to solutions of multiple solutes, both penetrable and impenetrable, of concentrations sufficiently high for the approximation not to work. By simple algebraic manipulation, Zelman introduced a pair of new reflection coefficients, and a third new parameter gamma which he misleadingly calls the "deviation from the dilute solution approximation." It is shown here that the original Kedem-Katchalsky form for the flow equations can be preserved in such a way that no new coefficients need be introduced and an explicit statement of the effect of the dilute solution approximation can be made. There is an option of using a new set of conjugate driving forces for the solute flows or, alternatively, incorporating the nondilute solution correction in the coefficients in a clear way.