The application of practical Kedem-Katchalsky equations in membrane transport

Abstract

Kedem-Katchalsky (K-K) equations, commonly used to describe the volume and solute flows of nonelectrolyte solutions across membranes, assume that the solutions on both sides are mixed. This paper presents a new contribution to the description of solute and solvent transfer through a membrane within the Kedem-Katchalsky formalism. The modified K-K equation obtained here, which expresses the volume flow (Jv), includes the effect of boundary layers of varied concentrations that form in the vicinity of the membrane in the case of poorly-mixed solutions. This equation is dependent on the following: membrane parameters (σ, Lp ω), complex h/M/l parameters (σsreflection, L ps-hydraulic permeability, ωs-solute permeability coefficients, δh, δl-thicknesses of concentration boundary layers), and solution parameters (c-concentration, ρ-density, v-kinematic viscosity, D-diffusion coefficient). In order to verify the elaborated equation concerning Jv, we calculated the following functions: J v = f (Δ c)Δp,Rc=const, J v = f (R C)Δp,Δ=const, and J v = f ((Δp)Δc,RC=const,. The J v equation was derived by means of two methods. © Versita Warsaw and Springer-Verlag Berlin Heidelberg 2006.