Mass Transfer of Binary Electrolytes in Membranes at High Concentrations

Abstract

Angeles, Calif. 90024 Flux equations derived utilizing irreversible thermodynamics give good correlation for high-flux cellulose acetate membrane performance in aqueous NaCI solutions up to 1.2 N. The membrane diffusion parameter in the electrolyte flux equation demonstrates a small concentration dependence and is correlated by a simple, empirical equation. The membrane diffusion parameter in the water flux equation is concentration-independent. Membrane behavior is essentially invariant over a 7-day period. The standard deviation is between 2.1 and 5.3%, 1.2 and 7.0%, and 24 and 394% for electrolyte, water, and coupling membrane transport parameters, respectively. Although the fraction of total transport through the membrane in reverse osmosis due to electrolyte-water coupling is generally small, the coupling terms aid in correlation of membrane transport data. The use of activity differences in place of concentration differences as driving forces contributes to better data correlation.

Membrane Potentials and Transport Parameters for Alkali and Alkaline Earth Chlorides across Cellulose Acetate Membranes

“…The data are plotted in Figures 5-8 in the manner described in previous publications (Bennion and Rhee, 1969;Johnson and Bennion, 1968; Osborn and Bennion, 1971;and Re and Bennion, 1973). The slopes in Figures 5 and 6 are the salt diffusion parameters, Le, and the intercepts are the coupling parameters Leo-The slopes in Figures 7 and 8 are the water diffusion parameters, Lq, and the intercepts are the coupling parameters Loe.…”

“…There have been a number of equations proposed, using various theoretical bases, to predict or at least correlate transport rates of ions and water across cellulose acetate membranes. Comparisons of various approaches have been summarized elsewhere (Osborn and Bennion, 1971; Choi and Bennion, 1973). It has often been convenient to place the various models into two categories.…”

Relative Mobilities of Alkali Cations in Modified Cellulose Acetate Membranes

“…A number of investigators have proposed equations and associated parameters which describe the flux of solvent and solute through cellulose acetate membranes. A critical summary of some of these equations has been presented by Osborn and Bennion (1971). Mathematical treatment of nonhomogeneous membranes have been presented elsewhere (Jagur-Grodzinski and Kedem, 1966; Kedem and Katchalsky, 1963).…”

Relative Transport Rates of Alkali Ions across Modified Cellulose Acetate Membranes

“…As an alternative way of describing flux equations, Spiegler (1958), Kedem and Katchalsky (1961), Wills and Lightfoot (1966), and Bennion (1966) developed flux equations by applying irreversible thermodynamic principles to the membrane-water-electrolyte system. A comparison of these various models was summarized by Osborn and Bennion (1971).…”