Membrane potential in charged porous membranes

For charged porous membranes, the separation efficiency to charged particle s and ions is affected by the electrical properties of the membrane surface . Such properties are most commonly quantified in terms of zeta-potential. In this paper, it is shown that the zeta-potential can be calculated numeri cally from the membrane potential. The membrane potential expression for ch arged capillary membranes in contact with electrolyte solutions at differen t concentrations is established by applying the theory of non-equilibrium t hermodynamic to the membrane process and considering the space-charge model . This model uses the Nernst-Planck and Navier-Stokes equations for transpo rt through pores, and the non-linear Poisson-Boltzmann equation, which is n umerically solved, for the electrostatic condition of the fluid inside pore s. The integral expressions of the phenomenological coefficients coupling t he differential flow (solute relative to solvent) and the electrical curren t with the osmotic pressure and the electrical potential gradients are esta blished and calculated numerically. The mobilities of anions and cations ar e individually specified. The variations of the membrane potential (or the apparent transport number of ions in the membrane pores) are studied as a f unction of different parameters: zeta-potential, pore radius, mean concentr ation in the membrane, ratio of external concentrations and type of ions. ( C) 1999 Elsevier Science B.V. All rights reserved.