Membrane Transport Characteristics of Ultrafine Capillaries

Abstract

A detailed study and further development of the capillary model for charged wide-pore membranes is presented. Previous work on this model has either linearized the Poisson–Boltzmann equation and/or assumed a small Debye length-to-tube-radius ratio, or ignored axial concentration gradients. None of these simplifications are made here. The problem is characterized by a set of nine coefficients coupling the various transport phenomena. We establish these coefficients and combine them to form “figures of merit” which describe the energy conversion capability of the membrane in its various conversion modes. The capillary membrane is found to be considerably more efficient in electrodialysis than in either osmosis or electro-osmosis.