Flows Through Charged Membranes. I. Flip-Flop Current vs Voltage Relation

Flow processes in a (porous) charged membrane separating two solutions of different concentration of the same electrolyte are studied theoretically, using a capillary model for the membrane and the Debye—Hückel approximation for the calculation of ion distributions in the double layer formed near fixed charges on the capillary wall. Steady-state solutions to the continuity equations derived are obtained subject to the external conditions that there is the passage of a constant forced electric current I through the membrane, the salt concentrations on both sides of the membrane are held constant, and a constant pressure is imposed on the more concentrated solution. The results yield a characteristic I vs transmembrane potential Δφ relation, which consists of two nearly straight lines of different slopes involving a discontinuous transition between them. This feature well compares to the experimental data obtained recently by Tasaki et al. with sintered glass membranes and thought by them to be significance in relation to the physiology of nerve excitation. It is shown that, in the framework of the theory presented, the occurrence of a discontinuous change in I at a certain particular potential mainly stems from the dependence of the electro-osmotic coefficient on salt concentration. The probable causes for the discrepancies between theory and experiment are discussed briefly.