The electrical conductance of semipermeable membranes III. bipolar flow-symmetric electrolytes

The first paper of this series presented a general formulation of the problem of stationary ion flow through membranes. The second treated in detail the special case of unipolar flow across membranes separating symmetric electrolytes. In this, the third paper of the series, we deal with another special case, that of bipolar flow between symmetric electrolytes. Here it is assumed that the total current is carried by both positive and negative permeant ions. The restriction to symmetric electrolytes implies that all ions present in the membrane and surrounding solutions have valences of identical absolute magnitude. After extracting from the general development a set of equations appropriate to the special case being considered, we outline a procedure for the numerical solution of the conductance problem for this case. Numerical results, presented as part of a discussion of approximate analytic methods of solution, establish the utility of these methods. A discussion of the significance of this work for membrane studies is presented in conclusion.