Stokes’s stream functions for ion association and dissociation in weak electrolytes

Abstract

The brownian motion theory of ion flow in a weak electrolyte that has attained a steady state in the presence of a uniform applied electric field is reformulated in terms of a Stokes stream function. The Stokes stream function describing the process of ion association is first derived and the equation of the streamlines and the association constant are obtained. The Stokes stream function describing the process of ion dissociation is then calculated with the aid of the solution of Onsager ( J . Chem . Phys . 2, 599-615 (1934)) for the ion-pair distribution function and the equation of the streamlines and the dissociation constant are found. An alternative derivation of the Stokes stream function for ion dissociation is presented by solving directly the second-order partial differential equation for the stream function. This derivation of the Stokes stream function yields the ion-pair distribution function in the process of the analysis and therefore provides an alternative method of solution for the ion-pair distribution function.