On the Onsager--Wilson Theory of Wien Effect on Strong Binary Electrolytes in a High External Electric Field

TL;DR

This paper critically re-examines the Onsager--Wilson theory of the Wien effect in strong electrolytes, addressing divergence issues in integral evaluations and providing alternative exact solutions to improve the theoretical understanding.

Contribution

It identifies divergence problems in Wilson's original integral evaluations and offers exact alternative solutions, enhancing the theoretical framework of the Wien effect.

Findings

Identified divergence in Wilson's flow velocity integrals.

Provided alternative exact evaluations of problematic integrals.

Laid groundwork for improved Wien effect conductivity formulas.

Abstract

In this review paper, we present and critically re-examine the formal expressions for the electrophoretic effect and the ionic field appearing in the unpublished Yale University PhD dissertation of W. S. Wilson which form the basis of the Onsager--Wilson theory of the Wien effect in the binary strong electrolyte solutions. It is pointed out that some of the integrals that make up the flow velocity formula obtained in the thesis and he evaluated at the position of the center ion in the ionic atmosphere (i.e., the coordinate origin) diverge. Therefore they cannot be evaluated by means of contour integrals in the manner performed in his thesis for the reason pointed out in the text of this paper. In this paper, the results for the integrals in question are presented, which are alternatively and exactly evaluated. The details will be described in the follow-up paper presented elsewhere together with the improved formula for the Wien effect on conductivity.