Wien Effect on Ionic Conductance of Binary Strong Electrolyte Solutions in a High External Electric Field

TL;DR

This paper applies an exact solution of the Stokes equation to analyze the Wien effect on ionic conductance in high electric fields, improving divergence issues and aligning well with experimental data.

Contribution

It introduces a divergence-free method to compute electrophoretic and relaxation time coefficients, enhancing the theoretical understanding of ionic conductance under high electric fields.

Findings

Accurately predicts ionic conductance of magnesium sulfate in high fields.

Improves upon Wilson's theory with better agreement to experimental data.

Provides insights into ion atmosphere motion and nonequilibrium liquid structure.

Abstract

In the preceding paper, the exact solution of Stokes equation was obtained for a binary strong electrolyte solution in an external electric field. In the present paper, the solution is applied to calculate the Wien effect on deviation from the Coulombic law of conduction in high fields. One of the important aims of the present line of work was in removing or avoiding the divergence difficulty in calculating the electrophoretic and relaxation time coefficients. The present work achieves that aim by calculating on the basis of computing the axial velocity profiles the position of the center of the ion atmosphere as a function of the reduced field strength and therewith computing the electrophoretic and relaxation time coefficients for the migrating spherical ion atmosphere at each value of the reduced field strength. With the electrophoretic and relaxation time coefficients thus calculated along the trajectory of the center of the ion atmosphere with regard to the reduced field strength, the equivalent ionic conductance of a magnesium sulfate solution is calculated and compared with experimental data in very good accuracy. It is also compared with the prediction by Wilson's theory and is found very much improved over the latter. Moreover, the present method is divergence-free unlike Wilson's theory. It therefore not only sheds a new light on the nonequilibrium liquid structure of ionic solutions and the motion of ion atmosphere in an electric field, but also shows how the Onsager--Wilson theory of conductance in electrolyte solutions should be applied to account for the Wien effect on ionic conductance.