The Hydrodynamic Solution for Flow Profiles in a Binary Strong Electrolyte Solution Under an External Electric Field

TL;DR

This paper explicitly calculates the velocity profiles of ions in a strong binary electrolyte under an electric field using hydrodynamic equations, providing insights into ionic movement and addressing mathematical challenges in the theory.

Contribution

It offers a complete hydrodynamic solution for flow profiles in electrolyte solutions under electric fields, overcoming divergence issues in previous theoretical approaches.

Findings

Explicit velocity and pressure profiles are derived.

Numerical examples illustrate ionic flow behavior.

Potential methods to eliminate divergence in calculations are discussed.

Abstract

In this paper, we follow the general idea of the Onsager--Wilson theory of strong binary electrolyte solutions and completely calculate the velocity profile of ionic flow by first formally solving the hydrodynamic (Stokes) equation for the ionic solutions subjected to an external electric field by a Fourier transform method and then explicitly evaluating the formal Fourier transform solutions as functions of spatial positions and field strength. Thus the axial and transversal components of the velocity and the accompanying nonequilibrium pressure are explicitly obtained. They are rare examples for solutions of a hydrodynamic equation for flow in an external electric field. The present results make it possible to investigate ways to overcome the mathematical difficulty (divergence) inherent to the method of evaluating the formal solutions that Wilson used in his dissertation on the conductance theory (namely, the Onsager--Wilson theory) for strong binary electrolytes. Some examples for the velocity profiles are numerically computed. They show how ions might move in the ionic solution under an external electric field. A possible way to get rid of the divergence causing terms for the electrophoretic effect is examined. In the sequels, the results obtained in this work will be applied to study ionic conductivity and related transport processes in electrolyte solutions.