  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.
