Ionization, ion recombination, and the transport of steady state electric current in low dielectric constant fluids

Abstract

The equations of transport of ions by conduction and diffusion in a low dielectric constant fluid contained between two infinite parallel plate electrodes are derived and solved. Ions are assumed to be generated uniformly at a constant rate in the fluid and consumed by recombination and by discharge at the electrode surfaces. The fourth order, non-linear differential system is solved numerically for several values of the parameters of the problem, to yield charge and concentrations as functions of position. The current against applied potential relationship is obtained from the solutions and is depicted graphically.

At low applied potential difference the current is proportional to the difference, although the conduction process, in general, is non-ohmic. When the ionization rate is large enough the conduction begins to approach ohmic conduction, however. At higher applied potential differences the current reaches a maximum value, limited by diffusion. The limiting current is smaller than that determined from solution of the equations with neglect of diffusion.