A dissociation-injection model for non-polar liquid conduction and wire-cylinder geometry

The conduction of a nonpolar liquid filling a cylindrical capacitor has been investigated with a model that includes both the dissociation of ionic pairs in the bulk of the liquid and charge injection at the inner electrode. Three different cases, of increasing complexity, have been analyzed. Firstly, injection has been neglected and the dissociation rate has been taken as constant. Then, the effect of the electric field on the dissociation rate has been considered. And, finally, a field dependent injection of charge has been also included in the model. The current voltage characteristics corresponding to these three models have been evaluated for different ratios of the electrodes radii. Approximate analytical expressions are provided for the charge density and electric field distributions over a wide range of parameters of physical interest.