Forced diffusion model for dark currents in low-conductivity fluids

An analysis of the potential and field profiles in low-dielectric constant liquids, where ions are thermally generated and recombine bimolecularly under applied voltage, is presented. The forced-diffusion model, which is described by a set of nonlinear differential equations, is solved numerically for a symmetrical case where the parameters of the positive and negative ions are equal. The solutions show a significant departure from the geometrical-potential distribution and the boundary conditions used lend themselves easily to generalization, which can include ion-injection and electron-transfer mechanisms.