Space-charge-limited current flow in a spherical double sheath

Abstract

The solutions presently obtained for counterflowing, space charge-limited negatively and positively charged particle currents between two spherical surfaces indicate that the current magnitudes exhibit the usual 3/2-power dependence on driving potential difference and square root dependence on particle charge/mass ratio. The magnitude of either current strongly depends on the radius ratio of the two spherical surfaces, while the relative magnitudes of the two counterflowing currents are related by the square root of the mass ratio of the two charged particle species and a radius ratio factor that lies in the 0.1-1.0 range.