Electrohydrodynamic motion due to space-charge limited injection of charges in cyclohexane

Abstract

A self-consistent numerical model is presented in order to study the electrohydrodynamic (EHD) motion generated by a stationary, space-charge limited injection of charge in the point-plane geometry. In this multiphysics model, the continuity equations for charge carriers and Poisson's equation are coupled with Navier-Stokes equations and the heat equation. This model is used to study the EHD motion of cyclohexane in the negative point-plane geometry for sharp points with tip radius of 0.2 μm. It is shown that the injection of charges from a very sharp point electrode results in the formation of a thin plume with high liquid velocity. The results show large differences in the liquid velocity close to the point electrode compared to the average velocity estimated by the well-known electrohydrodynamic mobility. The difference between the width of the charged core and the hydrodynamic plume is analyzed and presented. It is shown that the local heating of the liquid is strongly reduced by the convective losses generated by EHD motion. Finally, it is found that the liquid temperature in cyclohexane in the vicinitiy of sharp points under space charge limited injection can reach temperatures slightly above boiling temperature, without generating bubbles.