Charge diffusion versus Coulomb repulsion in finite amplitude electroconvection

The influence of charge diffusion on the nonlinear stability criterion and subsequent finite-amplitude electroconvection of an isothermal liquid layer subjected to weak unipolar injection is examined. It is shown that the solution, determined using a two-dimensional flux corrected transport algorithm, is a function of a nondimensional parameter, namely, the ratio of Coulombic repulsion to charge diffusion. Unless the parameter is >>1, diffusion has to be included. For small values of the parameter the nonlinear criterion approaches the linear one, thus substantially reducing the amplitude of the liquid velocity near the onset of convection.<>