Numerical computation of electrohydrodynamic motions of liquids subjected to unipolar injection

The application of a step voltage on a dielectric liquid confined between two plane parallel electrodes and subjected to an unipolar injection can give rise to an electrohydrodynamic (EHD) instability. The evolution of liquid motion and electrical charge distribution is obtained by numerically solving the governing equations. The equations are expressed in a 2-D vorticity-stream formulation and discretized with a group finite element scheme. Evolution from an initial perturbation shows that two different mechanisms of instability are involved in the transition from the liquid at rest to stable convective cells