Non-linear hydrodynamic stability of liquids subjected to unipolar injection

The phenomena occurring near the onset of instability of a layer of insulating liquid subjected to a unipolar injection are investigated both theoretically and experimentally. A simplified model and a nonlinear analysis based on the Galerkin method predict the existence of a nonlinear stability criterion lower than the linear one and, therefore, of a hysteresis loop associated with discontinuities of the steady current and liquid velocity at both criteria. Furthermore they give a justification for the appearance of hexagonal convective cells at critical voltage. Experiments performed with various liquids under space-charge-limited current conditions exhibit the predicted characteristics.