Electroconvection between coaxial cylinders of arbitrary ratio subjected to strong unipolar injection

• We investigate numerically the phenomenon of electroconvection.
• We study the stability of an annular layer subjected to an electric field.
• We show the appearance of a multicellular flow.
• We analyze the effect of the radius ratio on the flow and electric charge distribution.

This study deals with the electroconvection phenomenon that takes place in a dielectric liquid layer placed between two annular electrodes and subjected to the action of an electric field.The full set of governing equations describing the combined Electro-Hydro-Dynamic (EHD) flow is directly solved with the finite volume method.The development of electroconvective motion is investigated in details in the case of strong injection when the emitter electrode is the inner cylinder.We first examine the stability of such flow. As in the plane–plane configuration we have highlighted the existence of a linear and non-linear critical electric Rayleigh numbers giving rise to a hysteresis loop. The flow structure under the effect of the electric field is analyzed and the distribution of electric charge density is presented. In particular we investigate the effect of various parameters involved in this configuration, such as the radius ratio, injection strength and electric Rayleigh number.A multicellular convective pattern is particularly observed and it is shown that the number of cells is increased when the annular gap is narrower. Finally a significant increase of the rotational speed of the vortex with the electric Rayleigh number is recorded.