EHD convection in an enclosed rectangular domain

In this work, we present the results of numerical simulations of the EHD convection between parallel plates in a rectangular domain with no-slip boundary conditions at all the walls. The electroconvection between parallel plates in an infinite domain is a classic EHD problem. Experimental, theoretical and numeric studies show that when a high enough voltage is applied across the plates, the liquid is set into motion. The nature of the bifurcation is subcritical. A roll pattern is established where the maximum velocity of the liquid is higher than the drift velocity of the ions. As a consequence, regions voided of electric charge appears in the bulk. However, when the domain is enclosed by rigid walls, the nature of the bifurcation changes, becoming supercritical. Stable velocity rolls with a maximum velocity smaller than the drift velocity of the ions are possible. We present a numeric analysis of these new phenomena. The physical mechanism which leads to this situation is analyzed and discussed. The evolution of the bifurcation diagrams with the aspect ratio of the cavity is also provided and analyzed.