Numerical analysis of the stability of the electrohydrodynamic (EHD) electroconvection between two plates

The time evolution of the problem of electrohydrodynamic convection in a liquid between two plates is analysed numerically. The equations are non-dimensionalized using the ion drift velocity and the viscous time scales. Following the non-dimensionalization of the respective model, two different techniques have been used to describe the charge evolution, namely, the finite-element flux-corrected transport method and the particle-in-cell technique. The results obtained with the two schemes, apart from showing good agreement, have revealed the appearance of a two-roll structure not described in previous works. This is investigated in detail for both strong and weak injection.