Onset of convection in a finite two-dimensional container due to unipolar injection of ions

This work addresses the stability of a two-dimensional plane layer of a dielectric liquid enclosed in wall bounded cavities of different aspect ratios and subjected to unipolar injection of ions. Numerical simulations have been conducted to investigate the effect of lateral walls, especially in the development of the electroconvective instability. It is found that an unexpected change of the bifurcation nature occurs for certain cavity aspect ratios. We show that above the linear stability threshold for the rest state a supercritical bifurcation arises. This bifurcation takes place at a given value T_c¹ of the parameter T (the electric Rayleigh number). Then, a second subcritical bifurcation occurs at a second threshold T _c², featuring a typical hysteresis loop with an associated nonlinear criterion T_f, which is very characteristic of the Coulomb-driven convection. This behavior has been confirmed by different numerical codes based on different numerical methods. 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.