Effect of the mobility parameter on the oscillatory electro-convection of dielectric liquids subject to strong unipolar charge injection

Two-dimensional numerical calculations were carried out for the isothermal electro-convection in a dielectric liquid induced by the unipolar charge injection. In the dimensionless form, the system is mainly governed by the injection strength number (C), the electric Rayleigh number (T) and a mobility number (M). A strong injection case with C = 10 was considered. Along with the increase of the driving parameter T, oscillatory electro-convection occurs. Critical values of T corresponding to the onset of such oscillatory convection were shown to be highly dependent on M, and were accurately determined. Some precautions including the algorithm for the charge density equation were taken to reduce the numerical diffusion and to ensure the reliability of our findings.