Direct numerical simulation of the subcritical electroconvective instability in a dielectric liquid subjected to strong or weak unipolar injection

Abstract

This work addresses the characterization of the subcritical electroconvection instability that occurs in a plane layer of a dielectric liquid subjected to both strong and weak unipolar injections. Transient evolutions of electrohydrodynamic convection in a dielectric liquid between two parallel plates are analysed numerically to best determine the linear and non linear instability criteria, Tc and Tf, respectively. In strong injection as well as in weak injection the linear stability parameters Tc that we obtained by direct numerical simulations are very close to the ones predicted by the stability analysis. However, in both strong and weak injections, it is shown that the non linear criterion Tf provided by the stability analysis or the available analytical models differs from the one obtained from direct numerical simulation. These discrepancies are analysed and explained. In particular, in the case of weak injection the inertial terms play an important role in the development of the flow structure. This is reflected in a dependence of Tf on M, a dependence that has not been modelled by any analytical o semi-analytical approach, of the type of Felici hydraulic model. In this paper we put a particular emphasize on numerical computations in weak injection. We have successfully made computations for small values of the mobility parameter M in weak injection, computations that demand a very efficient numerical code. For M=5 and M=10 a steady convective regime has been captured. In the vicinity of M=15 the flow exhibits a perfect periodic regime with a well defined fundamental frequency while for M above 20 the flow is unsteady and turns out to be chaotic for higher values.