Stability analysis of electroconvection with a solid-liquid interface via the lattice Boltzmann method

In this paper, the electroconvective flow induced by the unipolar charge injection is extended from single-phase dielectric liquid to the solid-liquid interaction problem. The physical model with fully coupled mathematical equations is built in the liquid, solid, and interface for both the Ohmic and non-Ohmic solid models. An improved lattice Boltzmann model (LBM) is developed with three lattice Boltzmann equations for Poisson's equation, charge conservation equation, and Navier-Stokes equations, respectively. Our codes are first validated by the analytical solutions at the hydrostatic state. It is found that the LBM can well reproduce the discontinuous changes of electrical field and charge density at the interface and agrees well with the analytical results. Then, simulations are conducted under different governing parameters and interface position fl. Results show that the bifurcation of electroconvection in the presence of the solid-liquid interface is still of subcritical type, but both the linear and finite amplitude stability criteria increase due to a voltage drop happening at the solid phase. Besides, the stability criterion expressed by the electrical Rayleigh number Tc increases as the permittivity ratios Er and the mobility ratios Kr increase, but Tc decreases with the increasing of dimensionless electric conductivity S and the interface position fl.