Monotonic instability and overstability in two-dimensional electrothermohydrodynamic flow

Electrothermohydrodynamic convection driven by strong unipolar charge injection in the presence of a stabilizing inverse thermal gradient between two parallel electrodes is investigated by a linear stability analysis and a numerical simulation. The generalized Schur decomposition is used to solve for the eigenvalues of the linearized system revealing the critical parameters. The two relaxation time lattice Boltzmann method coupled to a fast Poisson solver is used to resolve the nonlinear system for the spatiotemporal distribution of flow field, electric field, charge density, and temperature. With strong charge injection and high electric Rayleigh number, the system exhibits electrothermoconvective vortices. The interactions between the stabilizing buoyancy force and the destabilizing electric force lead to overstability, where the flow constantly oscillates when instability evolves. A two-stage bifurcation is observed for overstability near the threshold Rayleigh number with a significant change in phase and amplitude. The effects of ion mobility and thermal diffusivity are characterized by the ratio of the counteracting forces.