Thermo-electrohydrodynamic convection in a differentially heated vertical slot

Abstract

International audienceApplication of a high-frequency a.c. electric field to a non-isothermal layer of dielectric fluid generates convective flow though the Thermo-Electrohydrodynamic (TEHD) instability. The driving force is dielectrophoretic (DEP) one, which arises from the thermal variation of dielectric permittivity $\epsilon$. This convection has attracted geophysicists' interest, as the DEP force can be regarded as thermal buoyancy force in an electric effective gravity $\mathbf{g}_e \propto \boldsymbol{\nabla}\mathbf{E}^2$, where $\mathbf{E}$ is the applied electric field. One can simulate thermal convection under different gravity conditions through this analogy by using different geometrical configurations of electrodes. In particular, the analogy enables us to examine global scale geophysical flows in a laboratory experiment with concentric spherical electrodes, e.g., Mantle convection considered in the GeoFlow experiments.A number of theoretical, numerical, and experimental investigations have been done recently in different electrode configurations. In the present talk, we report a theoretical study on the TEHD convection for moderate Prandtl number fluids ($Pr \lesssim 10$) in a tall vertical slot, where the lateral walls serve as planar electrodes imposing a temperature gradient as well as an electric field to a fluid layer. If both Grashof and electric Rayleigh number, $Gr=\alpha\Delta T g d^3/\nu^2$ and $L=\alpha\Delta T {\rm g}_e d^3/\nu\kappa$, respectively, are small, the flow system is in conduction regime, where natural convection develops to form a vertical shear flow except in the regions near the top and bottom walls. Either $Gr$ or $L$ exceeds a critical value, instabilities arise and a cellular secondary flow develops. The flow state in this convection regime is determined by seeking numerically an exact solution of governing nonlinear equations in the Fourier-Chebyshev spectral space. The flow behavior in the vicinity of the critical state is determined by following the path of solution in the $Gr$-$L$ phase space. The Nusselt number $Nu$ is computed to show that the Earth's gravity affects significantly the heat transfer in the TEHD convection