Electrohydrodynamic instability of a rotating couple stress dielectric fluid layer

Abstract

The simultaneous effect of rotation and a vertical AC electric field on the onset of electrohydrodynamic instability in a horizontal couple stress dielectric fluid layer caused by the dielectrophoretic force due to the variation in the dielectric constant with temperature is investigated. The boundaries of the fluid layer are considered to be either free–free or rigid–rigid or lower rigid–upper free which are either isothermal or insulated to temperature perturbations. The resulting eigenvalue problem is solved exactly for free-free isothermal boundaries. It is observed that oscillatory convection is not a preferred mode of instability as far as the dielectric fluids are concerned and the necessary conditions for its occurrence are found to be independent of applied vertical AC electric field. For the other combinations of velocity and temperature boundary conditions, the problem is solved numerically using the Galerkin method. In contrast to the non-rotating case, it is shown that a rotating fluid layer becomes destabilizing in the presence of couple stress for all the boundary conditions considered. The effect of increasing AC electric Rayleigh number is to increase the transfer of heat more effectively and hastens the onset of convection, while rotation inhibits the onset of electrohydrodynamic instability. Although the rigid-rigid boundaries enhance the stability when compared to free-free boundaries up to certain values of Taylor number, the situation gets reversed at high Taylor number domain which in turn depends on the value of couple stress parameter and boundary conditions. Isothermal boundaries display more stabilizing effect than insulated ones.