Electrohydrodynamic Stability of Two Superposed Viscous Fluids

Abstract

The electrohydrodynamic stability of a conducting viscous incompressible fluid topping a streaming dielectric viscous incompressible fluid layer is studied. The stability of the system in the general case for quadratic velocities is discussed, and the numerical calculations of the eigenvalue problem for long waves show that the normal electric field has a destabilizing effect and the effect of the electric field is greatly reduced by the increase of the thickness of the lower layer. The stability also depends on the velocity stratification. The special cases of plane Couette-Poiseuille flow of two superposed layers of fluids of different viscosities between two horizontal plates are considered. It is found that both plane Poiseuille and plane Couette flow can be unstable however small the Reynolds number is. The stability of the system is also examined for two cases by solving the eigenvalue problem for small Reynolds number. In the first case when the lower fluid is heavier than the upper one, the destabilizing influence of the electric field is observed. It is also reported that the critical potential is smaller for larger wavenumber α. For a given value of α(=α c ) the system is unstable even in the absence of electric field. The stable regions are enlarged by the increase of the depth ratio n. In the second case with equal densities, although the electric field behaves in a similar manner as in the previous case, the instability onset is faster because the critical values α c are smaller for this case.