Electroviscoelastic Instability of a Kelvin Fluid Layer Influenced by a Periodic Electric Force

The electroviscoelastic stability of a Kelvin fluid layer is discussed in the presence of the field periodicity. The surface elevations are governed by two transcendental coupled equations of Mathieu type which have not been attempted before. Analysis for the surface waves in axisymmetric modes and antisymmetric deformation which are governed by a single transcendental Mathieu equation is considered. The method of multiple scales expansion is applied to the stability analysis. The solution and the characteristic curves are obtained analytically. It is shown that the region between the two branches of the characteristic curves is unstable, whereas all points which lie outside the characteristic curves are stable. The special case of large viscosity is introduced for numerical calculations. It is found that the increase of kinematic viscosity, field frequency, and the elasticity parameter possesses a dual role in a damping nature. The phenomena of the coupled resonance is observed. The resonance region and the resonance points are functions of viscosity, elasticity, and field frequency, with nonlinear relations in the wavenumber. Copyright 1998 Academic Press.