Electrohydrodynamic Instability in a Viscoelastic Liquid Layer

The problem of the onset of instability in a horizontal layer of viscoelastic dielectric liquid under the simultaneous action of a vertical ac electric field and a vertical temperature gradient is analyzed. Applying linear stability theory, an equation of eighth order is derived. Under somewhat artificial boundary conditions, this equation can be solved exactly to yield the required eigenvalue relationship from which various critical values are determined in detail. It is shown that oscillatory modes of instability exist only when the thickness of the liquid layer is smaller than about 0.5 mm and for such a thin layer the force of electrical origin is much more important than buoyancy force.