The relation between surface charges and viscosity in interfacial stability influenced by a periodic electric force

Abstract

The stability of an electrified Rayleigh--Taylor problem under the influence of a periodic vertical electric field producing surface charges on the interface between two viscous fluids is investigated. The effects of surface tension, viscosity and gravity on the critical surface charge density and on the corresponding electric field are analyzed. The contribution of viscosity to the existence of surface charges on the interface is discussed. It is found that the surface charge density vanishes when the value of the viscosity ratio approaches one. In the case of a constant surface charge, viscosity seems to stabilize the flow as the viscosity ratio \(\mu\) differs from the critical value \(\mu = 1\). In the presence of a periodic field both the surface charge density and the viscosity enter in the stability criterion. The field frequency counteracts the destabilizing effect of surface charges at the critical value \(\mu = 1\). Furthermore, surface charge density is affected by the viscosity.