The linear stability between a Newtonian and a power-law fluid under a normal electric field

Abstract

In this paper, the linear stability of the interface between a Newtonian and a power-law fluid flowing in a microchannel subjected to an electric field applied normal to the flat interface is studied. The fluids are assumed to be immiscible, incompressible and leaky dielectric. The instability may arise due to different mechanisms; such as, the jumps in the electrical properties of the fluids, the non-Newtonian characteristic of the fluid that is demonstrated via the power-law index, and the viscosity stratification. In addition to these three mechanisms, the strength of the base flow plays an important role in determining the stability as opposed to the Newtonian/Newtonian fluid system. The aim of this paper is to investigate the effect of the interaction of these modes of instabilities through dispersion and neutral stability curves. For this purpose, the effects of the applied voltage observed through the electric number, the viscosity and the thickness ratios, the power-law index and the base flow strength are studied. For fast charge relaxation times, an analytical expression for the effect of the electric number is obtained. It can either have a stabilizing or a destabilizing effect similar to the Newtonian/Newtonian system. Lastly, it is found that for fast charge relaxation times, the kinematic condition is the main reason for the instability. Otherwise, for a general case, both the kinematic and the interfacial charge distribution are the dominant sources of instability.