Quantifying the linear stability of a flowing electrified two-fluid layer in a channel for fast electric times for normal and parallel electric fields

Motivated by the destabilization of a two-fluid layer flowing in a microchannel for efficient mixing or droplet formation, we study quantitatively the linear stability of the interface between two liquids subjected to an electric field parallel or normal to the flat interface. In the case of fast electric charge relaxation times, the equations for the perturbation can be significantly reduced [A. K. Uguz, O. Ozen, and N. Aubry, Phys. Fluids 20, 031702 (2008)]. Using a simple argument and without solving the equations, Uguz et al. determined the range of parameters over which the electric field is destabilizing, which is narrower for the parallel compared to the normal electric field. However, the argument of Uguz et al. was not amenable to the calculation of growth rates and neutral stability curves. In this paper, by solving the equations, we not only confirm the previous findings but also determine the quantitative linear stability properties, namely, the growth rates and neutral stability curves. Depending on the value of the physical parameters and when both the normal and parallel electric fields lead to instability, it is found that for the same electric potential gradient either the normal or the parallel electric field leads to the largest maximum growth rate. This result should be of interest for experimental purposes. (C) 2008 American Institute of Physics.