1993

In this thesis, we investigate three fluid dynamic problems involving various physical mechanisms which exhibit inter-facial instability. These problems have wide ranging industrial, scientific and engineering applications.

In the first problem, we investigate the linear stability of the unbounded Couette flow of two fluids separated by a plane interface. The exact dispersion relation is solved asymptotically and numerically to analyze the effects of the four stability prarmeter of the flow; the ratio of the viscosities, the ratio of the density, the surface tension and gravity. While our results confirm most of the earlier reported theories involving shear flows of fluids of equal densities, they also resolve the reported discrepancies between the numerical and the asymptotic solutions. For the general case of fluids with different densities, new asymptotic expressions for the growth rates of the flow are obtained and numerical calculations of marginal states are carried out in order to examine the effects of the stability parameters on the flow. The numerical results confirm the remarkable accuracy of our asymptotic expressions.

In the second problem, the electrohydrodynamic extension of the first problem is presented. Here, the plane interface is stressed by applying external electric fields normal to the interface. A linear stability analysis similar to that employed in the first problem is used to investigate the effects of six addition stability parameters on the stability of the flow; the ratio of the permitivities, the two conductivities, the two initial electric fields and the velocity of the upper fluid in the unperturbed motion. Various limiting cases having practical applications are investigated. We examine the effects of the electrical shear stresses and the initial streaming of the fluids on the onset of static instability. We also examine finite electric charge relaxation effects.