Nonlinear Electrohydrodynamic Stability of Cylindrical Structures

Abstract

This thesis is mainly concerned with the nonlinear electrohydrodynamic stability of a system of two conducting incompressible fluids under different electric conditions. Studying motion of inviscid fluids in cylindrical coordinate systems is the main objective of this work. \\e have studied the equations of motion for the system and the perturbation equations, by using the method of multiple scales to solve the boundary value- problem. This thesis consists of five chapters:

The first chapter is an introductory one, it is devoted to make a review of the previous studies of electrohydrodynamics. It shows all the mathematical background, concepts, principles and tools on which the subject is based. In chapter two, the problem of nonlinear electrohydrodynamic stability of a cylindrical interface, between two infinite conducting and incompressible fluids under the influence of an axial electric field, is studied. The fluids have the fom1 of coaxial cylindrical shells of different thicknesses in the absence of gravity. The including of the effect of the surface tension between the two fluids, bounded by dielectric central core and rigid cylinder, is considered. \\e studied the equations of motion for the system and the related boundary conditions. We use the method of multiple scales to expand various perturbation quantities to obtain uniformly valid expansions. In the linear stability theory, a dispersion relation that accounts the growth waves is derived. It is found that the uniform axial electric field plays a dual role in the stability picture.