 1  Author
 Mohamed Fahmy, ElSayed  Requires cookie*   Title
 Electrohydrodynamic Interfacial Stability Conditions in the Presence of Heat and Mass Transfer and Oblique Electric Fields    Abstract
 A novel mathematical formulation to deal with interfacial stability problems of the KelvinHelmholtz type with heat and mass transfer in the presence of oblique electric fields is presented. The perturbed system is composed of two homogeneous, inviscid, incompressible, dielectric, and streaming fluids separated by a horizontal interface, and bounded by two rigid planes. The effect of a phase transition on the instability is considered, and the linear dispersion relations are obtained and discussed. It is found that the electric field has a major effect and can be chosen to stabilize or destabilize the flow. For RayleighTaylor instability problems of a liquidvapor system it is found that the effect of mass and heat transfer enhances the stability of the system when the vapor is hotter than the liquid, although the classical stability criterion is still valid. For KelvinHelmholtz instability problems, however, the classical stability criterion is found to be substantially modified due to the effects of the electric field, mass and heat transfer. A new stability condition relating the magnitude and orientation of the electric field and the dielectric constants is obtained. Oblique electric fields are found to have stabilizing effects which are reduced by the normal components of the electric fields. The effects of orientation of the electric fields and fluid depths on the stability configuration are also discussed.   
Reference
 Z. Naturforsch. 54a, 470—47665 (1999); received June 9 1999   
Published
 1999   
Keywords
 Hydrodynamic Stability, Convection and Heat Transfer, Electrohydrodynamics   
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2  Author
 Mohamed Fahmy, ElSayed  Requires cookie*   Title
 Electrohydrodynamic KelvinHelmholtz Instability of Two Rotating Dielectric Fluids    Abstract
 A linear stability analysis of a novel electrohydrodynamic KelvinHelmholtz system consisting of the superposition of two uniformly rotating dielectric media is presented. The characteristic equation for such an arrangement is derived, which in turn yields a stability criterion for velocity differences of disturbances at a given rotation frequency. The conditions of stability for long and short wave perturbations are obtained, and their dependence on rotation, surface tension and applied electric field is discussed. Limiting cases for vanishing fluid velocities, rotation frequency, and applied electric field are also discussed. Under suitable limits, results of previous works are recovered. A detailed analysis for tangential and normal applied electric fields, in the presence and absence of surface charges, is carried out.   
Reference
 Z. Naturforsch. 53a, 17—26 (1998); received February 27 1997   
Published
 1998   
Keywords
 Hydrodynamic Stability, Electrohydrodynamics, Interfacial Instability, Rotational Flows, Dielectric Fluids   
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3  Author
 M. F. ElSayed, D. K. Callebaut  Requires cookie*   Title
 Nonlinear Electrohydrodynamic Stability of Two Superposed Bounded Fluids in the Presence of Interfacial Surface Charges    Abstract
 The method of multiple scales is used to analyse the nonlinear propagation of waves on the interface between two superposed dielectric fluids with uniform depths in the presence of a normal electric field, taking into account the interfacial surface charges. The evolution of the amplitude for travelling waves is governed by a nonlinear Schrödinger equation which gives the criterion for modulational instability. Numerical results are given in graphical form, and some limiting cases are recovered. Three cases, in the pure hydrodynamical case, depending on whether the depth of the lower fluid is equal to or greater than or smaller than the one of the upper fluid are considered, and the effect of the electric field on the stability regions is determined. It is found that the effect of the electric field is the same in all the cases for small values of the field, and there is a value of the electric field after which the effect differs from case to case. It is also found that the effect of the electric field is stronger in the case where the depth of the lower fluid is larger than the one of the upper fluid. On the other hand, the evolution of the amplitude for standing waves near the cutoff wavenumber is governed by another type of nonlinear Schrödinger equation with the roles of time and space are interchanged. This equation makes it possible to determine the nonlinear dispersion relation, and the nonlinear effect on the cutoff wavenumber.   
Reference
 Z. Naturforsch. 53a, 217—232 (1998); received January 23 1998   
Published
 1998   
Keywords
 Hydrodynamic Stability, Electrohydrodynamics, Nonlinearity, Interfacial Instability, Dielectric Fluids, Surface Charges   
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