Nonlinear electrohydrodynamic Kelvin-Helmholtz and Marangoni instabilities near the marginal state |
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Authors: | Abdel Raouf F Elhefnawy |
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Institution: | (1) Dept of Mathematics, Faculty of Science, Banha University, 13518 Banha, Egypt;(2) Present address: Department of Mathematics, T.T. Junior College of Al-Qunfudah, P.O. Box 1083, 21912 Al-Qunfudah, Saudi Arabia |
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Abstract: | The effects of surface tension and adsorption on the electrohydrodynamic Kelvin-Helmholtz instability are studied. The system is stressed by a normal electric field such that it allows for the presence of surface charges at the interface. The method used is that of multiple scales. The nonlinear Schrödinger equation describing the behavior of the disturbed system is derived. The stability of the perturbed system is discussed both analytically and numerically and the stability diagrams are obtained. At the critical point, a generalized formulation of the evolution equation is developed, which leads to the nonlinear Klein-Gordon equation. The various stability criteria are derived from this equation. |
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