Viscous flowing film instability down an inclined plane in the presence of constant electromagnetic field |
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| Institution: | 1. Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt;2. Department of Engineering Mathematics and Physics, Faculty of Engineering, Tanta University, Tanta, Egypt;1. Institute for Environmental Sciences, University of Geneva, Route de Drize 7, 1227 Carouge, Switzerland;2. GAP-Biophotonics, University of Geneva, Chemin de Pinchat 22, 1227 Carouge, Switzerland;1. GAP-Climate and Institute for Environmental Sciences, University of Geneva, Route de Drize 7, 1227 Carouge, Switzerland;2. GAP-Nonlinear, University of Geneva, Chemin de Pinchat 22, 1227 Carouge, Switzerland;1. School of Mechanical and Electrical Engineering, Gui Lin University of Electronic Technology, Gui Lin 541004, China;2. School of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom;3. National Microgravity Laboratory, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China;1. School of Mechanical and Electrical Engineering, Gui Lin University of Electronic Technology, Gui Lin 541004, China;2. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, CB30WA, United Kingdom;3. School of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom |
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| Abstract: | The present work deals with temporal stability properties of a falling liquid film down an inclined plane in the presence of constant electromagnetic field. Using the Kármán approximation, the problem is reduced to the study of the evolution equation for the free surface of the liquid film derived through a long-wave approximation. A linear stability analysis of the base flow is performed. Also, the solutions of stationary waves and Shkadov waves are introduced and discussed analytically by analyzing the linearized instability of the fixed points and Hopf bifurcation. |
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