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A thin conducting viscous film on an inclined plane in the presence of a uniform normal electric field: Bifurcation scenarios
Published in American Institute of Physics Inc.
2008
Volume: 20
   
Issue: 3
Abstract
A theory for two dimensional long and stationary waves of finite amplitude on a thin viscous liquid film down an inclined plane in the presence of uniform electric field at infinity is investigated. A set of exact averaged equations for the film flow system is described and linearized stability analysis of the uniform flow is performed using normal-mode formulation and the critical condition for linear instability is obtained. The linearized instability for the permanent wave equation, consistent to the second order in ε, is examined and the eigenvalue properties of the fixed points are classified in various parametric regimes. Numerical integration of the permanent wave equation as a third-order dynamical system is carried out. Different bifurcation scenarios leading to multiple-hump solitary waves or leading to chaos are exhibited in the parametric space. © 2008 American Institute of Physics.
About the journal
JournalData powered by TypesetPhysics of Fluids
PublisherData powered by TypesetAmerican Institute of Physics Inc.
ISSN10706631
Open AccessNo
Concepts (14)
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    Bifurcation (mathematics)
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    Conductive films
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    Eigenvalues and eigenfunctions
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    Electric field effects
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    Linear stability analysis
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    SOLITONS
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    Thin films
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    Wave equations
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    FILM FLOW
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    PERMANENT WAVE EQUATION
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    THIRD-ORDER DYNAMICAL SYSTEM
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    Uniform flow
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    Viscous flow
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    SOLITONS