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Electrified film on a porous inclined plane: Dynamics and stability
Published in
2010
Volume: 82
   
Issue: 1
Abstract
The time evolution of a thin conducting liquid film flowing down a porous inclined substrate is investigated when an electric field acts normal to the substrate. It is assumed that the flow through the porous medium is governed by Darcy's law together with Beavers-Joseph condition. Under the assumption of small permeability relative to the thickness of the overlying fluid layer, the flow is decoupled from the filtration flow through the porous medium. A slip condition at the bottom is used to incorporate the effects of the permeability of the substrate. From the set of exact averaged equations derived using integral boundary method for the film thickness and for the flow rate, a nonlinear evolution equation for the film thickness is derived through a long-wave approximation. A linear stability analysis of the base flow is performed and the critical Reynolds number is obtained. The results reveal that the substrate porosity in general destabilizes the liquid film flow and the presence of the electric field enhances this destabilizing effect. A weakly nonlinear stability analysis divulges the existence of supercritical stable and subcritical unstable zones in the wave number/Reynolds number parameter space and the results demonstrate how the neutral curves change as the intensity of the electric filed or the permeability of the porous medium is varied. The numerical solution of the nonlinear evolution equation in a periodic domain reveals that the base flow yields to surface structures that are either time independent waves of permanent form that propagate or time-dependent modes that oscillate slightly in the amplitude. Further, it is observed that the shape and amplitude of long-time waveforms are influenced by the permeability of the porous medium as well as by the applied electric field. The results reveal that the destabilization induced by the electric field in an otherwise stable film over a porous medium is exhibited in the form of traveling waves of finite amplitude. The presence of the porous substrate promotes the oscillatory behavior of the long-time waveform; however, the electric field has a tendency to suppress this oscillatory behavior. © 2010 The American Physical Society.
About the journal
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
ISSN15393755
Open AccessNo
Concepts (48)
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    Applied electric field
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    BASEFLOWS
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    BOUNDARY METHOD
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    CONDUCTING LIQUID
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    Critical reynolds number
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    DARCY'S LAW
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    DESTABILIZING EFFECT
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    ELECTRIC FILED
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    FILTRATION FLOW
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    FINITE AMPLITUDE
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    Flowthrough
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    FLUID LAYER
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    Inclined planes
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    LIQUID-FILM FLOW
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    LONG-WAVE APPROXIMATION
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    NONLINEAR EVOLUTION EQUATION
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    Numerical solution
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    Oscillatory behaviors
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    Parameter spaces
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    PERIODIC DOMAINS
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    Porous medium
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    POROUS SUBSTRATES
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    SLIP CONDITION
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    STABLE FILMS
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    SUBSTRATE POROSITY
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    SUPER-CRITICAL
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    Time evolutions
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    Time-dependent
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    Traveling wave
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    Wave forms
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    WEAKLY NON-LINEAR STABILITIES
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    Aerodynamics
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    Biology
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    Differential equations
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    ELECTRIC FIELD MEASUREMENT
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    Electric fields
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    Groundwater flow
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    Linear stability analysis
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    Liquid films
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    Machinery
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    Magnetic films
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    Numerical analysis
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    Porous materials
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    Reynolds equation
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    Reynolds number
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    Substrates
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    Wave equations
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    Nonlinear equations