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Thin film flow down a porous substrate in the presence of an insoluble surfactant: Stability analysis
- Anjalaiah,
Published in American Institute of Physics Inc.
2013
Volume: 25
   
Issue: 2
Abstract
The stability of a gravity-driven film flow on a porous inclined substrate is considered, when the film is contaminated by an insoluble surfactant, in the frame work of Orr-Sommerfeld analysis. The classical long-wave asymptotic expansion for small wave numbers reveals the occurrence of two modes, the Yih mode and the Marangoni mode for a clean/a contaminated film over a porous substrate and this is confirmed by the numerical solution of the Orr-Sommerfeld system using the spectral-Tau collocation method. The results show that the Marangoni mode is always stable and dominates the Yih mode for small Reynolds numbers; as the Reynolds number increases, the growth rate of the Yih mode increases, until, an exchange of stability occurs, and after that the Yih mode dominates. The role of the surfactant is to increase the critical Reynolds number, indicating its stabilizing effect. The growth rate increases with an increase in permeability, in the region where the Yih mode dominates the Marangoni mode. Also, the growth rate is more for a film (both clean and contaminated) over a thicker porous layer than over a thinner one. From the neutral stability maps, it is observed that the critical Reynolds number decreases with an increase in permeability in the case of a thicker porous layer, both for a clean and a contaminated film over it. Further, the range of unstable wave number increases with an increase in the thickness of the porous layer. The film flow system is more unstable for a film over a thicker porous layer than over a thinner one. However, for small wave numbers, it is possible to find the range of values of the parameters characterizing the porous medium for which the film flow can be stabilized for both a clean film/a contaminated film as compared to such a film over an impermeable substrate; further, it is possible to enhance the instability of such a film flow system outside of this stability window, for appropriate choices of the porous substrate characteristics. © 2013 American Institute of Physics.
About the journal
JournalData powered by TypesetPhysics of Fluids
PublisherData powered by TypesetAmerican Institute of Physics Inc.
ISSN10706631
Open AccessYes
Concepts (29)
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    Contamination
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    Growth rate
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    Porous materials
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    Reynolds number
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    Stability
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    Substrates
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    Surface active agents
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    Asymptotic expansion
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    Collocation method
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    CONTAMINATED FILMS
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    Critical reynolds number
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    EXCHANGE OF STABILITIES
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    FILM FLOWS
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    Frame-work
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    INSOLUBLE SURFACTANTS
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    MARANGONI
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    NEUTRAL STABILITY
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    Numerical solution
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    PARAMETERS CHARACTERIZING
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    POROUS LAYERS
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    Porous medium
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    POROUS SUBSTRATES
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    RATE INCREASE
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    Stability analysis
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    Stabilizing effects
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    THIN FILM FLOW
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    UNSTABLE WAVES
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    WAVE NUMBERS
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    Film growth