Long-wave instabilities of non-uniformly heated falling films

We consider the problem of a thin liquid layer falling down an inclined plate that is subjected to non-uniform heating. The plate temperature is assumed to be linearly distributed and both directions of the temperature gradient with respect to the flow are investigated. The film flow is not only inf...

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Bibliographic Details
Published in:Journal of fluid mechanics 2002-02, Vol.453, p.153-175
Main Authors: MILADINOVA, SVETLA, SLAVTCHEV, SLAVTCHO, LEBON, GEORGY, LEGROS, JEAN-CLAUDE
Format: Article
Language:English
Subjects:
Exact sciences and technology
Fluid dynamics
Free surfaces
Fundamental areas of phenomenology (including applications)
Hydrodynamic stability
Phase transitions
Physics
Stability analysis
Surface tension
Surface-tension-driven instability
Temperature gradients
Thin films
Waveform analysis
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Summary:We consider the problem of a thin liquid layer falling down an inclined plate that is subjected to non-uniform heating. The plate temperature is assumed to be linearly distributed and both directions of the temperature gradient with respect to the flow are investigated. The film flow is not only influenced by gravity and mean surface tension, but in addition by the thermocapillary force acting along the free surface. The coupling of thermocapillary instability and surface-wave instabilities is studied for two-dimensional disturbances. Applying the long-wave theory, a nonlinear evolution equation is derived. When the plate temperature is decreasing in the downstream direction, linear stability analysis exhibits a film stabilization, compared to a uniformly heated film. In contrast, for increasing temperature along the plate, the film becomes less stable. Numerical solution of the evolution equation indicates the existence of permanent finite-amplitude waves of different kinds. The shape of the waves depends mainly on the mean flow and the mean surface tension, but their amplitudes and phase speeds are influenced by thermocapillarity.
ISSN:0022-1120
1469-7645
DOI:10.1017/S0022112001006814