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Instability of a liquid film flow over a vibrating inclined plane

Published online by Cambridge University Press:  26 April 2006

David R. Woods  and
S. P. Lin
David R. Woods
Affiliation:
Department of Mechanical and Aeronautical Engineering, Clarkson University, Potsdam, NY 13699-5725, USA
S. P. Lin
Affiliation:
Department of Mechanical and Aeronautical Engineering, Clarkson University, Potsdam, NY 13699-5725, USA
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Abstract

The problem of the onset of instability in a liquid layer flowing down a vibrating inclined plane is formulated. For the solution of the problem, the Fourier components of the disturbance are expanded in Chebychev polynomials with time-dependent coefficients. The reduced system of ordinary differential equations is analysed with the aid of Floquet theory. The interaction of the long gravity waves, the relatively short shear waves and the parametrically resonated Faraday waves occurring in the film flow is studied. Numerical results show that the long gravity waves can be significantly suppressed, but cannot be completely eliminated by use of the externally imposed oscillation on the incline. At small angles of inclination, the short shear waves may be exploited to enhance the Faraday waves. For a given set of relevant flow parameters, there exists a critical amplitude of the plane vibration below which the Faraday wave cannot be generated. At a given amplitude above this critical one, there also exists a cutoff wavenumber above which the Faraday wave cannot be excited. In general the critical amplitude increases, but the cutoff wavenumber decreases, with increasing viscosity. The cutoff wavenumber also decreases with increasing surface tension. The application of the theory to a novel method of film atomization is discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 294 , 10 July 1995 , pp. 391 - 407
Copyright
© 1995 Cambridge University Press

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