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Analytical and numerical studies of the stability of thin-film rimming flow subject to surface shear

Published online by Cambridge University Press:  11 October 2005

M. VILLEGAS-DÍAZ ,
H. POWER  and
D. S. RILEY
M. VILLEGAS-DÍAZ
Affiliation:
School OF Mechanical, Manufacturing and Engineering Management, University of Nottingham, University Park, Nottingham NG7 2RD, UK
H. POWER
Affiliation:
School OF Mechanical, Manufacturing and Engineering Management, University of Nottingham, University Park, Nottingham NG7 2RD, UK
D. S. RILEY
Affiliation:
Division of Applied Mathematics, School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, [email protected]
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Abstract

Motivated by applications in rapidly rotating machinery, we have previously extended the lubrication model of the thin-film flow on the inside of a rotating circular cylinder to incorporate the effect of a constant shear applied to the free surface of the film and discovered a system rich in film profiles featuring shock structures. In this paper, we extend our model to include the effects of surface tension at leading order and take into account higher-order effects produced by gravity in order to resolve issues regarding existence, uniqueness and stability of such weak solutions to our lubrication model. We find, by analytical and numerical means, a set of feasible steady two-dimensional solutions that fit within a rational asymptotic framework. Having identified mathematically feasible solutions, we study their stability to infinitesimal two-dimensional disturbances. based on our findings, we conjecture which of the possible weak solutions are physically meaningful.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 541 , 25 October 2005 , pp. 317 - 344
Copyright
© 2005 Cambridge University Press

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