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Nonlinear instability of a contact line driven by gravity

Published online by Cambridge University Press:  25 June 2000

SERAFIM KALLIADASIS
Affiliation:
Department of Chemical Engineering, University of Leeds, Leeds LS2 9JT, UK

Abstract

A thin liquid mass of fixed volume spreading under the action of gravity on an inclined plane develops a fingering instability at the front. In this study we consider the motion of a viscous sheet down a pre-wetted plane with a large inclination angle. We demonstrate that the instability is a phase instability associated with the translational invariance of the system in the direction of flow and we analyse the weakly nonlinear regime of the instability by utilizing methods from dynamical systems theory. It is shown that the evolution of the fingers is governed by a Kuramoto–Sivashinsky-type partial differential equation with solution a saw-tooth pattern when the inclined plane is pre-wetted with a thin film, while the presence of a thick film suppresses fingering.

Type
Research Article
Copyright
© 2000 Cambridge University Press

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