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A thin drop sliding down an inclined plate

Published online by Cambridge University Press:  20 May 2015

E. S. Benilov  and
M. S. Benilov
E. S. Benilov*
Affiliation:
Department of Mathematics and Statistics, University of Limerick, Ireland
M. S. Benilov
Affiliation:
Departamento de Física, CCCEE, Universidade da Madeira, Largo do Município, 9000 Funchal, Portugal Instituto de Plasmas e Fusão Nuclear, Instituto Superior Técnico, Universidade de Lisboa, Portugal
*
†Email address for correspondence: Eugene.Benilov@ul.ie
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Abstract

We examine two- and three-dimensional drops steadily sliding down an inclined plate. The contact line of the drop is governed by a model based on the Navier-slip boundary condition and a prescribed value for the contact angle. The drop is thin, so the lubrication approximation can be used. In the three-dimensional case, we also assume that the drop is sufficiently small (its size is smaller than the capillary scale). These assumptions enable us to determine the shape of the drop and derive an asymptotic expression for its velocity. For three-dimensional drops, this expression is matched to a qualitative estimate of Kim et al. (J. Colloid Interface Sci., vol. 247, 2002, pp. 372–380) obtained for arbitrary drops, i.e. not necessarily thin and small. The matching fixes an undetermined coefficient in Kim, Lee and Kang’s estimate, turning it into a quantitative result.

JFM classification

Drops and Bubbles: Drops Interfacial Flows (free surface): Interfacial Flows (free surface) Interfacial Flows (free surface): Thin films
Type
Papers
Information
Journal of Fluid Mechanics , Volume 773 , 25 June 2015 , pp. 75 - 102
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Copyright
© 2015 Cambridge University Press 

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