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The asymptotics of the moving contact line: cracking an old nut

Published online by Cambridge University Press:  08 January 2015

David N. Sibley ,
Andreas Nold  and
Serafim Kalliadasis
David N. Sibley
Affiliation:
Department of Chemical Engineering, Imperial College London, London SW7 2AZ, UK
Andreas Nold
Affiliation:
Department of Chemical Engineering, Imperial College London, London SW7 2AZ, UK
Serafim Kalliadasis*
Affiliation:
Department of Chemical Engineering, Imperial College London, London SW7 2AZ, UK
*
†Email address for correspondence: [email protected]
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Abstract

For contact line motion where the full Stokes flow equations hold, full matched asymptotic solutions using slip models have been obtained for droplet spreading and more general geometries. These solutions to the singular perturbation problem in the slip length, however, all involve matching through an intermediate region that is taken to be separate from the outer–inner regions. Here, we show that the intermediate region is in fact an overlap region representing extensions of both the outer and the inner region, allowing direct matching to proceed. In particular, we investigate in detail how a previously seen result of the matching of the cubes of the free surface slope is justified in the lubrication setting. We also extend this two-region direct matching to the more general Stokes flow case, offering a new perspective on the asymptotics of the moving contact line problem.

JFM classification

Interfacial Flows (free surface): Interfacial Flows (free surface) Low-Reynolds-number flows: Low-Reynolds-number flows Mathematical Foundations: Mathematical Foundations
Type
Papers
Information
Journal of Fluid Mechanics , Volume 764 , 10 February 2015 , pp. 445 - 462
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Copyright
© 2015 Cambridge University Press 

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