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IMA Journal of Applied Mathematics Advance Access originally published online on October 24, 2007
IMA Journal of Applied Mathematics 2008 73(1):4-36; doi:10.1093/imamat/hxm042
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© The Author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Gravity-driven thin-film flow using a new contact line model

J. Billingham{dagger}

School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK

{dagger} Email: john.billingham{at}nottingham.ac.uk

Received on June 22, 2006; Accepted on May 8, 2007

In this paper, we consider how a new model for the motion of a contact line, proposed by Shikhmurzaev (1993, Int. J. Multiphase Flow, 19, 589-–610), affects predictions for the gravity-driven flow of a thin film down an inclined plane. We find that for sufficiently thin films, the model reduces to Navier slip with the contact angle equal to its static value, while for thicker films the model has a character of its own, with a slip region that becomes larger, the thicker the film and a contact angle that increases as the thickness of the film increases.

Keywords: thin film flow; moving contact line.


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