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The thin-film equation: recent advances and some new perspectives

Jürgen Becker and Günther Grün

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This paper is concerned with mathematical aspects of lubrication equations. In the first part, we discuss recent analytical achievements for various types of thin-film equations. Of interest are issues like (non-)uniqueness, wetting behaviour and contact line motion, in particular optimal propagation rates and waiting time or dead core phenomena. In the second part, we shall present novel numerical results for thin-film flow on heterogeneous substrates based on entropy consistent schemes. Finally, we will be concerned with new algorithmic concepts for the simulation of thin-film flow of shear-thinning liquids.


PACS

47.15.gm Thin film flows

47.50.-d Non-Newtonian fluid flows

47.85.mf Lubrication flows

Subjects

Fluid dynamics

Dates

Issue 9 (9 March 2005)

Received 24 November 2004

Published 18 February 2005



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