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Effective and microscopic contact angles in thin film dynamics

Published online by Cambridge University Press:  01 April 2000

MICHIEL BERTSCH ,
ROBERTA DAL PASSO ,
STEPHEN H. DAVIS  and
LORENZO GIACOMELLI
MICHIEL BERTSCH
Affiliation:
Dipartimento di Matematica, Università di Roma ‘Tor Vergata’, 00133 Roma, Italy
ROBERTA DAL PASSO
Affiliation:
Dipartimento di Matematica, Università di Roma ‘Tor Vergata’, 00133 Roma, Italy
STEPHEN H. DAVIS
Affiliation:
Department of Engineering Sciences and Applied Mathematics, Robert R. McCormick School of Engineering and Applied Science, Northwestern University, Evanston, IL 60208, USA
LORENZO GIACOMELLI
Affiliation:
Dipartimento di Matematica, Università di Roma ‘La Sapienza’, 00185 Roma, Italy
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Abstract

We introduce and analyse a class of quasi-self-similar solutions of the thin film equation to describe the dynamics of expanding liquid films on a solid surface. Using these solutions as intermediate asymptotics profiles, we obtain a quantitative expression for the shape of the film and a relation between the speed of the contact line and the macroscopic and microscopic contact angles.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 11 , Issue 2 , April 2000 , pp. 181 - 201
Copyright
2000 Cambridge University Press

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