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Travelling wave solutions for a thin-film equation related to the spin-coating process

Published online by Cambridge University Press:  17 July 2017

M. V. GNANN
Affiliation:
Center for Mathematics, Technical University of Munich, Boltzmannstr. 3, 85747 Garching near Munich, Germany email: gnann@ma.tum.de
H. J. KIM
Affiliation:
Institute of Applied Mathematics and IWR, University of Heidelberg, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany emails: kim.hyeonjeong@math.uni-heidelberg.de, knuepfer@uni-heidelberg.de
H. KNÜPFER
Affiliation:
Institute of Applied Mathematics and IWR, University of Heidelberg, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany emails: kim.hyeonjeong@math.uni-heidelberg.de, knuepfer@uni-heidelberg.de

Abstract

We study a problem related to the spin-coating process in which a fluid coats a rotating surface. Our interest lies in the contact-line region for which we propose a simplified travelling wave approximation. We construct solutions to this problem by a shooting method that matches solution branches in the contact-line region and in the interior of the droplet. Furthermore, we prove uniqueness and qualitative properties of the solution connected to the fourth-order nature of the equation, such as a global maximum in the film height close to the contact line, elevated from the average height of the film.

Type
Papers
Copyright
Copyright © Cambridge University Press 2017 

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