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

Journal article (2018)

Authors

M.V. Gnann Technische Universität München

H.J. Kim University of Heidelberg

H. Knüpfer University of Heidelberg

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External organisation

Thin fluid films Existence and uniqueness Non-linear fourth-order equations PDEs for fluid mechanics Travelling wave solutions

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http://resolver.tudelft.nl/uuid:796655d3-a25e-47da-bb4b-5509a7a6b601

Published Date

01-06-2018

Language

English

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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.