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pdes for fluid mechanics

European Journal of Applied Mathematics (1)

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Travelling wave solutions for a thin-film equation related to the spin-coating process
M. V. GNANN, H. J. KIM, H. KNÜPFER
Journal:

European Journal of Applied Mathematics / Volume 29 / Issue 3 / June 2018

Published online by Cambridge University Press:

17 July 2017, pp. 369-392
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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.