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

• Verfasst von: Gnann, Manuel Victor [VerfasserIn]
• Verfasst von: Kim, Hyeon Jeong [VerfasserIn]
• Verfasst von: Knüpfer, Hans [VerfasserIn]
• Titel: Travelling wave solutions for a thin-film equation related to the spin-coating process
• Verf.angabe: M.V. Gnann, H.J. Kim and H. Knüpfer
• Jahr des Originals: 2017
• Umfang: 24 S.
• Fussnoten: First published online 17 July 2017 ; Gesehen am 25.06.2018
• Titel Quelle: Enthalten in: European journal of applied mathematics
• Jahr Quelle: 2018
• Band/Heft Quelle: 29(2018), 3, S. 369-392
• ISSN Quelle: 1469-4425
• DOI: doi:10.1017/S0956792517000195
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1576822486

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.