Travelling wave solutions for a thin-film equation related to the spin-coating process
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 i...
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| Main Authors: | , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
2018
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| In: |
European journal of applied mathematics
Year: 2017, Volume: 29, Issue: 3, Pages: 369-392 |
| ISSN: | 1469-4425 |
| DOI: | 10.1017/S0956792517000195 |
| Online Access: | Verlag, Volltext: http://dx.doi.org/10.1017/S0956792517000195 Verlag, Volltext: https://www.cambridge.org/core/journals/european-journal-of-applied-mathematics/article/travelling-wave-solutions-for-a-thinfilm-equation-related-to-the-spincoating-process/BE8B259C30813C640242C786D900FBD2 
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| Author Notes: | M.V. Gnann, H.J. Kim and H. Knüpfer |
| Summary: | 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. |
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| Item Description: | First published online 17 July 2017 Gesehen am 25.06.2018 |
| Physical Description: | Online Resource |
| ISSN: | 1469-4425 |
| DOI: | 10.1017/S0956792517000195 |