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

  • M. V. GNANN (a1), H. J. KIM (a2) and H. KNÜPFER (a2)

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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MVG received funding from the International Max Planck Research School (IMPRS) of the Max Planck Institute for Mathematics in the Sciences (MIS) in Leipzig, the University of Michigan at Ann Arbor, and the National Science Foundation under Grant No. NSF DMS-1054115. MVG is also supported by the Deutsche Forschungsgemeinschaft (grant GN 109/1-1). HJK acknowledges support by NRF Grant(NRF-2015R1A6A3A03020924) provided by the National Research Foundation of Korea.

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European Journal of Applied Mathematics
  • ISSN: 0956-7925
  • EISSN: 1469-4425
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