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.
| Original language | English |
|---|---|
| Pages (from-to) | 369-392 |
| Number of pages | 24 |
| Journal | European Journal of Applied Mathematics |
| Volume | 29 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 1 Jun 2018 |
| Externally published | Yes |
Keywords
- existence and uniqueness
- non-linear fourth-order equations
- PDEs for fluid mechanics
- thin fluid films
- travelling wave solutions