# Jonas Jansen and Bastian Hilder: Thermocapillary Thin Film Flows: Periodic Steady States and Film Rupture

**Time: **
Tue 2023-10-10 14.00 - 15.00

**Location: **
Institut Mittag-Leffler, Seminar Hall Kuskvillan and Zoom

**Video link: **
Meeting ID: 921 756 1880

**Participating: **
Jonas Jansen and Bastian Hilder, Lund University

**Abstract:**

Thin fluid films on heated planes exhibit the formation of spatially periodic structures. These can take the form of regular polygonal pattern, which was experimentally observed by Henri Bénard in 1900, or film rupture. Later, it was understood that the emergence of these patterns is caused by thermocapillary effects and the mathematical problem is known as the Bénard–Marangoni problem.

In this talk, we will derive a deformational asymptotic model for the Bénard–Marangoni problem in the thin-film limit. In this model, the flat state destabilises via a (conserved) long-wave instability and periodic solutions bifurcate via a subcritical pitchfork bifurcation. We will demonstrate that the bifurcation curve can be extended to a global bifurcation branch. Moreover, we construct periodic stationary film-rupture solutions as limit points of the bifurcation branch.

This work is a collaboration with Gabriele Brüll.