15.04.2024 15:45 Jonas Jansen (Lund University):
Pattern Formation and Film Rupture in an Asymptotic Model of the Bénard– Marangoni problemMI 03.06.011 (Boltzmannstr. 3, 85748 Garching)

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 leading to dewetting phenomena. The emergence of these patterns is caused by the thermocapillary effect and the mathematical problem is known as the Bénard–Marangoni problem. In this talk, I will derive a deformational asymptotic model for the Bénard–Marangoni problem in the thin-film limit. In this model, the state of constant film height destabilises via a (conserved) long-wave instability and periodic solutions bifurcate via a subcritical pitchfork bifurcation. I will demonstrate that the bifurcation curve can be extended to a global bifurcation branch. Furthermore, periodic film-rupture solutions can be constructed as limit points of the bifurcation branch. The talk is based on joint work with Stefano Böhmer, Gabriele Brüll (both Lund) and Bastian Hilder.