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DY: Fachverband Dynamik und Statistische Physik

DY 41: Poster - Pattern/ Nonlinear Dyn./ Fluids/ Granular/ Critical Phen.

DY 41.9: Poster

Thursday, April 3, 2014, 17:00–19:00, P3

Heteroclinic snaking near a heteroclinic chain in dragged meniscus problems — •Mariano Galvagno¹, Dmitri Tseluiko¹, and Uwe Thiele^1,2 — ¹Department of Mathematical Sciences, Loughborough University, UK — ²Institut für Theoretische Physik, Universität Münster, Germany

We study the deposition of a non-volatile liquid film onto a flat heated inclined plate extracted from a bath at constant speed. We analyse steady-state meniscus solutions of a 2d long-wave mesoscopic hydrodynamic description that incorporates wettability via a Derjaguin (disjoining) pressure as the plate velocity is changed. We observe snaking behaviour when the plate inclination angle is above a certain critical value. Otherwise, the bifurcation curve is monotonic. The solutions along these curves are characterised by a foot-like structure [1] formed close to the meniscus. The foot is preceded by a thin precursor film further up the plate. We show that the snaking is related to the existence of infinitely many heteroclinic orbits close to a heteroclinic chain in an appropriate 3d phase space connecting the fixed points of the system [2]. [1] A. Münch, P.L. Evans, Phys. D 209, 2005. [2] M. Galvagno, D. Tseluiko, U. Thiele, arxiv.org/abs/1307.4618