Berlin 2008 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 21: Nonlinear dynamics, synchronization and chaos III
DY 21.3: Talk
Wednesday, February 27, 2008, 17:15–17:30, MA 001
Analysing sliding and depinning drops using efficient time-integration and path-following — •Philippe Beltrame1,2, Peter Talkner2, Peter Haenggi2, and Uwe Thiele1,3 — 1Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, D-01187 Dresden — 2Theoretische Physik I, Uni. Augsburg, Universitätsstr. 1, D-86159 Augsburg — 3School of Math., Loughborough University, Loughborough, LE11 3TU, UK
Pattern formation in thin liquid films represents a highly nonlinear phenomenon far from equilibrium. Its study requires a numerical treatment of the fully nonlinear system allowing for time integration of the dynamics and path-following to directly track equilibria. We present a code unifying both tasks for lubrication-type equations in analogy to a similar approach for the Navier-Stokes equations. We show that time-stepping based on an exponentiation propagation scheme is much better adapted to the lubrication equation than the classically used semi-implicit scheme, especially for the automatic adaptation of the timestep. The developed common numerical framework is applied to the three-dimensional phenomena of (1) Stable sliding drops on an inclined homogeneous substrate and the transition to sliding drops that emit secondary droplets (time integration); (2) Depinning scenarios and stick-slip motion of ridges and drops on a heteregeneous (striped) substrate (path-following and time-integration).
We acknowledge support by the EU and DFG under grants MRTN-CT-2004-005728 and SFB 486 B13.