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CPP: Fachverband Chemische Physik und Polymerphysik
CPP 9: Poster: Interfaces and Thin Films (joint session with DECHEMA and VDI)
CPP 9.36: Poster
Montag, 11. März 2013, 17:30–19:30, Poster C
Asymptotics of the Capillary-Driven Thin Film Equation — •Thomas Salez1, Michael Benzaquen1, Joshua D. McGraw2, Oliver Bäumchen2, Kari Dalnoki-Veress2, and Elie Raphaël1 — 1Gulliver, ESPCI, Paris, France — 2McMaster University, Hamilton, Canada
The study of polymer nanofilms is of tremendous importance in a variety of scientific fields, such as polymer physics, physiology, biophysics, micro-electronics, surface chemistry, and applied mathematics. In the lubrication approximation for viscous flows, the evolution of the free surface of such a film is governed by the capillary-driven thin film equation. We hereby present analytical [1] and numerical [2] treatments of this partial differential equation for a stepped initial profile, and compare the results to experiments on polystyrene [3]. Then, we derive the Green’s function of the linearized problem and therefore obtain the solution for any summable initial perturbation. In particular, we show that this solution uniformly converges in time towards a unique self-similar attractor that is precisely the Green’s function multiplied by the algebraic volume of the perturbation [4]. Finally, a numerical scheme enables us to conjecture the extension of this result to the nonlinear case, where the universal attractor appears to be identical to the one obtained in the linear case.
[1] Salez et. al PoF 24 102111 (2012), [2] Salez et al. EPJE 35 114 (2012), [3] McGraw et al. PRL 109 128303 (2012), [4] Benzaquen et al. submitted to SIAM (2012)