Eur. Phys. J. B 33, 457-467 (2003)
https://doi.org/10.1140/epjb/e2003-00186-3

3D Large scale Marangoni convection in liquid films

¹ Lehrstuhl für Theoretische Physik II, Brandenburgische Technische Universität Cottbus, Erich-Weinert-Strasse 1, 03046 Cottbus, Germany
² Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, 01187 Dresden, Germany

Corresponding author: ^a bes@physik.tu-cottbus.de

Received: 10 November 2002
Revised: 25 April 2003
Published online: 3 July 2003

Abstract

We study large scale surface deformations of a liquid film unstable due to the Marangoni effect caused by external heating on a smooth and solid substrate. The work is based on the thin film equation which can be derived from the basic hydrodynamic equations. To prevent rupture, a repelling disjoining pressure is included which accounts for the stabilization of a thin precursor film and so prevents the occurrence of completely dry regions. Linear stability analysis, nonlinear stationary solutions, as well as three-dimensional time dependent numerical solutions for horizontal and inclined substrates reveal a rich scenario of possible structures for several realistic fluid parameters.