Marangoni-driven liquid films rising out of a meniscus onto a nearly horizontal substrate
Please always quote using this URN:urn:nbn:de:0296-matheon-1525
- We revisit here the situation of a thin liquid film driven up an inclined substrate by a thermally induced Marangoni shear stress against the counter-acting parallel component of gravity. In contrast to previous studies, we focus here on the meniscus region, in the case where the substrate is nearly horizontal, so there is a significant contribution from the normal component of gravity. Our numerical simulations show that the time-dependent lubrication model for the film profile can reach a steady state in the meniscus region that is unlike the monotonic solutions found in [MÄunch, SIAM J. Appl. Math., 62(6):2045-2063, 2002]. A systematic investigation of the steady states of the lubrication model is carried out by studying the phase space of the corresponding third order ODE system. We find a rich structure of the phase space including multiple non-monotonic solutions with the same far-field film thickness.
Author: | Andreas Münch, Peter L. Evans |
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URN: | urn:nbn:de:0296-matheon-1525 |
Referee: | Jürgen Sprekels |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2004/08/20 |
Release Date: | 2004/07/18 |
Institute: | Humboldt-Universität zu Berlin |
Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS) | |
Preprint Number: | 143 |