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.

Download full text files

Export metadata

Additional Services

Share in Twitter Search Google Scholar
Metadaten
Author:Andreas Münch, Peter L. Evans
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
Verstanden ✔
Diese Webseite verwendet technisch erforderliche Session-Cookies. Durch die weitere Nutzung der Webseite stimmen Sie diesem zu. Unsere Datenschutzerklärung finden Sie hier.