This paper examines two related problems from liquid-film theory. Firstly, a steady-state flow of a liquid film down a pre-wetted plate is considered, in which there is a precursor film in front of the main film. Assuming the former to be thin, a full asymptotic description of the problem is developed and simple analytical estimates for the extent and depth of the precursor film's influence on the main film are provided. Secondly, the so-called drag-out problem is considered, where an inclined plate is withdrawn from a pool of liquid. Using a combination of numerical and asymptotic means, the parameter range where the classical Landau-Levich-Wilson solution is not unique is determined. © 2010 Cambridge University Press.
|Original language||English (US)|
|Number of pages||17|
|Journal||Journal of Fluid Mechanics|
|State||Published - Aug 18 2010|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: One of the authors (E.S.B.) is grateful for the hospitality of the Oxford Centre for Collaborative Applied Mathematics which hosted his sabbatical, and also acknowledges the support of the Science Foundation Ireland (RFP Grant 08/RFP/MTH1476 and Mathematics Initiative Grant 06/MI/005). This publication was based on work supported in part by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.