Abstract
In this paper we use the lubrication approximation to analyse three-dimensional unsteady flow of a thin film of Newtonian fluid around a symmetric slender moving dry patch on an inclined planar substrate. The flow being driven by gravity and a prescribed constant shear stress at the free surface. We obtain a novel unsteady travelling-wave similarity solution for the dry patch of uniform thickness, in which the dry patch travels at constant speed. This solution predicts that the dry patch has a parabolic shape which may be concave up or concave down the substrate. In all
cases investigated numerically the film thickness is found to increase monotonically away from the contact line.
cases investigated numerically the film thickness is found to increase monotonically away from the contact line.
| Original language | English |
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| Title of host publication | Proceedings of the 2nd International Symposium on Frontiers of Computational Sciences 2012 |
| Pages | 88-98 |
| Number of pages | 11 |
| Publication status | Published - 2012 |
| Event | 2nd international symposium on frontiers of computational sciences - Islamabad, Pakistan Duration: 28 Jun 2012 → 29 Jun 2012 |
Conference
| Conference | 2nd international symposium on frontiers of computational sciences |
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| Country/Territory | Pakistan |
| City | Islamabad |
| Period | 28/06/12 → 29/06/12 |
Keywords
- travelling-wave
- similarity solutions
- Newtonian fluid
- dry patch
- thin-film flow