Free-surface flow over a trapped bubble

Blyth, M. G. and Vanden-Broeck, Jean-Marc (2008) Free-surface flow over a trapped bubble. IMA Journal of Applied Mathematics, 73 (5). pp. 803-814. ISSN 0272-4960

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Abstract

We consider the free-surface flow of liquid of finite depth over a bubble trapped on a plane wall. The flow is assumed to be inviscid and irrotational. The problem is formulated using an integral equation and the solution is obtained numerically using a collocation method. The choices for the two contact angles where the bubble is attached to the wall are shown to depend crucially on the bubble drag. For supercritical flow, the bubble drag is zero and the contact angles are required to be equal. For either subcritical or critical flow, the bubble drag is non-zero. In either case, only one of the contact angles may be chosen freely and the second emerges as part of the solution. The effect of the free surface on the shape of the bubble is demonstrated under a variety of flow conditions.

Item Type: Article
Faculty \ School: Faculty of Science > School of Mathematics
Depositing User: Vishal Gautam
Date Deposited: 10 Mar 2011 13:04
Last Modified: 19 Jan 2023 10:30
URI: https://ueaeprints.uea.ac.uk/id/eprint/19822
DOI: 10.1093/imamat/hxn014

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