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Time-evolving bubbles in two-dimensional Stokes flow

Published online by Cambridge University Press:  26 April 2006

Saleh Tanveer
Affiliation:
Department of Mathematics, The Ohio State University, Columbus, OH 43210, USA
Giovani L. Vasconcelos
Affiliation:
Department of Mathematics, The Ohio State University, Columbus, OH 43210, USA Present address: Departamento de Física, Universidade Federal de Pernambuco, 50732-910 Recife, Brazil.

Abstract

A general class of exact solutions is presented for a time-evolving bubble in a two-dimensional slow viscous flow in the presence of surface tension. These solutions can describe a bubble in a linear shear flow as well as an expanding or contracting bubble in an otherwise quiescent flow. In the case of expanding bubbles, the solutions have a simple behaviour in the sense that for essentially arbitrary initial shapes the bubble its asymptote is expanding circle. Contracting bubbles, on the other hand, can develop narrow structures (‘near-cusps’) on the interface and may undergo ‘breakup’ before all the bubble fluid is completely removed. The mathematical structure underlying the existence of these exact solutions is also investigated.

Type
Research Article
Copyright
© 1995 Cambridge University Press

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