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Explicit solutions for Hele–Shaw corner flows

Published online by Cambridge University Press:  03 May 2005

I. MARKINA
Affiliation:
Departamento de Matemática, Universidad Técnica Federico Santa María, Casilla 110-V, Valparaíso, Chile email: irina.markina@mat.utfsm.cl, alexander.vasiliev@mat.utfsm.cl
A. VASIL'EV
Affiliation:
Departamento de Matemática, Universidad Técnica Federico Santa María, Casilla 110-V, Valparaíso, Chile email: irina.markina@mat.utfsm.cl, alexander.vasiliev@mat.utfsm.cl
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Abstract

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We consider two-dimensional bubbles in a corner flow in a Hele–Shaw cell of a viscous incompressible fluid that occupies the complement to a bubble. We discuss the governing equations, some basic properties of the free interface of the bubbles, their geometry, and construct explicit solutions that present asymmetric long bubbles analogous to the famous Saffman–Taylor fingers in a wedge of arbitrary angle $\alpha\in (0,2\pi)$.

Type
Papers
Copyright
2004 Cambridge University Press