Laplacian growth with an isolated bubble near a tip

Tamuz Danzig, Oded Agam

Research output: Contribution to journalArticlepeer-review

Abstract

We construct exact solutions for the Saffman-Taylor problem in a planar Hele-Shaw cell for the case of an isolated bubble near the tip of an expanding bubble in the limit of zero surface tension. This construction utilizes the integrability of the problem in the limit of vanishing surface tension. It exploits the connection, brought by the Schwarz function, between the constants of motion and the shape of the bubbles. The results of this paper provide a step toward the theoretical understanding of the dynamics of Saffman-Taylor problem in a Hele-Shaw cell with randomly distributed tiny bubbles.

Original languageAmerican English
Article number055105
JournalPhysical Review E
Volume104
Issue number5
DOIs
StatePublished - Nov 2021

Bibliographical note

Publisher Copyright:
© 2021 American Physical Society.

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