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arXiv · 1404.2312

Exact solutions for a periodic assembly of bubbles in a Hele-Shaw channel

Giovani L. Vasconcelos·Christopher C. Green
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Abstract

Exact solutions are reported for a periodic assembly of bubbles steadily co-travelling in a Hele-Shaw channel. The solutions are obtained as conformal mappings from a multiply connected circular domain in an auxiliary complex plane to the flow region in a period cell. The conformal mappings are constructed using the generalized Schwarz-Christoffel formula for multiply connected polygonal domains in terms of products of Schottky-Klein prime functions. It is shown that previous solutions for multiple steady bubbles in a Hele-Shaw cell are all particular cases of the solutions described herein. Examples of specific bubble configurations are discussed.

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Giovani L. Vasconcelos, Christopher C. Green. 2014-04-08. Exact solutions for a periodic assembly of bubbles in a Hele-Shaw channel. https://arxiv.org/abs/1404.2312

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