Doubly-periodic array of bubbles in a Hele-Shaw cell

Details Doubly-periodic array of bubbles in a Hele-Shaw cell Doubly-periodic array of bubbles in a Hele-Shaw cell

2010-09-29

arxiv.org/abs/1009.5969v1

Physics

Fluid Dynamics

15 pages, 12 figures

Scientific paper

10.1098/rspa.2010.0227

Exact solutions are presented for a doubly-periodic array of steadily moving bubbles in a Hele-Shaw cell when surface tension is neglected. It is assumed that the bubbles either are symmetrical with respect to the channel centreline or have fore-and-aft symmetry, or both, so that the relevant flow domain can be reduced to a simply connected region. By using conformal mapping techniques, a general solution with any number of bubbles per unit cell is obtained in integral form. Several examples are given, including solutions for multi-file arrays of bubbles in the channel geometry and doubly-periodic solutions in an unbounded cell.

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