Doubly-periodic array of bubbles in a Hele-Shaw cell
Fluid Dynamics
2010-09-30 v1
Abstract
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.
Cite
@article{arxiv.1009.5969,
title = {Doubly-periodic array of bubbles in a Hele-Shaw cell},
author = {Antônio M. P. Silva and Giovani L. Vasconcelos},
journal= {arXiv preprint arXiv:1009.5969},
year = {2010}
}
Comments
15 pages, 12 figures