Abstract
A model of the interaction of small, well-separated bubbles of one fluid propagating through another ‘‘resident’’ fluid in a Hele–Shaw cell is introduced and studied. In the model each bubble acts on the others by setting up a velocity field of the dipole type. A system of ordinary differential equations is developed for the bubble positions. The system is solved completely for the two-bubble problem. The three-bubble problem is addressed by numerical simulations. A set of self-similar motions are also found analytically. The dynamics of rows of bubbles is investigated analytically and via numerical simulations. Although clearly an extreme idealization, the model appears to shed considerable light on what to expect in laboratory experiments.
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