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New numerical solutions to the so-called selection problem for one and twosteadily translating bubbles in an unbounded Hele-Shaw cell are presented. Ourapproach relies on conformal mapping which, for the two-bubble problem,involves the Schottky-Klein prime function associated with an annulus. We showthat a countably infinite number of solutions exist for each fixed value ofdimensionless surface tension, with the bubble shapes becoming more exotic asthe solution branch number increases. Our numerical results suggest that asingle solution is selected in the limit that surface tension vanishes, withthe scaling between the bubble velocity and surface tension being different tothe well-studied problems for a bubble or a finger propagating in a channelgeometry.

The effect of surface tension on steadily translating bubbles in an unbounded Hele-Shaw cell