Title: The effect of surface tension on steadily translating bubbles in an unbounded Hele-Shaw cell,
Abstract: New numerical solutions to the so-called selection problem for one and two
steadily translating bubbles in an unbounded Hele-Shaw cell are presented. Our
approach relies on conformal mapping which, for the two-bubble problem,
involves the Schottky-Klein prime function associated with an annulus. We show
that a countably infinite number of solutions exist for each fixed value of
dimensionless surface tension, with the bubble shapes becoming more exotic as
the solution branch number increases. Our numerical results suggest that a
single solution is selected in the limit that surface tension vanishes, with
the scaling between the bubble velocity and surface tension being different to
the well-studied problems for a bubble or a finger propagating in a channel
geometry.