Infinite stream of Hele–Shaw bubbles

Exact solutions are presented for a steady stream of bubbles in a Hele–Shaw cell when the effect of surface tension is neglected. These solutions form a three-parameter family. For specified area and distance between bubbles, the speed of the bubble remains arbitrary when surface tension is neglected. However, numerical and analytical evidence indicates that this arbitrariness is removed by the effect of surface tension. The branch of solutions that corresponds to the McLean–Saffman finger solution were primarily studied. A dramatic increase was observed in bubble speeds when the distance between bubbles is on the order of a bubble diameter, which may have relevance to experiments done by Maxworthy [J. Fluid Mech. 173, 95 (1986)].