Selection in the Saffman-Taylor bubble and asymmetrical finger problem

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Abstract
A systematic study of the zero-surface-tension solutions for a bubble in a Hele-Shaw cell is made. Then the technique used for the Saffman-Taylor finger is applied to find how the actual solution for nonzero surface tension is selected out of this family. We find that only symmetrical bubbles are allowed. In particular, in the limit of zero surface tension we find that the velocity of the bubble is twice the velocity of the fluid at infinity. We also find in the case of Saffman-Taylor fingers that the symmetrical finger is selected against the asymmetrical ones.

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