Selection in the anomalous Saffman-Taylor fingers induced by a bubble.

Abstract

We investigate theoretically the selection in Saffman-Taylor fingers in the presence of a small bubble. Experimentally anomalous fingers have been found in this case, with relative width much smaller than what is found for the standard fingers. We study the case of a small bubble far ahead of the finger and solve the problem for zero surface tension. We then show that selection due to surface tension leads indeed to narrow fingers. Finally we consider the more complicated case (but more relevant experimentally) of a bubble sticking to the finger and find again that narrow fingers are allowed.