Pointed bubbles in slow viscous flow

Inviscid bubbles confined by the slow axisymmetric straining motion of a very viscous fluid are considered for the case when the surface tension is weak. The shape of the bubbles is determined using slender-body theory, and it is found that these bubbles have pointed ends, in agreement with well-established experimental results. The description obtained is invalid within exponentially small neighbourhoods of the ends and a local analysis suggests that the tips are cusp-like. In both the description of the major portion of the bubble and of the ends, there is an apparent non-uniqueness because a certain parameter can take on a countably infinite number of values. This non-uniqueness is not resolved.