Bubble in a corner flow

The distortion of a two dimensional bubble (or drop) in a corner of angle delta, due to the flow of an inviscid incompressible fluid around it, is examined theoretically. The flow and the bubble shape are determined as functions of the angle delta, the contact angle beta and the cavitation number gamma. The problem is formulated as an integrodifferential equation for the bubble surface. This equation generalizes the integrodifferential equations derived by VandenBroeck and Keller. The shape of the bubble is found approximately by using the slender body theory for bubbles presented by Vanden-Broeck and Keller. When gamma reaches a critical value gamma sub 0 (beta, delta), opposite sides of the bubble touch each other. Two different families of solution for gamma gamma sub 0 are obtained. In the first family opposite sides touch at one point. In the second family contact is allowed along a segment. The methods used to calculate these two families are similar to the ones used by Vanden-Broeck and Keller and Vanden-Broeck.