Bubble in a corner flow
Abstract
The distortion of a twodimensional 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 generalized the integrodifferential equations derived by VandenBroeck and Keller. The shape of the bubble is found approximately by using the slender body theory for bubbles. 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.
 Publication:

2d International Colloquium on Drops and Bubbles
 Pub Date:
 March 1982
 Bibcode:
 1982drbu.coll..336V
 Keywords:

 Bubbles;
 Corner Flow;
 Drops (Liquids);
 Fluid Mechanics;
 Free Boundaries;
 Shapes;
 Boundary Value Problems;
 Cavitation Flow;
 Differential Equations;
 GasSolid Interfaces;
 Incompressible Flow;
 Integral Equations;
 Inviscid Flow;
 Fluid Mechanics and Heat Transfer