Exact solutions for shapes of two-dimensional bubbles in a corner flow

A one-parameter family of exact solutions for the deformations of two-dimensional bubbles in a corner flow of an ideal liquid is obtained. The solutions correspond to the special case where the pressure inside the bubble equals the stagnation pressure. The parameter of the model is the corner angle. The solution family includes classical McLeod's solution which corresponds to the corner of angle pi. For the particular case of a right-angled corner, the solution describes the straining flow past a bubble. In view of the known analogy between the distributions of a planar electric field and the velocity field for a two-dimensional potential flow, our solutions give equilibrium configurations of the surface of a conducting liquid in an external electric field. (C) 2007 American Institute of Physics.