Multiple bubble dynamics and velocity selection in Laplacian growth without surface tension

Abstract

A new selection phenomenon in nonlinear interface dynamics is predicted. A generic class of exact regular unsteady multi-bubble solutions in a Hele-Shaw cell is presented. These solutions show that the case where the asymptotic bubble velocity, U, is twice greater than the velocity, V, of the uniform background flow, i.e., U=2V, is the only attractor of the dynamics. Contrary to common belief, the predicted velocity selection requires neither surface tension nor other external regularization.