Multiple bubble dynamics and velocity selection in Laplacian growth without surface tension
We predict a novel selection phenomenon in nonlinear interface dynamics out of equilibrium. Using a recently developed formalism based on the Schottky-Klein prime functions, we extended the existing integrable theory from a single interface to multiple moving interfaces. After applying this extended theory to the two-dimensional Laplacian growth, we derive a new rich class of exact non-singular solutions for the unsteady dynamics of an arbitrary assembly of air bubbles within a layer of a viscous ﬂuid in a Hele-Shaw cell. These solutions demonstrate that all bubbles reach an asymptotic velocity, U , which is precisely twice greater than the velocity, V , of the uniform background ﬂow, i.e., U = 2 V . The result does not depend on the number of bubbles. Contrary to common belief, the predicted velocity selection does not require surface tension or any other external regularization.