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

TL;DR

This paper predicts a new velocity selection phenomenon in Laplacian growth, showing that multi-bubble solutions naturally select a specific velocity ratio without surface tension, challenging previous assumptions.

Contribution

It introduces exact multi-bubble solutions demonstrating velocity selection in Hele-Shaw flows without surface tension, revealing a novel attractor in interface dynamics.

Findings

The velocity U = 2V is the only attractor for the bubble dynamics.

Velocity selection occurs without surface tension or external regularization.

Exact multi-bubble solutions are constructed and analyzed.

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.