On the breakup of air bubbles in Hele-Shaw cell

TL;DR

This paper investigates the breakup dynamics of air bubbles in Hele-Shaw cells, proposing conditions for breakup, methods to identify contraction points, and analyzing asymptotic behaviors under various controlled and natural scenarios.

Contribution

It introduces new sufficient conditions for bubble breakup, methods to locate contraction points, and studies asymptotic behaviors in bubble contraction within Hele-Shaw cells.

Findings

Derived conditions for bubble breakup.

Identified contraction points during bubble evolution.

Analyzed asymptotic contraction behaviors.

Abstract

We study the problem of breakup of an air bubble in a Hele-Shaw cell. In particular, we propose some sufficient conditions of breakup of the bubble, and ways to find the contraction points of its parts. We also study regulated contraction of a pair of bubbles (in which the rates of air extraction from the bubbles is controlled), and study various asymptotic questions (such as the asymptotics of contraction of a bubble to a degenerate critical point, and asymptotics of contraction of a small bubble in presence of a big bubble).