On the breakup of air bubbles in Hele-Shaw cell

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).