How soap bubbles change shape while maintaining a fixed volume of air?

TL;DR

This paper investigates how soap bubbles change shape while maintaining a fixed volume, combining experiments and theory to understand stability, shape transitions, and breakup phenomena in comparison to open films.

Contribution

It introduces a theoretical framework incorporating volume conservation via a Lagrange multiplier, revealing critical length thresholds and shape evolution differences between bubbles and films.

Findings

Identified a critical length beyond which bubbles irreversibly pinch off.

Demonstrated the role of volume conservation in shape transitions.

Compared stability profiles of bubbles and films, highlighting universal behaviors.

Abstract

We combine experiments and theoretical derivations to study the evolution of a stretched soap bubble and compare it with an open film to highlight the effect of volume conservation. We identify a critical length for both surfaces, beyond which a bottleneck develops in the middle and begins to shrink irreversibly, ultimately pinching off into multiple compartments. Before leaving the equilibrium regime, surface energy minimization governs the shape, which can be addressed theoretically via the variational method. In contrast to open films, soap bubble volume conservation introduces a Lagrange multiplier, analogous to a pressure difference, mediating long-range shape evolution. By examining how boundary constraints influence deformation, we contrast the bubble's convex-to-concave transition with the behavior of soap films under similar conditions. Our analysis of equilibrium and breakup regimes reveals critical differences between bubble and film stability profiles, shedding light on universal behaviors in non-equilibrium fluid mechanics, with implications for biological and material sciences.