Self-similarity with universal property for soap film and bubble in roll-off stage

TL;DR

This paper investigates the self-similar and universal behaviors in the thinning and breaking of soap bubbles during the roll-off stage, revealing scale-invariant profiles and early memory erasure in the process.

Contribution

It demonstrates the existence of self-similarity and universal properties in soap bubble profiles during specific regimes, extending understanding of bubble dynamics and scaling laws.

Findings

Self-similarity observed in bubble profiles during roll-off and cusp approach regimes.

Universal property where profiles are identical across different sizes when scaled appropriately.

Minimum radius scales as the square root of the countdown time, independent of volume and pulling speed.

Abstract

All children enjoy blowing soap bubbles that also show up in our bath and when we wash dishes. We analyze the thinning and breaking of soap bubble neck when it is stretched. To contrast with the more widely studied film whose boundaries are open, we concentrate on the bubble with a conserved air volume V. Like film (F), non-equilibrium state can be divided into four regimes for bubble (B): (1) roll-off, (2) cusp approach, (3) pinch-off and (4) breakup. We establish the existence of self-similarity in F-1, B-1 and B-3, and universal property in F-1 and B-1 for the profile of soap membrane. The former means that the profile at successive times can be mapped to a master curve after being rescaled by the countdown time \tau. Whiles, the latter further requires this master curve to be identical for different ring sizes R for film and different V and R for bubble while keeping V/R^3 fixed. The exhibition of universal property indicates that the process of memory erasing starts earlier than regime 3. We also found that the minimum radius scales as h_{min}~\tau ^{1/2}, independent of V and pulling speed. Note that the validity of our discussion is limited by the duration of roll-off regime from 10^{-2}~10^{-3} s.