Axisymmetric bubble pinch-off at high Reynolds numbers

TL;DR

This paper investigates the dynamics of bubble pinch-off at high Reynolds numbers, revealing different scaling laws for the minimum radius depending on symmetry and flow conditions, supported by analytical, numerical, and experimental results.

Contribution

It identifies the conditions under which symmetric and asymmetric bubble pinch-off behaviors occur and derives the corresponding scaling laws, validated through experiments.

Findings

Symmetric bubble pinch-off follows a specific scaling law involving a logarithmic correction.

Asymmetry in bubble shape leads to a different power-law scaling of the neck radius.

Experimental results confirm the theoretical and numerical predictions.

Abstract

Analytical considerations and potential flow numerical simulations of the pinch-off of bubbles at high Reynolds numbers reveal that the bubble minimum radius, $r_n$, decreases as $\tau\propto r_n^2 \, (-\ln{r_n^2})^{1/2}$, where $\tau$ is the time to break-up, when the local shape of the bubble near the singularity is symmetric. However, if the gas convective terms in the momentum equation become of the order of those of the liquid, the bubble shape is no longer symmetric and the evolution of the neck changes to a $r_n\propto\tau^{1/3}$ power law. These findings are verified experimentally.