The bursting of hollow droplets
Abstract
A bubble bursting from a drop of finite size (a hollow droplet) is the generic bursting event in a breaking wave, yet it has been studied almost exclusively at unbounded baths. We follow it from the puncture of the film to the spectrum of a spray, in axisymmetric simulations over liquid-to-gas volume ratios Λ from 1/16 to $512$ and Ohnesorge numbers from $0.005$ to $0.11$. Ejection ceases at Oh1=Ohc(1+2β/λ), with β≃0.83 and λ=(1+Λ)1/3: confinement extends ejection to bubbles too small to eject at a flat surface, and the distance δ=1−Oh/Oh1 to that boundary organizes everything that follows. The collapse, driven by capillary waves, is that of a gas thread pinching next to its mouth, whether the liquid shell is punctured once or twice. The ejected volume is Me=C δ Vred, with C≃0.013 and Vred=VgasVliq/(Vgas+Vliq) a reduced volume. Whatever the confinement, the first droplet is smallest at δ≃0.2 in units of the viscocapillary length ℓμ=μ2/(ρσ) and at δ≃0.3 in units of the bubble radius R0, where the unbounded bath also places its optimum. The largest reaches a tenth of R0. Between them the census is exponential, with a scale set by R0 and no lower cut-off: the smallest droplet a simulation records is set by its resolution, not by ℓμ, which belongs to the pinch singularity rather than to the droplets. Mixed over bubble populations, the census gives spray spectra in closed form, whose shape measures the population. The bursting also produces hollow droplets, each a potential new generator.
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BibTeX
@misc{ganancalvo2026bursting,
title = {{The bursting of hollow droplets}},
author = {Alfonso M. Ganan-Calvo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.26296},
eprint = {2608.26296},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.26296},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - The bursting of hollow droplets
AU - Alfonso M. Ganan-Calvo
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2608.26296
UR - https://arxiv.org/abs/2608.26296
AB - A bubble bursting from a drop of finite size (a hollow droplet) is the generic bursting event in a breaking wave, yet it has been studied almost exclusively at unbounded baths. We follow it from the puncture of the film to the spectrum of a spray, in axisymmetric simulations over liquid-to-gas volume ratios Λ from 1/16 to $512$ and Ohnesorge numbers from $0.005$ to $0.11$. Ejection ceases at Oh_1=Oh_c(1+2β/λ), with β≃0.83 and λ=(1+Λ)^1/3: confinement extends ejection to bubbles too small to eject at a flat surface, and the distance δ=1−Oh/Oh_1 to that boundary organizes everything that follows. The collapse, driven by capillary waves, is that of a gas thread pinching next to its mouth, whether the liquid shell is punctured once or twice. The ejected volume is M_e=C δ V_red, with C≃0.013 and V_red=V_gasV_liq/(V_gas+V_liq) a reduced volume. Whatever the confinement, the first droplet is smallest at δ≃0.2 in units of the viscocapillary length ℓ_μ=μ^2/(ρσ) and at δ≃0.3 in units of the bubble radius R_0, where the unbounded bath also places its optimum. The largest reaches a tenth of R_0. Between them the census is exponential, with a scale set by R_0 and no lower cut-off: the smallest droplet a simulation records is set by its resolution, not by ℓ_μ, which belongs to the pinch singularity rather than to the droplets. Mixed over bubble populations, the census gives spray spectra in closed form, whose shape measures the population. The bursting also produces hollow droplets, each a potential new generator.
ER -