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Enhanced singular jet formation in oil-coated bubble bursting

Nature Physics volume 19, pages 884–890 (2023)Cite this article

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Abstract

Bubble-bursting aerosols have a key role in mass and momentum transfer across interfaces. Previous studies report that the bursting of a millimetre-sized bare bubble at an aqueous surface produces jet drops with a typical size on the order of 100 μm. Here we show that jet drops can be as small as a few micrometres when the bursting bubble is coated by a thin oil layer. The faster and smaller jet drops result from the singular dynamics of the oil-coated cavity collapse. The air–oil–water compound interface offers a distinct damping mechanism to smooth out the precursor capillary waves during cavity collapse, leading to a more efficient focusing of the dominant wave and thus allowing singular jets over a much wider parameter space than that of a bare bubble. We develop a theoretical explanation for the parameter limits of the singular jet regime by considering the interplay between inertia, surface tension and viscous effects. Contaminated bubbles are widely observed, therefore previously unrecognized fast and small contaminant-laden jet drops may contribute to the aerosolization and airborne transmission of bulk substances.

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Fig. 1: Oil-coated bubble bursting at an aqueous surface.
Fig. 2: Characterization of jets produced from oil-coated bubble bursting.
Fig. 3: Cavity collapse and capillary wave propagation.
Fig. 4: Regime map of singular jets and jet drop generation by collective oil-coated bubble bursting.

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Data availability

Source data are provided with this paper and are available via Figshare at https://figshare.com/articles/dataset/Source_data_Enhanced_singular_jet_formation_in_oil-coated_bubble_bursting/21746309. All other data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

Code availability

The codes used for the Basilisk simulation in this study are available at http://basilisk.fr/sandbox/jtault/README. The codes for bubble shape calculation are available via Github at https://github.com/zyyang-mech/Enhanced-singular-jet-formation-in-oil-coated-bubble-bursting.

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Acknowledgements

We thank H. A. Stone at Princeton University for helpful discussions about the paper, S. Hilgenfeldt at the University of Illinois at Urbana-Champaign for discussions on wave modelling and V. Sanjay at the University of Twente for fruitful suggestions for the simulations. This work is partially supported by the American Chemical Society Petroleum Research Fund under grant number 61574-DNI9 (to J.F.)

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Author notes

  1. These authors contributed equally: Zhengyu Yang, Bingqiang Ji.

Authors and Affiliations

  1. Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, USA

    Zhengyu Yang, Bingqiang Ji & Jie Feng

  2. School of Engineering, Brown University, Providence, RI, USA

    Jesse T. Ault

  3. Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL, USA

    Jie Feng

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  1. Zhengyu Yang
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Contributions

B.J. and J.F. conceived the project. B.J. and J.F. designed the experiments. Z.Y. and B.J. conducted the experiments and analysed the results. Z.Y., B.J. and J.F. conducted the theoretical analysis. J.T.A. conducted the simulations with Basilisk. Z.Y. conducted other numerical analyses. J.T.A. and Z.Y. post-processed the simulation results. Z.Y., B.J., J.T.A. and J.F. discussed the results and wrote the paper.

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Correspondence to Jie Feng.

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Nature Physics thanks Radu Cimpeanu and Samantha McBride for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Experiment setup for the imaging of oil-coated bubble bursting.

a, Schematic drawings of the experiment setup. The oil-coated bubbles are generated from coaxial orifices, and observed with two high-speed cameras simultaneously. b, Zoom-in image of a typical oil-coated bubble at a free surface with μo = 19 mPa s and ψo = 6%.

Extended Data Fig. 2 Variation of oil volume composition in top jet drop from bursting of oil-coated bubbles with different oil volume fractions.

The data points denote the oil volume composition of the top jet drop for oil-coated bubble bursting (with 4.6 mPa s oil), obtained from simulations. Here ϕo represents oil volume composition in the top jet drop. The dashed line denotes the minimum oil volume fraction to produce an oil-only top jet drop estimated from experiments.

Extended Data Fig. 3 Bursting of bare bubbles of R ≈ 2 mm at liquid surfaces with increasing Ohw only produces non-singular jets.

A bare bubble with R = 2.1 ± 0.3 mm bursts at the surface of water (Ohw = 0.0026, a), 50 wt% glycerin-water solution (Ohw = 0.015, b), 4.6 mPa s silicone oil (Ohw = 0.025, c), and 70 wt% glycerin-water solution (Ohw = 0.06, d). The scale bar represents 1 mm.

Extended Data Fig. 4 Dimensionless jet velocity and radius from oil-coated bubble bursting.

a, Dimensionless jet velocity vj/vce as a function of oil volume fraction ψo at different oil viscosities μo. For the pure water case, vce = vcw is used. b, Dimensionless jet radius rj/R as a function of ψo. The hollow markers at the left vertical axes of a, b represent the case for a bare bubble of the same size bursting in pure water.

Extended Data Fig. 5 Comparison of the numerically calculated static shape of oil-coated bubbles (red dashed curves) with experimental images.

The static shapes of the bubbles with μo = 1.8 mPa s and ψo = 2.3% (a), 4.3% (b), and 12.6% (c) resting at the free surface prior to bursting are well captured by the numerical solutions with the fluid properties listed in Extended Data Table 1. The scale bar represents 1 mm.

Extended Data Fig. 6 Comparison of the experiment and simulation for oil-coated bubble bursting.

Left of each panel shows the experimental high-speed images of an oil-coated bubble bursting. Here μo = 19 mPa s, ψo = 4.2%. t = 0 represents the instant when a hole nucleates in the bubble cap. Right of each panel shows the simulation snapshots of corresponding cavity shape. The white, black, and grey regimes denote air, oil, and water phases, respectively. The scale bar represents 1 mm.

Extended Data Fig. 7 Characterization of the SW propagation for oil-coated bubble bursting.

a-b, Capillary wave propagation during the bursting of an oil-coated bubble with μo = 1.8 mPa s and ψo = 4.2% (a) and a bare bubble (b). White, black and grey colors represent air, oil, and water phases, respectively. The bubble radius R = 2 mm. The scale bar represents 1 mm. c, Angular wave position θ as a function of t* for oil-coated bubble bursting with R = 2 mm and μo = 4.6 mPa s at different ψo. d, Dimensionless SW wavelength λs/R as a function of ψo at θ = π/6 for oil-coated bubbles with μo = 4.6 mPa s.

Extended Data Fig. 8 Bubble bursting jet with different bulk liquid viscosities.

a-b, Regime map of jet singularity regarding oil fraction ψo and bulk liquid viscosity μw (or \({{{{\rm{Oh}}}}}_{{{{\rm{w}}}}}={\mu }_{{{{\rm{w}}}}}/{({\rho }_{{{{\rm{w}}}}}{{{R}}}{\gamma }_{{{{\rm{wa}}}}})}^{1/2}\)), with an coating oil viscosity of 1.8 mPa s (a) and 4.6 mPa s (b). c, Experimental snapshots of a singular jet produced by bubble bursting with μw = 22.5 mPa s, μo = 4.6 mPa s, and ψo = 1.0%. The red dashed line marks the bubble cap before rupturing. The scale bar represents 1 mm.

Extended Data Table 1 Physical properties of the liquids used in the experiments
Full size table

Supplementary information

Supplementary Information

Supplementary Discussion.

Supplementary Video 1

High-speed side view of a singular jet from an oil-coated bubble bursting with μo = 4.6 mPa s and ψo = 10%. R = 2.0 mm.

Supplementary Video 2

High-speed side view of a non-singular jet from a bare bubble with R = 1.9 mm bursting in pure water.

Supplementary Video 3

High-speed side view of the bottom of an oil-coated bubble bursting μo = 1.8 mPa s and ψo = 4.2%, showing capillary wave separation at the compound interface and tiny bubble entrapment at jet formation. R = 2.1 mm.

Supplementary Video 4

Simulation of a bare bubble with R = 2 mm bursting in water. Here white, grey and black regions represent air, oil and water, respectively.

Supplementary Video 5

Simulation of an oil-coated bubble bursting in water, with R = 2 mm, μo = 0.9 mPa s, and ψo = 4.2%. Here white, grey and black regions represent air, oil and water, respectively.

Supplementary Video 6

Simulation of an oil-coated bubble bursting in water, with R = 2 mm, μo = 4.6 mPa s, and ψo = 4.2%. Here white, grey and black regions represent air, oil and water, respectively.

Source data

Source Data Figs. 2–4

All source data for Figs. 2–4.

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Yang, Z., Ji, B., Ault, J.T. et al. Enhanced singular jet formation in oil-coated bubble bursting. Nat. Phys. 19, 884–890 (2023). https://doi.org/10.1038/s41567-023-01958-z

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