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Size amplification of jet drops due to insoluble surfactants

Jun Eshima1,*, Tristan Aurégan1,*, Palas Kumar Farsoiya2, Stéphane Popinet3, Howard A. Stone1, and Luc Deike1,4,†

  • *These authors contributed equally to this work.
  • †Contact author: ldeike@princeton.edu
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Phys. Rev. Fluids 10, 123604 – Published 30 December, 2025

DOI: https://doi.org/10.1103/t9k3-dqyc

Abstract

Surface bubbles in the environment or engineering configurations, such as the ocean-atmosphere interface, sparkling wine, or during volcanic eruptions typically live on contaminated surfaces. A particularly common type of contamination is surface active agents (surfactants). We consider the effect of insoluble surfactant on jet drop formation by bubble bursting. Contrary to the observed trend that surfactants decrease the ejected drop radius for bubbles with precursor capillary waves, we find that surfactants increase the ejected drop radius for bubbles without precursor capillary waves—a regime characteristic of small bubbles. Consequently, the results have fundamental implications for understanding aerosol distributions in contaminated conditions. We find that the trend reversal is due to the effect of Marangoni stresses on the focusing of the collapsing cavity. We demonstrate quantitative agreement on the jet velocity and drop size between laboratory experiments and numerical simulations by using the measured surface tension dependence on surfactant concentration as the equation of state for the simulations.

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References (69)

  1. F. Veron, Ocean spray, Annu. Rev. Fluid Mech. 47, 507 (2015).
  2. L. Deike, Mass transfer at the ocean–atmosphere interface: The role of wave breaking, droplets, and bubbles, Annu. Rev. Fluid Mech. 54, 191 (2022).
  3. D. C. Blanchard, The ejection of drops from the sea and their enrichment with bacteria and other materials: A review, Estuaries 12, 127 (1989).
  4. L. Bourouiba, The fluid dynamics of disease transmission, Annu. Rev. Fluid Mech. 53, 473 (2021).
  5. E. Ghabache, A. Antkowiak, C. Josserand, and T. Séon, On the physics of fizziness: How bubble bursting controls droplets ejection, Phys. Fluids 26, 121701 (2014).
  6. M. L. Rudolph, K. C. Sahu, N. Savva, A. Szilágyi, Z. Hórvölgyi, P. Márton, Á. Tajti, K. Szép, B. Balog, M. K. Tripathi et al., Bubble ascent and rupture in mud volcanoes, R. Soc. Open Sci. 11, 231555 (2024).
  7. A. Dixit, A. Oratis, K. Zinelis, D. Lohse, and V. Sanjay, Viscoelastic worthington jets and droplets produced by bursting bubbles, J. Fluid Mech. 1010, A2 (2025).
  8. Z. Yang, Y. Liu, and J. Feng, Jet size prediction in compound multiphase bubble bursting, Phys. Rev. Lett. 134, 214001 (2025).
  9. Z. Yang, B. Ji, J. T. Ault, and J. Feng, Enhanced singular jet formation in oil-coated bubble bursting, Nat. Phys. 19, 884 (2023).
  10. K. Sampath, N. Afshar-Mohajer, L. D. Chandrala, W.-S. Heo, J. Gilbert, D. Austin, K. Koehler, and J. Katz, Aerosolization of crude oil-dispersant slicks due to bubble bursting, J. Geophys. Res.: Atmos. 124, 5555 (2019).
  11. C. R. Constante-Amores, L. Kahouadji, A. Batchvarov, S. Shin, J. Chergui, D. Juric, and O. K. Matar, Dynamics of a surfactant-laden bubble bursting through an interface, J. Fluid Mech. 911, A57 (2021).
  12. J. Pierre, M. Poujol, and T. Séon, Influence of surfactant concentration on drop production by bubble bursting, Phys. Rev. Fluids 7, 073602 (2022).
  13. P. Pico, L. Kahouadji, S. Shin, J. Chergui, D. Juric, and O. K. Matar, Surfactant-laden bubble bursting: Dynamics of capillary waves and worthington jet at large bond number, Phys. Rev. Fluids 9, 083606 (2024).
  14. E. Vega and J. Montanero, Influence of a surfactant on bubble bursting, Exp. Therm Fluid Sci. 151, 111097 (2024).
  15. A. H. Woodcock, C. F. Kientzler, A. B. Arons, and D. C. Blanchard, Giant condensation nuclei from bursting bubbles, Nature (London) 172, 1144 (1953).
  16. D. C. Blanchard, Bursting of bubbles at an air–water interface, Nature (London) 173, 1048 (1954).
  17. L. Duchemin, S. Popinet, C. Josserand, and S. Zaleski, Jet formation in bubbles bursting at a free surface, Phys. Fluids 14, 3000 (2002).
  18. J. S. Lee, B. M. Weon, S. J. Park, J. H. Je, K. Fezzaa, and W.-K. Lee, Size limits the formation of liquid jets during bubble bursting, Nat. Commun. 2, 367 (2011).
  19. P. L. L. Walls, L. Henaux, and J. C. Bird, Jet drops from bursting bubbles: How gravity and viscosity couple to inhibit droplet production, Phys. Rev. E 92, 021002(R) (2015).
  20. C. F. Brasz, C. T. Bartlett, P. L. L. Walls, E. G. Flynn, Y. E. Yu, and J. C. Bird, Minimum size for the top jet drop from a bursting bubble, Phys. Rev. Fluids 3, 074001 (2018).
  21. L. Deike, E. Ghabache, G. Liger-Belair, A. K. Das, S. Zaleski, S. Popinet, and T. Séon, Dynamics of jets produced by bursting bubbles, Phys. Rev. Fluids 3, 013603 (2018).
  22. A. Berny, L. Deike, T. Séon, and S. Popinet, Role of all jet drops in mass transfer from bursting bubbles, Phys. Rev. Fluids 5, 033605 (2020).
  23. A. M. Gañán-Calvo, Revision of bubble bursting: Universal scaling laws of top jet drop size and speed, Phys. Rev. Lett. 119, 204502 (2017).
  24. A. M. Gañán-Calvo, Scaling laws of top jet drop size and speed from bubble bursting including gravity and inviscid limit, Phys. Rev. Fluids 3, 091601(R) (2018).
  25. J. M. Gordillo and J. Rodríguez-Rodríguez, Capillary waves control the ejection of bubble bursting jets, J. Fluid Mech. 867, 556 (2019).
  26. F. J. Blanco-Rodríguez and J. Gordillo, On the sea spray aerosol originated from bubble bursting jets, J. Fluid Mech. 886, R2 (2020).
  27. B. W. Zeff, B. Kleber, J. Fineberg, and D. P. Lathrop, Singularity dynamics in curvature collapse and jet eruption on a fluid surface, Nature (London) 403, 401 (2000).
  28. C.-Y. Lai, J. Eggers, and L. Deike, Bubble bursting: Universal cavity and jet profiles, Phys. Rev. Lett. 121, 144501 (2018).
  29. L. Deike, B. G. Reichl, and F. Paulot, A mechanistic sea spray generation function based on the sea state and the physics of bubble bursting, AGU Adv. 3, e2022AV000750 (2022).
  30. M. Mazzatenta, M. A. Erinin, B. Néel, and L. Deike, Linking emitted drops to collective bursting bubbles across a wide range of bubble size distributions, J. Fluid Mech. 1015, A8 (2025).
  31. X. Wang, G. B. Deane, K. A. Moore, O. S. Ryder, M. D. Stokes, C. M. Beall, D. B. Collins, M. V. Santander, S. M. Burrows, C. M. Sultana, and K. A. Prather, The role of jet and film drops in controlling the mixing state of submicron sea spray aerosol particles, Proc. Natl. Acad. Sci. USA 114, 6978 (2017).
  32. A. M. Gañán-Calvo, The ocean fine spray, Phys. Fluids 35, 023317 (2023).
  33. X. Jiang, L. Rotily, E. Villermaux, and X. Wang, Submicron drops from flapping bursting bubbles, Proc. Natl. Acad. Sci. USA 119, e2112924119 (2022).
  34. H. Manikantan and T. M. Squires, Surfactant dynamics: Hidden variables controlling fluid flows, J. Fluid Mech. 892, P1 (2020).
  35. B. Néel, M. A. Erinin, and L. Deike, Role of contamination in optimal droplet production by collective bubble bursting, Geophys. Res. Lett. 49, e2021GL096740 (2022).
  36. Y.-C. Liao, E. I. Franses, and O. A. Basaran, Deformation and breakup of a stretching liquid bridge covered with an insoluble surfactant monolayer, Phys. Fluids 18, 022101 (2006).
  37. M. Sussman and E. G. Puckett, A coupled level set and volume-of-fluid method for computing 3d and axisymmetric incompressible two-phase flows, J. Comput. Phys. 162, 301 (2000).
  38. M. O. Abu-Al-Saud, S. Popinet, and H. A. Tchelepi, A conservative and well-balanced surface tension model, J. Comput. Phys. 371, 896 (2018).
  39. S. Popinet, An accurate adaptive solver for surface-tension-driven interfacial flows, J. Comput. Phys. 228, 5838 (2009).
  40. S. Popinet and collaborators, Basilisk, http://basilisk.fr.
  41. A. Berny, S. Popinet, T. Séon, and L. Deike, Statistics of jet drop production, Geophys. Res. Lett. 48, e2021GL092919 (2021).
  42. M. Saini, V. Sanjay, Y. Saade, D. Lohse, and S. Popinet, Implementation of integral surface tension formulations in a volume of fluid framework and their applications to marangoni flows, J. Comput. Phys. 542, 114348 (2025).
  43. P. K. Farsoiya, S. Popinet, H. A. Stone, and L. Deike, Coupled volume of fluid and phase field method for direct numerical simulation of insoluble surfactant-laden interfacial flows and application to rising bubbles, Phys. Rev. Fluids 9, 094004 (2024).
  44. S. S. Jain, A model for transport of interface-confined scalars and insoluble surfactants in two-phase flows, J. Comput. Phys. 515, 113277 (2024).
  45. See Supplemental Material at http://link.aps.org/supplemental/10.1103/t9k3-dqyc for details of the numerical simulation and additional experimental data.
  46. Y. Toba, Drop production by bursting of air bubbles on the sea surface (ii) theoretical study on the shape of floating bubbles, J. Ocean. Soc. Japan 15, 121 (1959).
  47. H. Princen, Shape of a fluid drop at a liquid-liquid interface, J. Colloid Sci. 18, 178 (1963).
  48. A. Berny, Bubbleshape. H (2021), http://basilisk.fr/sandbox/aberny/bubble/bubbleShape.h.
  49. C. R. Constante-Amores, J. Chergui, S. Shin, D. Juric, J. Castrejón-Pita, and A. A. Castrejón-Pita, Role of surfactant-induced marangoni stresses in retracting liquid sheets, J. Fluid Mech. 949, A32 (2022).
  50. D. B. Shaw and L. Deike, Film drop production over a wide range of liquid conditions, Phys. Rev. Fluids 9, 033602 (2024).
  51. S. Poulain, E. Villermaux, and L. Bourouiba, Ageing and burst of surface bubbles, J. Fluid Mech. 851, 636 (2018).
  52. S. Poulain and L. Bourouiba, Biosurfactants change the thinning of contaminated bubbles at bacteria-laden water interfaces, Phys. Rev. Lett. 121, 204502 (2018).
  53. B. Ji, Z. Yang, Z. Wang, R. H. Ewoldt, and J. Feng, Secondary bubble entrainment via primary bubble bursting at a viscoelastic surface, Phys. Rev. Lett. 131, 104002 (2023).
  54. V. Fainerman, S. Lylyk, E. Aksenenko, L. Liggieri, A. Makievski, J. Petkov, J. Yorke, and R. Miller, Adsorption layer characteristics of triton surfactants part 2. Dynamic surface tension and adsorption, Colloids Surf., A 334, 8 (2009).
  55. V. Fainerman, S. Lylyk, E. Aksenenko, A. Makievski, J. Petkov, J. Yorke, and R. Miller, Adsorption layer characteristics of triton surfactants 1. Surface tension and adsorption isotherms, Colloids Surf., A 334, 1 (2009).
  56. R. Miller, E. Aksenenko, and V. Fainerman, Dynamic interfacial tension of surfactant solutions, Adv. Colloid Interface Sci. 247, 115 (2017).
  57. M. A. Erinin, C. Liu, X. Liu, W. Mostert, L. Deike, and J. H. Duncan, The effects of surfactants on plunging breakers, J. Fluid Mech. 972, R5 (2023).
  58. N.-S. Cheng, Formula for the viscosity of a glycerol-water mixture, Ind. Eng. Chem. Res. 47, 3285 (2008).
  59. K. Takamura, H. Fischer, and N. R. Morrow, Physical properties of aqueous glycerol solutions, J. Petrol. Sci. Eng. 98-99, 50 (2012).
  60. V. M. Kaganer, H. Möhwald, and P. Dutta, Structure and phase transitions in langmuir monolayers, Rev. Mod. Phys. 71, 779 (1999).
  61. F. Crameri, Scientific colour maps (7.0.1), Zenodo (2021), https://zenodo.org/records/5501399.
  62. T. Aurégan and L. Deike, Surface bubble lifetime in the presence of a turbulent air flow, and the effect of surface layer renewal, arXiv:2505.04819 [J. Fluid. Mech. (to be published)].
  63. A. Sierou and J. R. Lister, Self-similar recoil of inviscid drops, Phys. Fluids 16, 1379 (2004).
  64. D. P. Gaver and J. B. Grotberg, The dynamics of a localized surfactant on a thin film, J. Fluid Mech. 213, 127 (1990).
  65. D. Quéré, Fluid coating on a fiber, Annu. Rev. Fluid Mech. 31, 347 (1999).
  66. S. Rodríguez-Aparicio, A. Cebrián-García, E. J. Vega, J. M. Montanero, and M. G. Cabezas, Critical bubble bursting in real water, Effect of surface-active contaminants, arXiv:2507.17671.
  67. T. J. Boerner, S. Deems, T. R. Furlani, S. L. Knuth, and J. Towns, Access: Advancing innovation: Nsf's advanced cyberinfrastructure coordination ecosystem: Services & support, in Practice and Experience in Advanced Research Computing 2023: Computing for the Common Good (2023), pp. 173–176.
  68. https://basilisk.fr/sandbox/jeshima/jet_drop_surfactant_effect/
  69. J. Eshima, T. Aurégan, P. K. Farsoiya, S. Popinet, H. Stone, and L. Deike, Data set for “Size amplification of jet drops due to insoluble surfactants”, Princeton University, 2025, https://datacommons.princeton.edu/discovery/catalog/doi-10-34770-1pf8-xy34.

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Phys. Rev. Fluids 10, 123604– Published 30 December, 2025
  • Received 12 July 2025
  • Accepted 3 November 2025
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