- Open Access
Balloon regime: Drop elasticity leads to complete rebound
Phys. Rev. Research 8, 023022 – Published 7 April, 2026
DOI: https://doi.org/10.1103/9gxn-thst
Abstract
When a highly elastic drop of a polymer solution hits a superhydrophobic surface at a high speed, a growing tail-like filament emerges vertically from the impact spot as the contact line recedes. Notably, the ligament transitions into a balloonlike shape before detaching completely from the surface (balloon regime). The ligament formation is attributed to liquid impalement upon impact into the surface protrusion spacing, and elastic forces due to polymers prevent ligament breakup. The detachment of the ligament happens when polymeric stresses balance or overcome the adhesion at the surface. This study shows that tuning droplet rheology and surface roughness enables droplets to rebound completely and without splashing at high impact speeds.
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References (55)
- Y. S. Joung and C. R. Buie, Aerosol generation by raindrop impact on soil, Nat. Commun. 6, 6083 (2015).
- T. Gilet and L. Bourouiba, Fluid fragmentation shapes rain-induced foliar disease transmission, J. R. Soc. Interface 12, 20141092 (2015).
- L. Bourouiba, The fluid dynamics of disease transmission, Annu. Rev. Fluid Mech. 53, 473 (2021).
- C. D. Modak, A. Kumar, A. Tripathy, and P. Sen, Drop impact printing, Nat. Commun. 11, 4327 (2020).
- D. Lohse, Fundamental fluid dynamics challenges in inkjet printing, Annu. Rev. Fluid Mech. 54, 349 (2022).
- H. Wu, N. Mendel, D. van den Ende, G. Zhou, and F. Mugele, Energy harvesting from drops impacting onto charged surfaces, Phys. Rev. Lett. 125, 078301 (2020).
- S. Shiri and J. C. Bird, Heat exchange between a bouncing drop and a superhydrophobic substrate, Proc. Natl. Acad. Sci. USA 114, 6930 (2017).
- A. L. Yarin, Drop impact dynamics: Splashing, spreading, receding, bouncing…, Annu. Rev. Fluid Mech. 38, 159 (2006).
- A. M. Karim, Physics of droplet impact on various substrates and its current advancements in interfacial science: A review, J. Appl. Phys. 133, 030701 (2023).
- N. Fujisawa, T. Yamagata, K. Hayashi, and T. Takano, Experiments on liquid droplet impingement erosion by high-speed spray, Nucl. Eng. Des. 250, 101 (2012).
- J. Poloprudský, A. Chlupová, I. Šulák, T. Kruml, and S. Hloch, Surface and subsurface analysis of stainless steel and titanium alloys exposed to ultrasonic pulsating water jet, Materials 14, 5212 (2021).
- A. Nastic, M. Vijay, A. Tieu, and B. Jodoin, High speed water droplet impact erosive behavior on dry and wet pulsed waterjet treated surfaces, Phys. Fluids 35, 053609 (2023).
- A. Milionis, C. S. Sharma, R. Hopf, M. Uggowitzer, I. S. Bayer, and D. Poulikakos, Engineering fully organic and biodegradable superhydrophobic materials, Adv. Mater. Interfaces 6, 1801202 (2019).
- T. Zhu, Y. Cheng, J. Huang, J. Xiong, M. Ge, J. Mao, Z. Liu, X. Dong, Z. Chen, and Y. Lai, A transparent superhydrophobic coating with mechanochemical robustness for anti-icing, photocatalysis and self-cleaning, Chem. Eng. J. 399, 125746 (2020).
- Y. Zhang, Z. Zhang, J. Yang, Y. Yue, and H. Zhang, A review of recent advances in superhydrophobic surfaces and their applications in drag reduction and heat transfer, Nanomaterials 12, 44 (2021).
- H. Xu, A. Clarke, J. P. Rothstein, and R. J. Poole, Sliding viscoelastic drops on slippery surfaces, Appl. Phys. Lett. 108, 241602 (2016).
- L. Chen, Y. Wang, X. Peng, Q. Zhu, and K. Zhang, Impact dynamics of aqueous polymer droplets on superhydrophobic surfaces, Macromolecules 51, 7817 (2018).
- L.-H. Luu and Y. Forterre, Giant drag reduction in complex fluid drops on rough hydrophobic surfaces, Phys. Rev. Lett. 110, 184501 (2013).
- R. Rabbi, A. Kiyama, J. S. Allen, and T. Truscott, Droplet lift-off from hydrophobic surfaces from impact with soft-hydrogel spheres, Commun. Phys. 5, 331 (2022).
- V. Bergeron, D. Bonn, J. Y. Martin, and L. Vovelle, Controlling droplet deposition with polymer additives, Nature (London) 405, 772 (2000).
- D. Bartolo, A. Boudaoud, G. Narcy, and D. Bonn, Dynamics of non-Newtonian droplets, Phys. Rev. Lett. 99, 174502 (2007).
- P. Dhar, S. R. Mishra, and D. Samanta, Onset of rebound suppression in non-Newtonian droplets post-impact on superhydrophobic surfaces, Phys. Rev. Fluids 4, 103303 (2019).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/9gxn-thst for a description of experimental, numerical methods, and Supplemental Movie S1, which includes Refs. [38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55].
- A. B. D. Cassie and S. Baxter, Wettability of porous surfaces, Trans. Faraday Soc. 40, 546 (1944).
- R. N. Wenzel, Resistance of solid surfaces to wetting by water, Ind. Eng. Chem. 28, 988 (1936).
- D. Bartolo, F. Bouamrirene, E. Verneuil, A. Buguin, P. Silberzan, and S. Moulinet, Bouncing or sticky droplets: Impalement transitions on superhydrophobic micropatterned surfaces, Europhys. Lett. 74, 299 (2006).
- M. Reyssat, A. Pépin, F. Marty, Y. Chen, and D. Quéré, Bouncing transitions on microtextured materials, Europhys. Lett. 74, 306 (2006).
- T. Deng, K. K. Varanasi, M. Hsu, N. Bhate, C. Keimel, J. Stein, and M. Blohm, Nonwetting of impinging droplets on textured surfaces, Appl. Phys. Lett. 94, 133109 (2009).
- V. A. Del Grosso and C. W. Mader, Speed of sound in pure water, J. Acoust. Soc. Am. 52, 1442 (1972).
- B. Zhao, X. Wang, K. Zhang, L. Chen, and X. Deng, Impact of viscous droplets on superamphiphobic surfaces, Langmuir 33, 144 (2017).
- K. R. Langley, E. Q. Li, I. U. Vakarelski, and S. T. Thoroddsen, The air entrapment under a drop impacting on a nano-rough surface, Soft Matter 14, 7586 (2018).
- X. Deng, F. Schellenberger, P. Papadopoulos, D. Vollmer, and H.-J. Butt, Liquid drops impacting superamphiphobic coatings, Langmuir 29, 7847 (2013).
- X. Li, et al., Spontaneous charging affects the motion of sliding drops, Nat. Phys. 18, 713 (2022).
- S. Shumaly, F. Darvish, X. Li, A. Saal, C. Hinduja, W. Steffen, O. Kukharenko, H.-J. Butt, and R. Berger, Deep learning to analyze sliding drops, Langmuir 39, 1111 (2023).
- A. V. Bazilevskii, V. M. Entov, M. M. Lerner, and A. N. Rozhkov, Failure of polymer solution filaments, Polym. Sci. Ser. A 39, 316 (1997).
- S. L. Anna and G. H. McKinley, Elasto-capillary thinning and breakup of model elastic liquids, J. Rheol. 45, 115 (2001).
- P. P. Bhat, S. Appathurai, M. T. Harris, M. Pasquali, G. H. McKinley, and O. A. Basaran, Formation of beads-on-a-string structures during break-up of viscoelastic filaments, Nat. Phys. 6, 625 (2010).
- J. W. Drelich, L. Boinovich, E. Chibowski, C. Della Volpe, L. Hołysz, A. Marmur, and S. Siboni, Contact angles: History of over 200 years of open questions, Surf. Innov. 8, 3 (2020).
- 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).
- G. Bradski, The OpenCV Library, Dr. Dobb's J. Softw. Tools 25, 120 (2000).
- W. H. Press and S. A. Teukolsky, Savitzky–Golay smoothing filters, Comput. Phys. 4, 669 (1990).
- J. Dinic, Y. Zhang, L. N. Jimenez, and V. Sharma, Extensional relaxation times of dilute, aqueous polymer solutions, ACS Macro Lett. 4, 804 (2015).
- A. Franco-Gómez, H. Onuki, Y. Yokoyama, Y. Nagatsu, and Y. Tagawa, Effect of liquid elasticity on the behaviour of high-speed focused jets, Exp. Fluids 62, 41 (2021).
- S. Popinet, An accurate adaptive solver for surface-tension-driven interfacial flows, J. Comput. Phys. 228, 5838 (2009).
- S. Popinet et al., Basilisk C (2013–2024), http://basilisk.fr (accessed 16 December 2024).
- S. Popinet, Numerical models of surface tension, Annu. Rev. Fluid Mech. 50, 49 (2018).
- J. U. Brackbill, D. B. Kothe, and C. Zemach, A continuum method for modeling surface tension, J. Comput. Phys. 100, 335 (1992).
- R. Comminal, J. Spangenberg, and J. H. Hattel, Robust simulations of viscoelastic flows at high Weissenberg numbers with the streamfunction/log-conformation formulation, J. Non-Newtonian Fluid Mech. 223, 37 (2015).
- R. Fattal and R. Kupferman, Constitutive laws for the matrix-logarithm of the conformation tensor, J. Non-Newtonian Fluid Mech. 123, 281 (2004).
- J. H. Snoeijer, A. Pandey, M. A. Herrada, and J. Eggers, The relationship between viscoelasticity and elasticity, Proc. R. Soc. A 476, 20200419 (2020).
- B. Purnode and M. J. Crochet, Polymer solution characterization with the fene-p model, J. Non-Newtonian Fluid Mech. 77, 1 (1998).
- P. C. Sousa, P. M. Coelho, M. S. N. Oliveira, and M. A. Alves, Polymer solution characterization with the fene-p model, Chem. Eng. Sci. 66, 998 (2011).
- 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).
- K. Yokoi, D. Vadillo, J. Hinch, and I. Hutchings, Numerical studies of the influence of the dynamic contact angle on a droplet impacting on a dry surface, Phys. Fluids 21, 072102 (2009).
- L. Gordillo, T.-P. Sun, and X. Cheng, Dynamics of drop impact on solid surfaces: Evolution of impact force and self-similar spreading, J. Fluid Mech. 840, 190 (2018).