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Beyond Tate's law: Geometric control of pendant drop detachment

Bauyrzhan K. Primkulov*

  • *Contact author: bauyrzhan.primkulov@yale.edu

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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