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  • Open Access

Thin-Film Drainage Becomes Singular at Saddles

Simeon Djambov1,2, Alice Marcotte3, François Gallaire1, and Pier Giuseppe Ledda4,*

  • *Contact author: piergiuseppe.ledda@unica.it
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Phys. Rev. Lett. 137, 164002 – Published 15 October, 2026

DOI: https://doi.org/10.1103/6dfx-zb87

Abstract

From coating curved parts to creeping lava, thin-film gravitational drainage over complex surfaces can produce abrupt accumulation, usually associated with sharp edges or defects. Here, experiments, simulations, and asymptotics show that a smooth saddle alone generates a logarithmically singular ridge, regularized within a dynamic region where drainage balances hydrostatic pressure and capillarity. In a Newtonian lubrication picture, this mechanism can inform redistribution in manufacturing and geophysics, motivating extensions to complex rheology and interacting geometric features.

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Phys. Rev. Lett. 137, 164002– Published 15 October, 2026
  • Received 2 June 2026
  • Accepted 18 September 2026
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