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arXiv · 2606.11881

Thin-film drainage becomes singular at saddles

Simeon Djambov·Alice Marcotte·François Gallaire·Pier Giuseppe Ledda
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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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Simeon Djambov, Alice Marcotte, François Gallaire, Pier Giuseppe Ledda. 2026-09-14. Thin-film drainage becomes singular at saddles. https://arxiv.org/abs/2606.11881

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