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Thin-film drainage becomes singular at saddles
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.
Versions
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BibTeX
@misc{djambov2026thinfilm,
title = {{Thin-film drainage becomes singular at saddles}},
author = {Simeon Djambov and Alice Marcotte and François Gallaire and Pier Giuseppe Ledda},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.11881},
eprint = {2606.11881},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.11881},
}
RIS
TY - UNPB
TI - Thin-film drainage becomes singular at saddles
AU - Simeon Djambov
AU - Alice Marcotte
AU - François Gallaire
AU - Pier Giuseppe Ledda
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2606.11881
UR - https://arxiv.org/abs/2606.11881
AB - 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.
SN - 0031-9007
SN - 1079-7114
ER -