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Visco-frictional trapping of particles percolating through a submerged granular medium

Pierre Philippe*

Florian Brunier-Coulin†

Yacine Khidas‡

  • *Contact author: pierre.philippe@inrae.fr
  • †Contact author: florian.brunier-coulin@univ-amu.fr
  • ‡Contact author: yacine.khidas@univ-eiffel.fr
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Phys. Rev. E 113, 035406 – Published 5 March, 2026

DOI: https://doi.org/10.1103/vzry-6rrd

Abstract

Particle filtration through a porous medium is a much-studied field because of its numerous industrial or natural applications, particularly for deep-bed and cake-type filtration regimes. The percolation regime has received relatively less attention and corresponds to the continuous motion of particles in a porous environment under the principal effect of gravity and generally without any interaction other than contact with the porous matrix. In the present case, both the moving particles and the porous medium are composed of spherical particles of diameters d and D, respectively. Dry percolation has been analyzed under such conditions and exhibits lateral diffusion, as well as a constant mean transit velocity that scales with gD (with D the coarse grain diameter and g gravity). The behavior is significantly different in the case studied here, where the porous stack is fully saturated by a liquid at rest. A previous study experimentally investigated the transition from deep filtration to the percolation regime under laminar flow conditions by matching the refractive index of the liquid to that of the particles of the porous system [C. Ghidaglia et al., Phys. Rev. E 53, R3028 (1996)]. Here, based on the same experimental technique, we focus on the particular case where there is no fluid flow and identify a different type of particle trapping, in contrast with either the dry condition or liquid flow situation. We show that this capture, which can exhibit high metastability, stems from a combination of solid friction and viscous lubrication, which strongly reduces the velocity of the moving particles and can also suppress any rebound. The complementary roles of the packing structure and both the size and shape of the particles are also highlighted.

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Phys. Rev. E 113, 035406– Published 5 March, 2026
  • Received 7 November 2025
  • Accepted 29 January 2026
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