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  • Letter
  • Open Access

Flow through porous media at the percolation transition

Mirko Residori1,2, Suvendu Mandal3, Axel Voigt1,4,5, and Christina Kurzthaler2,4,5,*

  • *Contact author: ckurzthaler@pks.mpg.de
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Phys. Rev. Research 7, L012032 – Published 12 February, 2025

DOI: https://doi.org/10.1103/PhysRevResearch.7.L012032

Abstract

We study low-Reynolds-number fluid flow through a two-dimensional porous medium modeled as a Lorentz gas. Using extensive finite-element simulations we fully resolve the flow fields for packing fractions approaching the percolation threshold. Near the percolation transition, we find a power-law scaling of the flow rate versus the packing fraction with an exponent of ≈5/2, which was predicted earlier by mapping the macroscopic flow to a discrete flow network [B. I. Halperin et al., Phys. Rev. Lett. 54, 2391 (1985)]. Importantly, we observe a rounding of the scaling behavior at small system sizes, which can be rationalized via a finite-size scaling ansatz. Finally, we show that the distribution of the kinetic energy exhibits a power-law scaling over several decades at small energies, originating from collections of self-similar, viscous eddies in the dead-end channels. Our results lay the foundation for unraveling critical behavior of complex fluids omnipresent in biological and geophysical systems.

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Phys. Rev. Research 7, L012032– Published 12 February, 2025
  • Received 31 May 2024
  • Accepted 21 January 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by Max Planck Society.

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