Flow Through Porous Media at the Percolation Transition

Fuente: arXiv
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Main Authors: Residori, Mirko, Mandal, Suvendu, Voigt, Axel, Kurzthaler, Christina
Format: Preprint
Published: 2024
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_version_ 1866917672054161408
author Residori, Mirko
Mandal, Suvendu
Voigt, Axel
Kurzthaler, Christina
author_facet Residori, Mirko
Mandal, Suvendu
Voigt, Axel
Kurzthaler, Christina
contents 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 pressure drop with an exponent of $\approx 5/2$, which has been predicted earlier by mapping the macroscopic flow to a discrete flow network [Phys. Rev. Lett. 54, 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.
format Preprint
id arxiv_https___arxiv_org_abs_2405_12381
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Flow Through Porous Media at the Percolation Transition
Residori, Mirko
Mandal, Suvendu
Voigt, Axel
Kurzthaler, Christina
Fluid Dynamics
Soft Condensed Matter
Statistical Mechanics
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 pressure drop with an exponent of $\approx 5/2$, which has been predicted earlier by mapping the macroscopic flow to a discrete flow network [Phys. Rev. Lett. 54, 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.
title Flow Through Porous Media at the Percolation Transition
topic Fluid Dynamics
Soft Condensed Matter
Statistical Mechanics
url https://arxiv.org/abs/2405.12381