Flow Through Porous Media at the Percolation Transition
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866917672054161408 |
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| 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 |
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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 |