Darcy's law of yield stress fluids on a treelike network
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arXiv
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| Hauptverfasser: | , , , , , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866916104805285888 |
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| author | Schimmenti, Vincenzo Maria Lanza, Federico Hansen, Alex Franz, Silvio Rosso, Alberto Talon, Laurent De Luca, Andrea |
| author_facet | Schimmenti, Vincenzo Maria Lanza, Federico Hansen, Alex Franz, Silvio Rosso, Alberto Talon, Laurent De Luca, Andrea |
| contents | Understanding the flow of yield stress fluids in porous media is a major challenge. In particular, experiments and extensive numerical simulations report a non-linear Darcy law as a function of the pressure gradient. In this letter, we consider a tree-like porous structure for which the problem of the flow can be resolved exactly thanks to a mapping with the directed polymer (DP) with disordered bond energies on the Cayley tree. Our results confirm the non-linear behavior of the flow and expresses its full pressure-dependence via the density of low-energy paths of DP restricted to vanishing overlap. These universal predictions are confirmed by extensive numerical simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_06048 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Darcy's law of yield stress fluids on a treelike network Schimmenti, Vincenzo Maria Lanza, Federico Hansen, Alex Franz, Silvio Rosso, Alberto Talon, Laurent De Luca, Andrea Soft Condensed Matter Disordered Systems and Neural Networks Understanding the flow of yield stress fluids in porous media is a major challenge. In particular, experiments and extensive numerical simulations report a non-linear Darcy law as a function of the pressure gradient. In this letter, we consider a tree-like porous structure for which the problem of the flow can be resolved exactly thanks to a mapping with the directed polymer (DP) with disordered bond energies on the Cayley tree. Our results confirm the non-linear behavior of the flow and expresses its full pressure-dependence via the density of low-energy paths of DP restricted to vanishing overlap. These universal predictions are confirmed by extensive numerical simulations. |
| title | Darcy's law of yield stress fluids on a treelike network |
| topic | Soft Condensed Matter Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2208.06048 |