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Article Dans Une Revue Physical Review E Année : 2023

Darcy's law of yield stress fluids on a treelike network

Résumé

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's 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 states of DP restricted to vanishing overlap. These universal predictions are confirmed by extensive numerical simulations.
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Dates et versions

hal-04262567 , version 1 (05-12-2023)

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Vincenzo Maria Schimmenti, Federico Lanza, Alex Hansen, Silvio Franz, Alberto Rosso, et al.. Darcy's law of yield stress fluids on a treelike network. Physical Review E , 2023, 108 (2), pp.L023102. ⟨10.1103/PhysRevE.108.L023102⟩. ⟨hal-04262567⟩
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