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arXiv · 2208.06048

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

Vincenzo Maria Schimmenti·Federico Lanza·Alex Hansen·Silvio Franz·Alberto Rosso·Laurent Talon·Andrea De Luca
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Abstract

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.

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Vincenzo Maria Schimmenti, Federico Lanza, Alex Hansen, Silvio Franz, Alberto Rosso, Laurent Talon, Andrea De Luca. 2022-08-11. Darcy's law of yield stress fluids on a treelike network. https://doi.org/10.1103/physreve.108.l023102

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