Darcy’s Law for Yield Stress Fluids – Archive ouverte HAL

Chen Liu 1 Andrea de Luca 2 Alberto Rosso 3 Laurent Talon 1

Chen Liu, Andrea de Luca, Alberto Rosso, Laurent Talon. Darcy’s Law for Yield Stress Fluids. Physical Review Letters, American Physical Society, 2019, 122 (24), pp.245502. ⟨10.1103/PhysRevLett.122.245502⟩. ⟨hal-02165315⟩

Predicting the flow of non-Newtonian fluids in a porous structure is still a challenging issue due to the interplay between the microscopic disorder and the nonlinear rheology. In this Letter, we study the case of a yield stress fluid in a two-dimensional structure. Thanks to an efficient optimization algorithm, we show that the system undergoes a continuous phase transition in the behavior of the flow, controlled by the applied pressure difference. In analogy with studies of plastic depinning of vortex lattices in high−Tc superconductors, we characterize the nonlinearity of the flow curve and relate it to the change in the geometry of the open channels. In particular, close to the transition, a universal scale-free distribution of the channel length is observed and explained theoretically via a mapping to the Kardar-Parisi-Zhang equation.

  • 1. FAST – Fluides, automatique, systèmes thermiques
  • 2. Rudolf Peierls Center for Theoretical Physics
  • 3. LPTMS – Laboratoire de Physique Théorique et Modèles Statistiques

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