Darcy's Law for Yield Stress Fluids.
Phys Rev Lett
; 122(24): 245502, 2019 Jun 21.
Article
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| MEDLINE
| ID: mdl-31322393
ABSTRACT
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-T_{c} 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.
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2019
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Article