Generalization of Darcy's law for Bingham fluids in porous media: from flow-field statistics to the flow-rate regimes

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Thibaud Chevalier, Laurent Talon

Abstract

In this paper, we numerically investigate the statistical properties of the nonflowing areas of Bingham fluid in two-dimensional porous media. First, we demonstrate that the size probability distribution of the unyielded clusters follows a power-law decay with a large size cutoff. This cutoff is shown to diverge following a power law as the imposed pressure drop tends to a critical value. In addition, we observe that the exponents are almost identical for two different types of porous media. Finally, those scaling properties allow us to account for the quadratic relationship between the pressure gradient and velocity.

References

Oct 8, 2005·Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences·Irina Ginzburg, Konrad Steiner
Dec 12, 2013·The European Physical Journal. E, Soft Matter·Laurent Talon, Daniela Bauer
Jul 16, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·J Bleyer, P Coussot
Oct 30, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·T ChevalierP Coussot

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Citations

Jul 19, 2015·The European Physical Journal. E, Soft Matter·Thibaud Chevalier, Laurent Talon
May 15, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Thibaud ChevalierAndreas G Yiotis
May 17, 2017·Physical Review. E·T ChevalierL Talon
Jul 20, 2019·Physical Review Letters·Chen LiuLaurent Talon
Aug 27, 2016·Physical Review Letters·F Zami-PierreY Davit
Aug 11, 2017·Transport in Porous Media·Santanu SinhaAlex Hansen
Dec 2, 2020·ACS Applied Materials & Interfaces·Xiaoli ShanZhixing Gan

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