Breaking of non-Newtonian character in flows through a porous medium

Thibaud Chevalier (1) , Stéphane Rodts (1) , Xavier Chateau (2) , Christophe Chevalier (3) , Philippe Coussot (4)

1 navier umr 8205 - Laboratoire Navier
2 Rhéophysique
3 IFSTTAR/GER - Département Géotechnique, Eau et Risques
4 Physique des milieux poreux

From NMR measurements we show that the velocity field of a yield stress fluid flowing through a disordered well-connected porous medium is very close to that for a Newtonian fluid. In particular, it is shown that no arrested regions exist even at very low velocities, for which the solid regime is expected to be dominant. This suggests that these results obtained for strongly nonlinear fluid can be extrapolated to any nonlinear fluid. We deduce a generalized form of Darcy's law for such materials and provide insight into the physical origin of the coefficients involved in this expression, which are shown to be moments of the second invariant of the strain rate tensor.

Domains: Materials and structures in mechanics [physics.class-ph]; Materials and structures in mechanics [physics.class-ph]

Thibaud Chevalier, Stéphane Rodts, Xavier Chateau, Christophe Chevalier, Philippe Coussot. Breaking of non-Newtonian character in flows through a porous medium. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2014, 89, pp.023002. ⟨10.1103/physRevE.89.023002⟩. ⟨hal-00944452⟩