Darcy's law for yield stress fluid flowing through a porous medium

Thibaud Chevalier (1) , Christophe Chevalier (2) , Xavier Clain (1) , Jean Claude Dupla (1) , Jean Canou (1) , Stéphane Rodts (1) , Philippe Coussot (3)

1 navier umr 8205 - Laboratoire Navier
2 IFSTTAR/GERS/SRO - Sols, Roches et Ouvrages Géotechniques
3 Physique des milieux poreux

We measured the pressure drop vs flow rate during the flow, in a wide range of velocities, of well controlled yield stress fluids through confined packings of glass beads of different sizes. A detailed analysis of the data makes it possible to extract a general expression for the pressure drop vs flow rate curve through a porous medium as a function of the flow rate and the characteristics of the system. This general law has a form similar to the Herschel-Bulkley model describing the rheological behavior of such fluids in simple shear, i.e. it expresses as the sum of a critical (yielding) pressure drop and a flow rate dependent term. This law involves the rheological parameters of the fluid, one characteristic length of the medium, and two coefficients which only depend on the structure of the porous medium. The first coefficient is related to the path of maximum width throughout the porous medium while the second coefficient reflects the pore size distribution. The values of these coefficients were determined in the case of a granular packing. © 2012 Elsevier B.V.

Domaines: Sciences de l'ingénieur [physics]; Matériaux

Thibaud Chevalier, Christophe Chevalier, Xavier Clain, Jean Claude Dupla, Jean Canou, et al.. Darcy's law for yield stress fluid flowing through a porous medium. Journal of Non-Newtonian Fluid Mechanics, 2013, 195 (-), pp.57-66. ⟨10.1016/j.jnnfm.2012.12.005⟩. ⟨hal-00946083⟩