Micromechanical schemes for Stokes to Darcy homogenization of permeability based on generalized Brinkman inhomogeneity problems

François Bignonnet (1, 2)

1 GeM - Institut de Recherche en Génie Civil et Mécanique
2 IEG - Interactions Eau-Geomatériaux

Mean field homogenization schemes are formulated for the Stokes to Darcy upscaling of the permeability on the basis of generalized inhomogeneity problems in which flow is described by Brinkman equations. The average velocity and drag force concentrations for flow in a potentially composite inclusion are characterized in terms of a permeability contribution tensor and an equivalent permeability, which allow for the direct transposition to Stokes to Darcy upscaling of most homogenization schemes available in elasticity (selfconsistent, differential, Mori-Tanaka, Maxwell, ...). The unified framework extends existing effective medium and cell model permeability estimates. Its flexibility is illustrated on a panel of microstructures of porous media: granular or fibrous materials, materials with spanning cylindrical or crack-like pores, double porosity materials with disconnected or connected meso-porosity and compared with existing or newly produced full field simulation results.

Mots clés: Permeability; Homogenization; Porous Media; Stokes flow; Brinkman equation; Effective medium

Domaines: Mécanique des solides [physics.class-ph]; Mécanique des fluides [physics.class-ph]

François Bignonnet. Micromechanical schemes for Stokes to Darcy homogenization of permeability based on generalized Brinkman inhomogeneity problems. International Journal of Engineering Science, 2022, 172, pp.103622. ⟨10.1016/j.ijengsci.2021.103622⟩. ⟨hal-03594654⟩