Derivation of Macroscopic Filtration Law for Transient Linear Viscoelastic Fluid Flow

B. Khuzhayorov (1) , Jean-Louis Auriault (2) , Pascale Royer (2)

1 Academy of Sciences of Republic of Uzbekistan
2 3SR - Laboratoire sols, solides, structures - risques [Grenoble]

This work is concerned with deriving a macroscopic filtration law for describing transient linear viscoelastic fluid flow in porous media. This is performed using a homogenisation technique, i.e. by upscaling the heterogeneity scale description. The macroscopic filtration law is expressed in Fourier space as a generalised Darcy's law with a dynamic permeability tensor. This model is valid at low Reynolds and Deborah numbers. Analytical results are determined in the particular case of the flow of an Oldroyd fluid in a bundle of capillary tubes and are compared to those obtained by a corresponding phenomenological model.

Mots clés: Homogenization; Filtration law; Linear viscoelastic fluid; Dynamic permeability

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

B. Khuzhayorov, Jean-Louis Auriault, Pascale Royer. Derivation of Macroscopic Filtration Law for Transient Linear Viscoelastic Fluid Flow. International Journal of Engineering Science, 2000, 38 (5), pp.487-504. ⟨10.1016/S0020-7225(99)00048-8⟩. ⟨hal-01714089⟩