Symmetry of viscous permeability tensor in porous media

Abstract

The symmetry of the viscous permeability tensor in a porous media is analyzed. The practical importance of this property is that it can be used to assess the validity and accuracy of numerical simulations in the emerging field of bottom-up approaches for microstructure optimization of sound absorbing materials. The statistical properties of the porous frame can be defined in homogenization volumes with dimensions much smaller than the wavelength of the acoustic waves that propagate in the saturating fluid. Viscous permeability tensor is reduced to a constant diagonal element in a plane perpendicular to the axis of a porous material with hexagonal symmetry. This property can be used for error estimation of numerical computation.