Saturated versus non-saturated two-scales permeability

A crucial step in many composites manufacturing processes is the impregnation of fibrous medium with the resin. The fundamental property needed to quantify the flow is the permeability of the fibrous medium. Process models require the permeability as input data to predict flow patterns and pressure fields. Efficient numerical techniques are needed to solve homogenization problems with geometrical data coming from high-resolution images, involving two-scales and linear fluids. Within this frame-work, this work addresses the question of how to compute the macroscopic permeability from a microscopic description consisting of a viscous fluid flow model defined in a two-scale porous medium, considering the saturated and unsaturated cases.