Non-Newtonian purely viscous flow through isotropic granular porous media

An analytical model for predicting non-Newtonian purely viscous power law flow through isotropic granular porous media is proposed. Application of the method of volume averaging leads to macroscopic momentum transport equations describing the physical flow phenomena within the porous medium. The geometrical properties of the granular porous medium are incorporated through the introduction of a rectangular representative unit cell model. The relative positioning of neighbouring cells leads to staggered- and non-staggered arrays of solid constituents. Volume partitioning of the flow domain allows for the tortuosity to be expressed as a ratio of fluid volumes. In order to support the assumption of average geometrical isotropy of the unit cell model, a weighted average is performed over the different arrays. The coefficient obtained from the averaging procedure is based purely on physical principles. Through application of an asymptotic matching technique, the proposed model produces pressure gradient predictions for Reynolds numbers within the entire laminar flow regime. The analytical model is compared to published experimental data to verify the validity of the model.