An analytical pore-scale, shear stress model for purely viscous non-Newtonian fluids traversing porous media

An analytical model for incompressible, generalized Newtonian fluids traversing different types of porous media is proposed. This model is based on the volume averaging of the governing equations. Interstitial quantities are obtained through means of a pore-scale model. For flow through porous media, in the Darcy regime, the interstitial fluid–solid interaction component is written in terms of the interstitial wall shear stress. The wall shear stress is obtained by assuming simple velocity profiles in the interstitial channels. Approximations are made in order to obtain explicit expressions for the wall shear stress in terms of the average interstitial channel velocities. The final analytical expressions obtained for predicting the flow through porous media can easily be implemented numerically and allow for a wide variety of practical implementations. Generalized Newtonian fluids traversing a porous structure adjacent to a free-flow domain were modelled numerically. The results for Newtonian fluids were compared to an analytical model from literature.