Pore-scale hydrodynamics of non-Newtonian power-law fluids across a partially blocked porous medium in a confined channel

Transport of non-Newtonian fluids in porous media is pervasive in many natural and industrial applications. However, capturing the rheological behaviors of fluids by direct experimental techniques is challenging at the pore-scale. This paper outlines the pore-scale hydrodynamic interactions of non-Newtonian power-law fluids across a partially blocked porous medium in the laminar flow regime by computational fluid dynamics. The porous medium consists of an array of uniformly arranged square pillars. We explore the complex interplay of power-law rheology and Reynolds number on the microscopic flow field at the pore-scale. We capture the momentum transfer at the permeable interface between the porous and non-porous regions through stream-wise and span-wise velocity components and average volumetric flow rates at each pore-throat. Our results unveil a significant augmentation in stream-wise momentum by shear-thinning behavior and a diminution in momentum by shear-thickening behavior of the fluid through the porous medium. Further, the flow-leakage at the top interface purely depends on the combined effects of Reynolds number and power-law index. The channel pressure drop between the windward and leeward faces of the porous medium increases with the power-law index at low Reynolds number, while it decreases at high Reynolds number. Moreover, we provide a simple numerical framework to comprehend how the power-law behavior of the fluid dynamically regulates the flow field at the pore-scale.