Mobility and Pore-Scale Fluid Dynamics of Rate-Dependent Yield-Stress Fluids Flowing through Fibrous Porous Media

The steady ow of viscoplastic uids through brous porous media is studied numerically and theoretically. We consider uids with a plastic yield stress and a rate-dependent viscosity that can be described by the HerschelBulkley model. We rst investigate the pore-scale ow characteristics through numerical simulations for ow transverse to a square array of bers with comprehensive parametric studies to independently analyze the e ects of the rheological properties of the uid and the geometrical characteristics of the brous medium. Our numerical simulations show that the critical Bingham number at which the ow transitions from a fully-yielded regime to locally unyielded regions depends on the medium porosity. We develop a scaling model for describing the bulk characteristics of the ow, taking into account the coupled e ects of the medium porosity and the uid rheology. This model enables us to accurately predict the pressure-drop velocity relationship over a wide range of Bingham numbers, power-law indices, and porosities with a formulation that can be applied to a square or a hexagonal array of bers. The ultimate result of our scaling analysis is a generalized form of Darcy's law for HerschelBulkley uids with the mobility coe cient provided as a function of the system parameters. Based on this model, we construct a modi ed Bingham number rescaled with a suitable porosity function, which incorporates all the rheological and pore-scale parameters that are required to determine the dominant ow regime.