  Present work attempts to identify the roles of flow- and geometric-variables
on the scaling factor which is a necessary parameter for modeling the apparent
viscosity of non-Newtonian fluid in porous media. While idealizing the porous
media microstructure as arrays of circular and square cylinders, present study
uses multi-relaxation time lattice Boltzmann method to conduct pore-scale
simulation of shear thinning non-Newtonian fluid flow. Variation in the size
and inclusion ratio of the solid cylinders generates wide range of porous media
with varying porosity and permeability. Present study also used stochastic
reconstruction technique to generate realistic, random porous microstructures.
For each case, pore-scale fluid flow simulation enables the calculation of
equivalent viscosity based on the computed shear rate within the pores. It is
observed that the scaling factor has strong dependence on porosity,
permeability, tortuosity and the percolation threshold, while approaching the
maximum value at the percolation threshold porosity. Present investigation
quantifies and proposes meaningful correlations between the scaling factor and
the macroscopic properties of the porous media.
