Flow of power-law fluids in self-affine fracture channels

The two-dimensional pressure driven flow of non-Newtonian power-law fluids in self-affine fracture channels at finite Reynolds number is calculated. The channels have constant mean aperture and two values zeta=0.5 and 0.8 of the Hurst exponent are considered. The calculation is based on the lattice-Boltzmann method, using a different technique to obtain a power-law variation in viscosity, and the behavior of shear-thinning, Newtonian, and shear-thickening liquids is compared. Local aspects of the flow fields, such as maximum velocity and pressure fluctuations, are studied, and the non-Newtonian fluids are compared to the (previously studied) Newtonian case. We find a scaling relation between permeability and mean aperture in the low Reynolds number regime, generalizing an earlier result for Newtonian fluids. As the Reynolds number increases, we observe the same sequence of transitions to nonlinearity found in intergranular porous media. Furthermore, the permeability results may be collapsed into a master curve of friction factor vs Reynolds number, using a scaling similar to that employed for power-law fluids in porous media.