  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 novel method 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, were studied, and the non-Newtonian
fluids were compared to the (previously-studied) Newtonian case. The
permeability results may be collapsed into a master curve of friction factor
vs. Reynolds number using a scaling similar to that employed for porous media
flow, and exhibits a transition from a linear regime to a more rapid variation
at Re increases.
