Permeability of self-affine rough fractures

The permeability of two-dimensional fractures with self-affine fractal roug hness is studied via analytic arguments and numerical simulations. The limi t where the roughness amplitude is small compared with average fracture ape rture is analyzed by a perturbation method, while in the opposite case of n arrow aperture, we use heuristic arguments based on lubrication theory. Num erical simulations, using the lattice Boltzmann method, are used to examine the complete range of aperture sizes, and confirm the analytic arguments.