  Models of porous media are often applied to relatively small systems, which
leads not only to system-size-dependent results, but also to phenomena that
would be absent in larger systems. Here we investigate one such finite-size
effect: anisotropy of the permeability tensor. We show that a non-zero angle
between the external body force and macroscopic flux vector exists in
three-dimensional periodic models of sizes commonly used in computer
simulations and propose a criterion, based on the system size to the grain size
ratio, for this phenomenon to be relevant or negligible. The finite-size
anisotropy of the porous matrix induces a pressure gradient perpendicular to
the axis of a porous duct and we analyze how this effect scales with the system
and grain sizes.
