Influence of pore roughness on high-frequency permeability

The high-frequency behavior of the fluid velocity patterns for smooth and corrugated pore channels is studied. The classical approach of Johnson et al. [J. Fluid Mech. 176, 379 (1987)] for smooth geometries is obtained in different manners, thus clarifying differences with Sheng and Zhou [Phys. Rev. Lett. 61, 1591 (1988)] and Avellaneda and Torquato [Phys. Fluids A 3, 2529 (1991)]. For wedge-shaped pore geometries, the classical approach is modified by a nonanalytic extension proposed by Achdou and Avellaneda [Phys. Fluids A 4, 2561 (1992)]. The dependency of the nonanalytic extension on the apex angle of the wedge was derived. Precise numerical computations for various apex angles in two-dimensional channels confirmed this theoretical dependency, which is somewhat different from the original Achdou and Avellaneda predictions. Moreover, it was found that the contribution of the singularities does not alter the parameters of the classical theory by Johnson et al.