Frequency-dependent viscous flow in channels with fractal rough surfaces

Frequency-dependent viscous ow in channels with fractal rough surfaces Andrea Cortis a) and James G. Berryman Earth Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA The viscous dynamic permeability of some fractal-like channels is studied. For our particular class of geometries, the ratio of the pore surface area-to-volume tends to ∞ (but has a nite cuto), and the universal scaling of the dynamic permeability, k(ω), needs modication. We performed accurate numerical computations of k(ω) for channels characterized by deterministic fractal wall surfaces, for a broad range of fractal dimensions. The pertinent scaling model for k(ω) introduces explicitly the fractal dimension of the wall surface for a range of frequencies across the transition between viscous and inertia dominated regimes. The new model provides excellent agreement with our numerical simulations. a) Electronic mail: acortis@lbl.gov