Critical behavior in flow through a rough-walled channel

We study flow through a single rough-walled channel by numerical simulation and present a theory for single channels and networks of channels that predicts scale dependency of the transport properties. The rough channel is modeled as the void space between two self-affine fractal surfaces. Flow fields are obtained from numerical simulations using 3D lattice gas methods which solve the Navier-Stokes equations. The flow simulations are performed at low Reynolds number. It is in this regime that we study the effect of the surface topography on the flow for various values of the mean aperture of the rough channel. For the case of tight uncorrelated channel walls we predict a power law dependency of the permeability on the length of a single rough channel measured in the direction of the main pressure gradient. (C) 1999 Published by Elsevier Science B.V. All rights reserved.