Homogenisation of flow through periodic networks

Using a discrete version of the method of multiple scales, the problem of fluid flow through an arbitrary periodic network of one-dimensional channels is homogenized to give Darcy flow. A simple, low-dimensional, linear algebra problem gives the effective permeability in terms of the channel conductances. The results are illustrated with an investigation of the statistical properties of effective permeability for a variety of random networks, as well as an evaluation of the correlation between permeability and network tortuosity.