Flow through anisotropic networks

This paper presents an analysis of Hagen-Poiseulle flow through plane random anisotropic networks of interconnected channels. Macroscopic permeability tensor of the network is expressed in terms of statistico-geometrical characteristics like the degree of anisotropy in channel orientations, average co-ordination number of the network and first two moments of channel length distribution. Analytical results are illustrated and verified using numerical analysis of flow in a simulated random network. The emphasis of the paper is on the effects of anisotropy on distributions of flow rates in channels. It is shown that, due to anisotropy the maximum flow rate generally occurs in channels that are not aligned along the direction of the macroscopic pressure gradient.     

Flow through anisotropic networks

This paper presents an analysis of Hagen-Poiseulle flow through plane random anisotropic networks of interconnected channels. Macroscopic permeability tensor of the network is expressed in terms of statistico-geometrical characteristics like the degree of anisotropy in channel orientations, average co-ordination number of the network and first two moments of channel length distribution. Analytical results are illustrated and verified using numerical analysis of flow in a simulated random network. The emphasis of the paper is on the effects of anisotropy on distributions of flow rates in channels. It is shown that, due to anisotropy the maximum flow rate generally occurs in channels that are not aligned along the direction of the macroscopic pressure gradient.     

Statistical aspects of flow in a random network of channels

This paper presents a detailed statistical analysis of Hagen-Poiseuille flow in plane random isotropic networks of interconnected channels. The emphasis is on statistico-geometrical features of networks that affect macroscopic permeability. It is shown that permeability of a network depends on its average co-ordination number, the first two moments of the channel length distribution and other explicitly identifiable geometrical features. Distributions of flow rates in channels and average flow rates are established by minimization of the rate of energy dissipation. Theoretical developments are interpreted in the context of classical statistical mechanics. Analytical results are illustrated and verified using numerical analysis of flow in a simulated random network.