ANALYSIS OF EFFECTIVE AXIAL DIFFUSION IN BRANCHING NETWORKS

Diffusional transport in a network of branching conduits is considered. The branching network is idealized as an ensemble of identical branching segments. Starting with the general species continuity equation, multiscale perturbation analysis is used to derive a one-dimensional, effective transport equation for species concentration. The macrotransport equation contains an effective diffusion coefficient, D*, which arises naturally from the analysis. D* can be computed from a local diffusion problem posed on an individual branching segment of the ensemble network. The local relations defining D* bear clear similarity to their counterparts for transport in spatially periodic porous media. Although this study was originally directed to ward describing gas diffusion in the peripheral airspaces of the lung, the results provide insight for other transport processes occurring in branching networks.