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Analysis of effective axial diffusion in branching networks
Author(s) -
Federspiel William J.
Publication year - 1992
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690381013
Subject(s) - branching (polymer chemistry) , statistical physics , diffusion equation , anomalous diffusion , diffusion , perturbation (astronomy) , convection–diffusion equation , physics , mathematics , chemistry , mechanics , computer science , thermodynamics , innovation diffusion , engineering , knowledge management , organic chemistry , quantum mechanics , metric (unit) , operations management
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 toward describing gas diffusion in the peripheral airspaces of the lung, the results provide insight for other transport processes occurring in branching networks.