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The effective diffusivity of fibrous media
Author(s) -
Koch D. L.,
Brady J. F.
Publication year - 1986
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.690320407
Subject(s) - thermal diffusivity , péclet number , radius , volume fraction , mechanics , mass diffusivity , mass transfer , convection , thermodynamics , chemistry , physics , computer security , computer science
A procedure based on averaging the conservation equations in a homogeneous, disordered fibrous medium is used to demonstrate that in the limit of long times, macroscopic versions of Fick's and Fourier's laws may be used to relate the average flux to the average gradient in driving force. The asymptotic behavior in the limit of low volume fraction of the effective diffusivity (or conductivity) in such a medium is determined for all values of the Peclet number, P = Ua/D f , where U is the average velocity through the bed, a is the fiber radius, and D f is the molecular diffusivity of the solute in the fluid. The convective disturbance caused by the fibers is found to have a large influence on the rate of mass transfer even at moderate Peclet numbers and low volume fraction.