The effective diffusivity of fibrous media

Abstract

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.