Knudsen flow through a random bed of unidirectional fibers

A rigorous variational upper bound for the permeability of a porous medium made up of long fibers oriented with axes mutually parallel, but perpendicular to the direction of flow, are formulated and expressed in terms of the appropriate statistical properties of the random fiber bed. Explicit calculations for the two‐dimensional model pore structure made up of overlapping fibers give a permeability coefficient 2π2/(16+π2). The result is quite different from the well‐known value (12)/(13) obtained by Derjaguin in three dimensions.