The effect of random fiber orientation on Knudsen permeabilities

Variational upper bound calculations of the permeability to Knudsen flow are performed for several beds of overlapping, long fibers. When the fiber axes are oriented at random, perpendicular to the direction of the net flow, the permeability factor 0.7489 is slightly smaller than the corresponding factor 0.7630 for fiber axes mutually parallel. For fibers with axes oriented at random in three dimensions, the well-known result 12/13 of Derjaguin is obtained for fiber beds.