Theoretical consideration of permeation resistance of fluid through a particle packed layer

The well-known Kozeny–Carman equation has often been used for the prediction of permeation resistance for a fluid passing through particle layers in the Stokes regime. However, a significant error is encountered when the Kozeny–Carman equation is used for particle beds having a wide particle size distribution and/or non-spherical particle shape. This study has investigated theoretically the effects of particle polydispersity and shape factor on the permeation resistance of either a gas or a liquid through a particle layer. With the assumption of a lognormal particle size distribution, two theoretical relations among the parameters involved have been derived. The derivations are based on the so-called channel theory and drag theory. The functional forms of these two equations are analogous with respect to the effects of the particle polydispersity and shape. In both models, the geometric standard deviation and the particle shape factor play an important role in the estimate of the permeation resistance. Their effects on the permeation resistance will not be negligible. From the experimental comparison and practical applications, the model based on the Drag theory is found to be more useful and quantitative than that of the Channel theory. It is because the defined parameters in the former are clearer than those in the latter.