Packing fraction of particles with a lognormal size distribution

This paper addresses the packing and void fraction of polydisperse particles with a lognormal size distribution. It is demonstrated that a binomial particle size distribution can be transformed into a continuous particle-size distribution of the lognormal type. Furthermore, an original and exact expression is derived that predicts the packing fraction of mixtures of particles with a lognormal distribution, which is governed by the standard deviation, mode of packing, and particle shape only. For a number of particle shapes and their packing modes (close, loose) the applicable values are given. This closed-form analytical expression governing the packing fraction is thoroughly compared with empirical and computational data reported in the literature, and good agreement is found.