Packing fraction of continuous distributions

This study addresses the packing and void fraction of polydisperse particles with geometric and lognormal size distribution. It is demonstrated that a bimodal discrete particle distribution can be transformed into said continuous particle-size distributions. Furthermore, original and exact expressions are presented that predict the packing fraction of these particle assemblies. For a number of particle shapes and their packing modes (close, loose) the applicable parameters are given. The closed-form analytical expression governing the packing fractions are thoroughly compared with empirical and computational data reported in the literature, and good agreement is found.