Sizing and packing of particles – Characterization of mono-, di- and trimodal particle assemblies

Jarl B. Rosenholm*

*Corresponding author for this work

Research output: Contribution to journalReview Article or Literature Reviewpeer-review

4 Citations (Scopus)
87 Downloads (Pure)


The influence of particle size and shape on the properties of mono-, di- and trimodal particle assemblies is evaluated. The relative increase of surface area over bulk when particle size is reduced renders particles in the colloid (10–100 nm) and nano (1–10 nm) ranges extraordinary properties. Asymmetric particle shapes are characterized by sphericity and represented by equivalent spheres. The average diameter of particle size classes (size ranges) of powders are dependent on two experimentally determined properties. Average particle sizes (median, mean and mode) for each size class are extracted from size distributions of powders. Mono-, di- and trimodal particle packing efficiency is expressed as volume fractions and inverted volume fractions of close-packed hard spheres and related to standard cubic, orthoromic, tetragonal-sphenoidal and rombohedral-hexagonal packing properties. Simple models are presented to reveal the relative influence of fine, medium, and coarse particles and their ratios on powder properties. Experimental challenges relate to the influence of test compartment size and shape on particle layering and of particle shape on packing density. Particle asymmetry induces preferential aggregation through bond and site percolation resulting in dense closed or loose open cluster structures relating to particle segregation. Clusters may be characterized by structural fractals while textural fractals identify the particles involved. A modified Flory-Huggins lattice model for macromolecular solutions enables determination of combinatory entropy for cluster formation. A model is presented which relates time dependent volume fraction to logarithmic time dependence of compaction. This review concerns mixing of dry particles which corresponds to molecular processes at the gaseous (continuum, vacuum) reference state.

Original languageEnglish
Article number102887
Number of pages23
JournalAdvances in Colloid and Interface Science
Publication statusPublished - May 2023
MoE publication typeA2 Review article in a scientific journal


  • Cluster energy
  • Dependence on test compartment
  • Fractal dimensions
  • Mono-, di- and trimodal particle packing
  • Particle size and shape
  • Particle size classes from distribution


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