Evaluation of gravitational consolidation of binary powder mixtures by modified Heckel equation

Consolidation of powders by tapping is an important quality test but it is time and material consuming, which encourages the use of mathematical modelling. This article aims to study this gravitational consolidation dynamics by using nine binary mixtures consisting of cellets and powdered microcrystalline cellulose (MCC102), differing in size, shape, and consolidation properties.


  • Three models were used to study the consolidation dynamics of binary mixtures.
  • A cellet concentration-dependent relationship was noted for the Hausner ratio.
  • The Kawakita model fitted consolidation dynamics well up to 80% (w/w) of cellets.
  • The modified Heckel model fitted the data comparably up to 50% (w/w) of cellets.
  • The best but opposite mixture trend was noted with Varthalis & Pilpel model.

To describe the correlation between number of taps and powder bed density/ porosity, the modified Heckel equation. (MH) was newly introduced and compared to the models by Kawakita (KW) and Varthalis & Pilpel (VP). High coefficients of determination were observed by applying the traditional KW model up to 80% of cellets, while a comparable fitting adequacy was obtained with the MH equation up to 50% of cellets in the mixtures. An increased content of MCC102 increased fitting adequacy in the MH and KW model, whereas a nearly opposite mixture trend was observed for the VP model.

Read the article here

Petra Svačinová, Oliver Macho, Žofie Jarolímová, Martin Kuentz, Ľudmila Gabrišová, Zdenka Šklubalová, Evaluation of gravitational consolidation of binary powder mixtures by modified Heckel equation, Powder Technology, Volume 408, 2022, 117729, ISSN 0032-5910,

You might also like