A model to estimate the size of nanoparticle agglomerates in gas−solid fluidized beds

Research Paper


The estimation of nanoparticle agglomerates’ size in fluidized beds remains an open challenge, mainly due to the difficulty of characterizing the inter-agglomerate van der Waals force. The current approach is to describe micron-sized nanoparticle agglomerates as micron-sized particles with 0.1–0.2-μm asperities. This simplification does not capture the influence of the particle size on the van der Waals attraction between agglomerates. In this paper, we propose a new description where the agglomerates are micron-sized particles with nanoparticles on the surface, acting as asperities. As opposed to previous models, here the van der Waals force between agglomerates decreases with an increase in the particle size. We have also included an additional force due to the hydrogen bond formation between the surfaces of hydrophilic and dry nanoparticles. The average size of the fluidized agglomerates has been estimated equating the attractive force obtained from this method to the weight of the individual agglomerates. The results have been compared to 54 experimental values, most of them collected from the literature. Our model approximates without a systematic error the size of most of the nanopowders, both in conventional and centrifugal fluidized beds, outperforming current models. Although simple, the model is able to capture the influence of the nanoparticle size, particle density, and Hamaker coefficient on the inter-agglomerate forces.


Van der Waals Hydrogen bond Fluidization Aggregates Interaction Nanoparticle processing Modeling and simulation 



The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/ 2007–2013) / ERC Grant, Agreement no 279632.

Supplementary material

11051_2013_2055_MOESM1_ESM.pdf (128 kb)
Supplementary material 1 (PDF 129 kb)


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of Chemical EngineeringDelft University of TechnologyDelftThe Netherlands

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