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Volume 110
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Investigation into nanoparticle fluidization characteristics with electrostatic force-modified population balance model
Juhui Chen a *, Ke Chen a, Dan Li a, Zhirui Zhao a, Michael Zhuravkov b c, Lapatsin Siarhei b c, Wenrui Jiang c
a School of Mechanical and Power Engineering, Harbin University of Science and Technology, Harbin, 150080, China
b Heilongjiang Key Laboratory for International Cooperation on Gear Transmission of Maritime and Air Equipment, Harbin, 150001, China
c School of Mechatronics Engineering, Harbin Institute of Technology, Harbin, 150001, China
10.1016/j.partic.2026.01.003
Volume 110, March 2026, Pages 14-27
Received 22 November 2025, Revised 24 December 2025, Accepted 4 January 2026, Available online 10 January 2026, Version of Record 20 January 2026.
E-mail: chenjuhui@hrbust.edu.cn; b0222li@126.com
Highlights

• A population balance model modified based on electrostatic forces is proposed.

• The modified PBM values align with the experimental data.

• Analysis of electrostatic force impact on aggregate diameter distribution.

• Nanoparticle aggregation, aggregate diameter, and pressure drop were analyzed.


Abstract

Within the two-fluid model framework integrated with particle dynamics theory, this study explicitly incorporates interparticle electrostatic forces to derive formulas for aggregation and breakage kernels of nanoparticle aggregates. Accordingly, an electrostatic-force-modified Population Balance Model (PBM) is proposed to track and characterize nanoparticle aggregation and breakage processes. To quantify the evolution of aggregate volume fractions and diameters, the flow characteristics of SiO2 nanoparticles in a microfluidized bed are numerically investigated. The results demonstrate that the modified PBM enhances the dispersion of aggregates and improves fluidization quality. The electrostatic force increases with growing aggregate diameter. When nanoparticles enter the fully fluidized stage, the synergistic interplay among electrostatic repulsion, Brownian diffusion, and turbulent forces collectively regulates aggregate formation and breakage. This leads to a more organized spatial distribution of aggregates and a gradual reduction in local pressure drop fluctuations over time. Furthermore, the bed pressure difference increases significantly under the combined influence of gas velocity and electrostatic forces.

Graphical abstract
Keywords
Modified PBM; Aggregation and breakage; Electrostatic force; Microfluidized bed
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