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Volume 117
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A multi-stage DEM-PBM coupling framework for the comparative evaluation of coalescence mechanisms
Dongling Wu a *, Bo Liu a, Ping Zhou a, Zhuo Chen a *, Liu Liu a, Haikun Xu b, Wei Chen c
a School of Energy Science and Engineering, Central South University, Changsha, 410083, China
b Information and Network Center, Central South University, Changsha, 410083, China
c School of Intelligent Manufacturing Ecosystem, Xi'an Jiaotong-Liverpool University, Suzhou, 215123, China
10.1016/j.partic.2026.06.037
Volume 117, October 2026, Pages 92-103
Received 29 March 2026, Revised 24 June 2026, Accepted 29 June 2026, Available online 14 July 2026, Version of Record 28 July 2026.
E-mail: dongling.wu@csu.edu.cn; chenzhuo@csu.edu.cn
Highlights

• Multi-stage coalescence and breakage criteria were developed.

• DEM-PBM coupling method was developed, incorporating both coalescence and breakage kernel functions.

• Two types of mechanism were compared regarding colliding and coalescence behavior.


Abstract

Wet granulation serves as a fundamental unit operation within various industrial sectors for the agglomeration of particulate materials. The process, governed by particle collisions, coalescence, and breakage, directly determines critical granule attributes, most notably size distribution, which dictates final product quality. This study presents a multi-stage theoretical and computational framework to analyze coalescence dynamics. Building upon a soft-sphere model, the particle collision process is deconstructed into three sequential stages, with distinct theoretical criteria established for coalescence and breakage at each phase. Deterministic kernel functions for these events are derived from principles of the Discrete Element Method (DEM). A novel, two-way coupled DEM-Population Balance Model (PBM) is subsequently developed and validated. This integrated model is employed to conduct a comparative analysis of two distinct coalescence mechanisms (designated Type I and Type II), evaluating their influence on predicted granule size evolution and process parameters. The findings demonstrate that the Type II mechanism provides a more reliable representation of granulation dynamics. Specifically, under the Type II framework, coalescence efficiency converges to stable, size-dependent values, suggesting that the assumption of a constant efficiency employed in prior models may hold validity only within limited size ranges. In contrast, the Type I mechanism predicts the formation of fewer agglomerates during the initial approaching and final separation stages, which leads to a systematic overestimation of granule strength.

Graphical abstract
Keywords
Wet granulation; DEM-PBM; Multi-collision stage; Coalescence mechanism; Coalescence; Breakage
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