(208g) Evaluation of the First-Order Breakage Rate Hypothesis Via a Multi-Scale DEM-PBM Approach
First-order breakage kinetics is a fundamental tenet in the population balance modeling of milling processes which has been used with much success for more than half of a century. First-order breakage kinetics assumes that the rate of breakage of a given particle size is proportional to the weight of particles only of that size and independent of the population density. Because of the lack of particle-scale information obtainable for milling processes, it is difficult to validate such an important assumption in the modeling of such processes.
In order to investigate the first-order breakage assumption, this study formulates a particle-scale breakage rate constant of the linear time-variant population balance model (PBM) for batch dry-milling. The breakage rate constant separates material properties from the milling environment which is defined by the impact energy distribution obtained by the discrete element method (DEM). In contrast to a companion study which only simulated a mono-sized feed (Capece et al., 2014), polydispersed feeds along with the grinding media were simulated. The breakage rate constant determined by experiments and DEM simulations of the ball milling of polydispersed silica glass were in close agreement confirming the validity of the proposed methods.
The breakage rate constant formulated in this study also allowed a detailed and rigorous energy-based analysis of the milling environment which provided insight into the origin of first-order breakage kinetics and the time-invariance of the breakage rate constant. Feeds of varying polydispersity and the time-wise evolution of the particle size distribution (PSD) were simulated in DEM to show that the PSD does not affect the specific breakage rate constant as assumed in first-order breakage. The adherence to first-order breakage kinetics was attributed to the low feed loading in the mill and absence of particle beds where mechanical multi-particle interactions can cause non-first-order breakage. It was found that a threshold impact energy must be accounted for in the analysis of DEM results because the majority of low energy impacts do not contribute to particle breakage. Without rigorous assessment of the impact energy distribution, DEM simulations may lead to an erroneous evaluation of milling performance.
The findings of this study contribute to a unified DEM−PBM framework to model and analyze milling process and demonstrate that milling performance can be quantified from particle-scale interactions using DEM. It is expected that the DEM−PBM framework formulated here may elucidate other fundamental breakage behavior such as non-first-order or non-linear kinetics in addition to the first-order kinetics already investigated.
Capece M, Bilgili E, Dave R. Formulation of a physically motivated breakage rate parameter for dry ball milling via the discrete element method. AIChE Journal. 2014; DOI: 10.1002/aic.14451.