Energy and population balances in comminution process modelling based on the informational entropy

We present a new prototype acoustic chemometric approach for prediction of powder particle size distributions, intended for in-line implementation. The standard basic solutions demand that calibration be carried out on representative, ‘non-segregated’ reference powder samples. However, as practical powder flow with no segregation is extremely difficult to achieve with the precision needed for calibration, there will always be a significant uncertainty in the reference values relative to what is actually measured. The problem is flow segregation. In order to solve this problem, we have designed a completely new acoustic chemometric approach, which by way of contrast forces the flowing powder mass to segregate as much as possible by various mechanical means. The new approach measures the acoustic signals from an integrated series of segregated, part-sample characteristics. The calibration X-data matrix now becomes a three-way matrix, which demands a three-way calibration solution to ‘unscramble’ the latent information in the maximally segregated powder sample. Thus the problem is now the solution. Our earlier forays into this matter, which were based on two-way calibrations, have all been limited by a severe ‘particle size ratio’ bracket outside which destructive self-damping has effectively negated practical, useful accuracy and precision. The new approach allows a much greater range of contrasting particle sizes. Our first-generation results achieved by using three-way PLS-R as well as the standard two-way calibrations show that it is more precise than all earlier attempts and can be used for many-component mixtures without extensive further modifications. We also look at the feasibility of quantifying for prediction of in-line particle size distributions in an industrial environment. Copyright © 2000 John Wiley & Sons, Ltd.

A combined experimental and DEM approach to determine the breakage of particles in an impact mill

Scale-up procedure of parameter estimation in selection and breakage functions for impact pin milling

Grinding kinetics of amorphous powder obtained by sol–gel process

This paper demonstrates an application of artificial neural network (ANN) for determination of underflow and overflow densities of hydrocyclone separators. The discussions are extended and further results are presented for the prediction of particle size distributions in the underflow and overflow streams. The fit of the experimental results against the predicted results are illustrated and a statistical analysis is made. It is shown that, once the history of the operations are known, the ANN proves to he a useful tool for predicting future separation efficiencies. This approach has a potential to eliminate the need for installation of expensive on-line instruments for density measurements and particle size analyses. This approach can be applied in similar situations in the mineral processing industry.

Cryogenic grinding performance of scrap tire rubber by devulcanization treatment with ScCO2

Three simple methods are presented for predicting particle size distribution (PSD) percentiles when subjecting a pharmaceutical crystallization wet-milled slurry to a single temperature cycle for two of Biogen's drug substances. The methods are (I) a mathematical manipulation of the wet-milled PSD based on particle death during dissolution; (II) a linear empirical model fit of product PSD percentiles as a function of the wet-milled PSD percentiles and the amount of material dissolved; and (III) a nonlinear model fit to the change in PSD as a function of the amount of material dissolved and the particle surface area/volume ratio. The three methods were verified on production scale batches. Method II's approach was also used for particle size control during manufacture by implementing a temperature solved from the model using the batch's wet-milled particle size percentiles and a final target size. Method III was found to be the most accurate at prediction because it models particle surface area to volume ratio influencing crystal dissolution and growth rates. Method II was found to be not as accurate as method III; however, it was easily implementable during process control at the production scale. Method I provided the quickest estimate of final particle size using only the initial PSD and a solubility expression. Method III was recommended for best particle size prediction.

A comparison of dry and wet grinding of a quartzite ground in a small batch ball mill

Scale up and simulation of Vertimill™ pilot test operated with copper ore

Particle size distribution (PSD) is a critical quality attribute influencing dissolution, bioavailability, and manufacturability of pharmaceutical solid and suspension dosage forms. Traditional experimental approaches for particle size optimization and dissolution evaluation are time-consuming, resource-intensive, and often retrospective, limiting predictive capability. Recent advancements in artificial intelligence (AI) and machine learning (ML) offer transformative solutions by enabling data-driven prediction of PSD and its impact on dissolution behavior. Machine learning algorithms, including ensemble methods such as Light Gradient Boosting Machine (LightGBM) and artificial neural networks, can integrate formulation variables, process parameters, and analytical data to accurately predict particle size and polydispersity. These AI-based models facilitate early identification of critical formulation risks, support Quality by Design (QbD) principles, and reduce experimental workload. Moreover, coupling PSD predictions with dissolution modeling allows estimation of in vitro drug release profiles, particularly for poorly soluble drugs, without extensive repetitive testing. The integration of in-line and at-line particle size monitoring techniques with AI-driven models further enables real-time quality prediction and proactive process control. Despite these advantages, challenges remain in model interpretability, generalizability, regulatory acceptance, and dependence on high-quality datasets. Addressing these limitations through explainable AI, standardized validation, and robust data strategies is essential for broader industrial adoption. Overall, AI-based prediction of PSD–dissolution relationships represents a promising pathway toward knowledge-driven pharmaceutical development, offering accelerated formulation optimization, improved product quality, and alignment with regulatory and Pharma 4.0™ initiatives.

A technique of analysing mineral breakage by using irradiated size fractions is developed. Particular emphasis is placed upon the special errors associated with such a technique.The Broadbent-Callcott matrix analysis of breakage is found to be the most suitable to interpret these experimental results. Further investigation shows that their concepts are correct, but a simple model based upon the assumption of a constant selection function is not always adequate.The practice of expressing the breakage function as a step matrix is shown to be valid, and its accuracy of predicting product size distributions under different conditions is exhibited. The procedure of postulating a standard breakage function is shown to be unnecessary, but convenient, since any breakage function suffices, provided that it is used in conjunction with its companion selection function.

This study investigated the ultra-fine coal grinding performance of four low- to moderate-cost grinding media: ceramic balls, granular sand, alumina beads, and silica beads. The kinetic grinding tests were conducted using a stirred mill, while different operating conditions, including the media size, solids concentration, and the addition of viscosity modifiers, were examined. Characterization studies in terms of particle size, shape, and surface morphology were further performed to support the experimental findings. Moreover, using population balance modeling, grinding simulation was performed in Matlab to forecast the particle size distribution based on the specific energy input and experimental size-related data. The results showed that silica beads generated the finest product size with a P80 of 5.9 µm from a feed size of 24.4 µm while having a specific energy (SE) input of 309 kWh/ton, compared to ceramic balls and alumina beads. Nonetheless, the least energy consumption of 109 kWh/ton was achieved by alumina beads; however, yielding a coarser product size of 15.5 µm. In addition, test results indicate that choosing suitable media sizes, reducing the solids concentration, and using viscosity modifiers enhance coal ultra-fine grinding performance. Under the optimized testing conditions, a P80 of 2.7 µm was produced with a corresponding SE input of 270 kWh/ton using silica beads ranging from 420 to 850 µm and a dispersant dosage of 14 kg/ton. Moreover, the mathematical models, generated based on the breakage function, selection function, and particle swarm optimization, provided an accurate forecast of the particle-size distribution at the end of the study.

Poly(butylene succinate) (PBS) is a biodegradable polyester that finds many applications in the fields of personal care and cosmetics due to its excellent properties, such as the easy processibility, good thermal resistance, and adequate rates of degradation in aqueous media. For this reason, in the present work PBS microparticles are produced through nonaqueous suspension polycondensations at different operation conditions for the first time. Particularly, the present work investigates the effects of operation variables on particle size and molar mass distributions of the final products. The obtained results indicate that both time and temperature affect the final characteristics of the produced material, although temperature is the most influential variable. Besides, it is shown that particle size distributions are controlled by the rates of particle coalescence, with the increase of average particle diameters with the increase of stirring speed in the analyzed experimental range.

A novel hyperspectral microscope imaging technology for rapid evaluation of particle size distribution in matcha

Efficient simulation of close-coupled gas atomisation can nowadays be used to improve machine designs and to gain understanding of the complex phenomena taking place in the atomisation process. Two-stage multiphase models can predict particle size distributions by using an Eulerian approach for the primary atomisation and Lagrangian particle tracking for the secondary atomisation. Previous numerical results confirm that these models correctly predict trends of median particle size for varying gas-to-melt mass flow rate ratios, although significant differences between predicted and measured particle size distribution spreads indicate that models need to be improved. In this work, different coupling hypotheses between the primary and secondary atomisation stages are addressed to optimize the model’s capacity to predict the entire particle size distribution. By comparing experimental results with simulations obtained with varying surfaces of particle injections and corresponding boundary conditions, an improved model with better predictive capacity has been obtained.