Simple Methods to Predict Particle Size for Growth-Only Systems Undergoing One or More Temperature Cycles

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.

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.

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.

By incorporating complex chemical kinetics for both gaseous and particulate phases with a fixed sectional aerosol dynamics model, a detailed description of the properties of carbonaceous nanoparticles formed in the pyrolysis of carbon suboxide behind a reflected shock wave can be obtained. The model successfully predicted the induction time, growth rate and particle yield for the shock tube experiment. The calculated time-dependent particle volume fractions were in good agreement with the measured optical densities, and the averaged particle diameters were in reasonable agreement with the measured particle size using LII (laser-induced incandescence) and TEM (transmission electron microscope). The predicted particle size distribution as a function of residence time showed an evolution from the power law shape to a bi-modal shape. The temperature dependence of particle properties has been also investigated. The second bell at the high temperature range, which has been argued as resulting from particle nucleation behind the incident wave during the experiment, was found in the numerical simulation of particle formation behind the reflected shock wave where no incident wave is included. Analysis of the simulation results showed that the double bell-shaped particle yield arises from the different particle nucleation timescales and the changing surface growth rates at different temperatures.

Wet chemistry approaches have been widely used to synthesize nanoparticle suspensions with different size and shape. Controlling particle size is crucial for tailoring the properties of the nanofluid. In this study, we simulated the particle size growth during a thermal-chemical nanofluid synthesis routine. The simulation was based on the population balance model for aggregation kinetics, which is coupled with thermal decomposition, nucleation and crystal growth kinetics. The simulation result revealed a typical burst nucleation mechanism towards self-assembly of supersaturated monomers in the nanoparticle formation process and the shift from monodispersed particles to polydispersed particles by the particle-particle coagulation.

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

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.

Grinding kinetics of amorphous powder obtained by sol–gel process

Nucleation and Growth Kinetics of MgO in Molten Steel

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

Modelling soot formation in a premixed flame using an aromatic-site soot model and an improved oxidation rate

In this study, the nonlinear numerical calculation for the effect of radiant heat feedback on the unsteady burning of metalized propellant was conducted. During the initial motor pressurization from ignition to steady value, radiant heat feedback from the particles (Al, A12O3) in the gas phase may play a crucial role in determining the burning characteristics of propellants. Linear temperature dependence of specific heat and thermal conductivity, and radiant heat feedback in the condensed phase based on experimental data were accounted. And the chemical reaction in the condensed phase was considered as a surface reaction within the very thin layer adjacent to the propellant surface. The phenomenological flame model, known as apymodel, was used to model the heat distribution in the gas phase. Even the flow is intrinsically two phase; gas phase and particles of aluminum and aluminum oxide (Al^Os), only particles were assumed as the major sources of radiation. The most crucial factor in evaluating radiant heat flux is the volume fraction of particles in the gas region. Since the most of Al particles do not vaporize at the temperatures of burning surface, a fraction of metal still resides in the gas phase and agglomerate to a big size. It is not surprise there is still no general description in predicting particle size distribution during the propellant combustion. With the appropriate experimental model, it is not difficult to evaluate radiant properties of particles. Then the coupled energy equation of gas phase and radiant transfer equation were solved simultaneously. And the energy equation of condensed phase could provide the burning rate of the propellants The primitive results indicate that the radiant heat transfer can influence the unsteady burning characteristics while motor pressurization occurs.

An Al-Mg-Si-Cu alloy was artificially aged for 0.13, 0.5 or 2 hours at 170°C after natural ageing times of 0.03, 3 or 168 hours. Three dimensional atom probe (3DAP) analysis and tensile testing were performed in the artificially aged and naturally aged conditions. The experimental data were used to determine model inputs such as particle size distributions and volume fractions of particles. The principle of the model is to numerically simulate the isothermal transformation of clusters, zones and/or precipitates by dividing the starting particle distribution into a series of discrete size classes and control volumes. Standard physically-based equations are used to simulate particle growth and/or dissolution by adjusting enthalpy, entropy and interfacial energy values to obtain a good fit between model predictions and 3DAP results. The predicted particle size distributions and volume fractions are then used to model yield strengths in a wide range of naturally aged and under-aged conditions.

A new aerosol model, the Model of Aerosol Dynamics, Reaction, Ionization, and Dissolution (MADRID) has been developed to simulate atmospheric particulate matter (PM). MADRID and the Carnegie‐Mellon University (CMU) bulk aqueous‐phase chemistry have been incorporated into the three‐dimensional Models‐3/Community Multiscale Air Quality model (CMAQ). The resulting model, CMAQ‐MADRID, is applied to simulate the August 1987 episode in the Los Angeles basin. Model performance for ozone and PM is consistent with current performance standards. However, organic aerosol was underpredicted at most sites owing to underestimation of primary organic PM emissions and secondary organic aerosol (SOA) formation. Nitrate concentrations were also sometimes underpredicted, mainly owing to overpredictions in vertical mixing, underpredictions in relative humidity, and uncertainties in the emissions of primary pollutants. Including heterogeneous reactions changed hourly O3 by up to 17% and 24‐hour average PM2.5, sulfate2.5, and nitrate2.5 concentrations by up to 3, 7, and 19%, respectively. A SOA module with a mechanistic representation provides results that are more consistent with observations than that with an empirical representation. The moving‐center scheme for particle growth predicts more accurate size distributions than a typical semi‐Lagrangian scheme, which causes an upstream numerical diffusion. A hybrid approach that simulates dynamic mass transfer for coarse PM but assumes equilibrium for fine PM can predict a realistic particle size distribution under most conditions, and the same applies under conditions with insignificant concentrations of reactive coarse particles to a bulk equilibrium approach that allocates transferred mass to different size sections based on condensational growth law. In contrast, a simple bulk equilibrium approach that allocates transferred mass based on a given distribution tends to cause a downstream numerical diffusion in the predicted particle size distribution.

Particle breakage in milling operations is often modeled using population balance models (PBMs). A discrete element method (DEM) model can be coupled with a PBM in order to explicitly identify the effect of material properties on breakage rate. However, the DEM-PBM framework is computationally expensive to evaluate due to high-fidelity DEM simulations. This limits its application in continuous process modeling for dynamic simulation, optimization, or control purposes. The current work proposes the use of surrogate modeling (SM) techniques to map mechanistic data obtained from DEM simulations as a function of processing conditions. To demonstrate the benefit of the SM-PBM approach in developing integrated process models for continuous pharmaceutical manufacturing, a comill-tablet press model integration utilizing the proposed framework is presented. The SM-PBM approach is in excellent agreement with the DEM-PBM approach to predict particle size distributions (PSDs) and dynamic holdup, with a maximum sum of square errors of 0.0012 for PSD in volume fraction and 0.93 for holdup in grams. In addition, the time taken to run a DEM simulation is in the order of days whereas the proposed hybrid model takes few seconds. The SM-PBM approach also enables comill-tablet press model integration to predict tablet properties such as weight and hardness. The proposed hybrid framework compares well with a DEM-PBM framework and addresses limitations on computational expense, thus enabling its use in continuous process modeling.