ARR - Annual Report

Over the past year we have built on a previously developed mechanistic model of granuleswelling and disintegration behaviour, with the aim to create a practical, fast tool for predicting and designing wet-granulated product performance. This work integrates physics with machine learning so that routine formulation inputs can be turned into reliable performance curves in seconds.

Core Models

• Mechanistic Performance Models (Single-granule Swelling → PBM Disintegration). Coupled single-granule swelling with population balance disintegration model to predict: Rp(t)  (granule radius) and F(t) (released-mass/ particles-released fraction).
• Physics-Informed Neural Network (PINN). A neural network implementation of the same physics that preserves mechanistic meaning while enabling efficient learning across formulations.
• ANN-Based Parameter Mapper. A supervised neural network that ingests standard formulation descriptors (e.g., L/S ratio, %SSG, filler type, %HPMC, initial porosity, skeletal density) and predicts the mechanistic parameters required by the Mechanistic model.

The workflow (Figure A) has been implemented and delivers rapid, physics-based forward prediction by converting formulation descriptors into mechanistic parameters, then full disintegration performance curves. Following further experimental validation, it will be ready to incorporate inverse modelling. Once incorporated, this inverse model will optimize formulation inputs and granulation conditions to give a desired released fraction at specific times.

modelling. Once incorporated, this inverse model will optimize formulation inputs and granulation conditions to give a desired released fraction at specific times.

1. Executive Summary

Flexible Intermediate Bulk Containers (FIBCs), commonly known as 'Bulk Bags,' are essential for transporting bulk materials across a wide range of industries and applications. These bags offer significant advantages, such as lightweight construction, compact storage, dust-free discharge, antistatic properties, and cost-effectiveness, while also providing versatility. For processing plants, while FIBCs offer significant advantages in handling bulk materials, the lack of established methods to predict their discharge rates and prevent blockages presents unique challenges. Addressing these factors is crucial to fully realising the plant’s capacity to maximise uptime and throughput.

This project was initiated in response to the International Fine Particle Research Institute (IFPRI) and its industry members' need for a better understanding of FIBC discharge behaviour. The report marks the first phase of this project, which takes a hybrid approach by combining numerical work using Discrete Element Method (DEM) simulations with experimental and theoretical methods to study the geometry of flexible bins and their discharge regimes. A comprehensive literature review has been conducted, covering flow theories, material properties, consolidation loads, and bin stresses.

By incorporating fundamental bulk material theory and leveraging recent advancements in the study of bulk solid mechanics, the project aims to develop flow models for FIBCs. Experimental testing will play a critical role, as we examine the discharge patterns of specific powders and analyse their flow properties in our laboratory. The report concludes with an outline of the next steps required to complete the research.

Experimental Approach to Investigate the Rheology of Powders

We propose an experimental approach to investigate the rheology of powders and their behavior during compaction and aeration processes. The first step is to develop protocols to synthetize and characterize model cohesive granular materials. The aim is to synthetize particles with tailored properties (stiffness and adhesion) using two technics (micro-polymer particles, or polymer coated silica particles).

Steps Involved

1. The first step involves developing protocols to synthetize and characterize model cohesive granular materials.
2. The second step involves developing tools to characterize particle properties and their bulk rheology.
3. The third step will involve studying different flow configurations encountered in packaging processes.
4. The final step concerns the coupling with air.

The presence of inter-particle cohesion in powders and grains, such as capillary bridges due to moisture, can drastically change their mechanical properties. For instance, cohesion causes grains to agglomerate into clumps of sizes much larger than the size of the constituent particles. The agglomeration of granules makes the processing of such materials challenging, particularly during drying under agitation processes, where agglomerates can reduce the overall efficiency of processes. The methods of drying a mixture of particles and liquid affect the state of agglomeration of the final dried product, particularly through the influence of impacts and shear forces on the agglomerates.

Our research direction in this area is based on the development of model experiments to understand and model the mechanics, size distribution, and time evolution of particle agglomerates. By controlling cohesion and grain properties, as well as the input of energy in the system, we hope to shed some light on the mechanical behavior of agglomerates to develop models at that can closely connect cohesion to agglomerate mechanics. Then, thanks to the models that will be developed, we will be able to consider industrial powders, such as calcium carbonate or powders used in the food industry, among other examples.

During the first year of the project, we developed an oscillating system consisting of a mechanical shaker and a quasi-2D transparent box, which allowed us to observe the agglomerates being mechanically agitated. Experiments with glass beads and water have illustrated the role of acceleration and amplitude of oscillation in determining the agglomerate sizes. In parallel, a second prototype, relying on airflow through a deposited bed, was designed. These tools were described in our last annual report, ARR-51-16 (2022-2023).

Following in-depth interactions and suggestions from IFPRI members, we have since modified the airflow setup to produce a much higher shear in a small region of the total setup during Year 2 of the project. Using small-diameter nozzles now allows us to reach considerably larger flow rates and shear stresses than we studied in the first year. This new setup, its characterization and some results are presented in the following. In addition, some members mentioned their need to also consider lower shear, and we have thus finalized the construction and characterization of a rotating drum, which was in our initial proposal to study the effects of low and moderate amounts of shear on drying wetted grains.

During this year, we were also invited to write a review article for the Royal Society of Chemistry journal Soft Matter, discussing the current state-of-the-art experimental techniques to study model cohesion in granular systems and some perspectives on future research. Since this review may likely be of general interest to some IFPRI members and was also initially strongly motivated by the interactions with IFPRI members, we have included the peer-reviewed version of this manuscript at the beginning of this annual report.

Finally, since our understanding of the evolution of the inter-particle force during drying is very limited, we have further developed an apparatus to measure the temporal evolution of the forces between individual particles during drying in our laboratory. These measurements will also help us to design model agglomerates to better estimate the shear rate and the effect of agitation on the time-evolution of particle agglomerates.

During the first term of the project, our investigation on screw feeder performance had three components. The first was to formulate two mechanics-based models for the kinematics and mechanics of non-cohesive powders: a simple model that relies on several simplifying approximations, and a more detailed continuum model that predicts the variations of velocity, packing fraction and stress within the feeder. Both models make the interesting prediction that the feed rate is maximum for a specific value of p/(2R!), the ratio of the screw pitch to barrel diameter of the feeder. The second component of our work was to conduct DEM simulations to validate the models and guide experimental efforts. The third component was to conduct experiments on a custom-built feeder assembly to test the model predictions and to extend/refine the model. Overall, we find good agreement between the experimental data, DEM simulations, and model predictions for non-cohesive powders (such as glass beads). In particular, the simulations and experiments verify the model predictions of the feed rate being maximum at a certain ratio of pitch to diameter of the screw. The experiments also identify the free surface at the feeder exit as being responsible for feed rate fluctuations for dry powders, and show that the fluctuations may be mitigated by appropriate end-cap design. The combination of theoretical analysis, DEM simulations, and experiments yielded substantial insight.

In the current (renewed) term of the project, we have focused on understanding the flow of cohesive powders in feeders. To quantify the effect of cohesion, we first created powders of controlled cohesion by combining a small quantity of glycerol to dry glass beads. Interestingly, the experiments show that the feed rate as a function of p/(2R!) shows the same qualitative trend as for dry powders. However, the feed rate fluctuations for cohesive powders are quite different from those seen in dry powders. A lacuna in the current understanding of cohesive powders is that there is no reliable constitutive model. To address this, we have initiated a study to determine the flow rule, a relationship between the strain rate and stress, for cohesive powders. Our initial studies on horizontal rotating drums point to the formation of clusters or agglomerates that crucially affect the flow of cohesive powders. On the modelling front, we have shown that the non-local model correctly predicts a complex dilatancy-driven secondary flow seen in experiments and DEM simulations, thereby increasing confidence on the model.

In ongoing work, we are conducting DEM simulations and experiments to quantify the formation and persistence of clusters in cohesive powders and determine how they influence their flowability.

We present the results of an experimental and theoretical study on the atomization process of high viscosity and polymeric fluids. The current year’s study was on the development of a model for the atomization process in swirl and fan nozzles. The primary atomization in such nozzles results in the formation of filaments and long ligaments, which breakup into droplets. Therefore, the first part of the current study was to determine the size distribution of the droplets that form by the breakup of such filaments. The second part of the current study was to develop a model to predict the droplet sizes using knowledge developed based on our experiments.

Atomization Model for Swirl and Fan Nozzles:

We propose a primary atomization model based on the interaction of two breakup mechanisms: the growth of surface wave and the formation of perforations, as shown by figure 1. At the nozzle orifice (zone 1), small scale surface waves are formed due to a high relative velocity between the liquid sheet and ambient gas. As the surface waves grow (zone 2), the liquid sheet forms alternating thick and thin regions due to the nonlinearity of the surface wave. The thin region becomes thinner as the sheet expands and perforations appear. As these perforations expand (zone 3), streamwise filaments form as the boundaries of these perforations approach each other. Close to the breakup position (zone 4), the growth of these perforations will eventually be stopped by the thick regions on the liquid sheet. As these streamwise filaments detach from the liquid sheet, the liquid sheet breaks up and forms filaments. As a result, in zone 5, there are two types of filaments formed: the thin streamwise filaments formed from the breakup of thin regions due to perforations, and the thick spanwise filaments formed from the thick regions due to the surface wave. These filaments become thinner due to the lateral velocity and eventually in zone 6, these two types of filaments break up into droplets due to surface waves and form the spray with a wide range of droplet sizes. The breakup of the liquid sheet is accompanied by the growth in wavelength of the surface waves: the distances between the thick regions at zone 4 are much larger than those in zone 1.

The production of fine powders and particles, such as milk powder, food additives like vitamins, pharmaceutical ingredients, and industrial ceramics, heavily relies on spray drying technologies. In standard spray drying, a liquid or slurry feed is atomized into fine droplets using high-pressure nozzles within a chamber filled with hot gas. This process achieves rapid drying by subjecting droplets to intense energy transfer, facilitating liquid evaporation in a short time. However, modern industrial requirements demand advancements in energy efficiency as well as product quality, necessitating improvements in spray drying technology. Energy efficiency is a crucial factor in spray drying, as conventional systems operate with high inlet gas temperatures between, consuming significant energy for gas heating. Spray drying systems can optimize energy utilization by reducing drying time without compromising product quality. Alongside energy efficiency, product quality in spray drying is paramount. Specific attributes, such as particle porosity, size, and density distribution, must be controlled to meet industry standards. Achieving precise product characteristics necessitates a detailed understanding of the drying process and its parameters, requiring advanced control strategies to meet strict quality specifications.

One promising technique to improve spray drying efficiency is foam spray drying, which involves injecting inert gas (e.g., nitrogen) into the feedstock at high pressures (typically above 50 bar). This pressurized feed is then atomized, releasing pressure at the nozzle outlet and allowing the feed to expand [1-2]. The rapid pressure depletion causes gas-saturated droplets to form bubbles, which alter the drying dynamics and the characteristics of the final product. Compared to standard spray drying, foam spray drying increases dryer throughput, reduces residence time, and modifies product properties. Although foam spray drying has been empirically explored, existing studies often focus on specific products without providing a reliable physics-based model to generalize findings across different parameters and scales.

Foam spray drying involves complex heat, mass, and momentum transfers between three phases (liquid, gas, and solid) within each droplet/particle, as well as interactions with the surrounding hot gas environment [3]. Compared to conventional spray drying, foam spray drying introduces additional complexities due to the presence of gas bubbles within the liquid matrix. These bubbles affect heat transfer by creating localized regions of lower thermal conductivity, alter mass transfer by influencing the diffusion of water vapor and dissolved gases, and impact momentum transfer by disrupting the liquid flow. Furthermore, bubble dynamics including nucleation, growth, and collapse can significantly modify the drying process by redistributing liquid and altering the capillary flow. These unique factors make foam spray drying more challenging to fully understand compared to non-foamed spray drying [4]. Therefore, focusing on a single slurry droplet, typically ranging from 20 to 180 μm in diameter, allows to study physical effects behind drying dynamics, which can be scaled up to the entire dryer using computational models.

In foam spray drying, individual solution or slurry (the focus of present study) droplets, containing liquid saturated with gas and dispersed solid particles, undergo rapid phase changes as they encounter atmospheric pressure within the drying chamber. The sudden pressure depletion initiates bubble nucleation within the droplets. At the same time, the gas solubility in the liquid phase decreases sharply, prompting the release of dissolved gas into those nucleated bubbles. This process varies based on nozzle type, which controls the pressure release rate, the magnitude of the pressure depletion, and droplet size, influencing both bubble nucleation and growth mechanisms [1].

The drying process of foam spray drying is influenced by the unique presence of bubbles within the slurry droplets, raising critical questions about their role in flow dynamics, drying kinetics and the eventual formation of solid structures and porosity. This study investigates these questions by exploring the coupled effects of heat, mass, and momentum transfer during foam spray drying. Through a dynamic pore network model, we examine the interactions between bubbles and liquid flow, highlighting their impact on drying kinetics and bubble dynamics. The findings provide new insights into the complex physics of foam spray drying and establish a foundation for optimizing this process for industrial applications.

Over the past decades our understanding of the wet granulation process and our ability to predict it computationally have made significant strides. However, despite these advancements we have yet to fully leverage models for granulation and other particulate processes to optimize the predictive design of granular product performance.

The goal of this research is to bridge this gap by linking process models with product performance models for wet granulation. To this end, a novel granule performance model has previously been developed within this project. This multi-scale model, which simulates swelling-driven granule disintegration and dispersion, has been specifically designed to integrate with existing wet granulation process models.

To validate these models, novel experiments were conducted in collaboration with the University of Strathclyde. The experimental results provided essential data for parameterizing the models, and have also offered deeper insights into the rate processes governing granule disintegration and dispersion.

Recent work has focussed on the recruitment of a new researcher who will support the project, Amir Arjmandi-Tash. The development of a surrogate model using Gaussian Process regression has commenced, to enable the eventual solution of the inverse problem.

Overall the work in our IFPRI project has focused on how, moving away from model systems containing spherical colloids with near hard interactions, we can widen the range of rheological responses by changing the properties of the building blocks of the suspensions, so that even in simple formulations a wide range of behaviors can be ”built in”, i.e. obtaining formulation guidelines to do “more with less” or simplifying formulations from within. At the same time we use novel experimental methods. We also developed a constitutive model for simplified industrial suspensions, based on insights from the advanced rheological methods (stress de-convolution) and using models taking into account plastic flow behaviour using an Eyring like approach and a viscoelastic upper convected Maxwell model.

For the this second IFPRI period we now focus on :

1. Particle roughness has been identified to generate surprising effects in colloidal gels and could both be tool to engineer materials from within for rheology or gravitational stability. The effect of roughness will now be explored more systematically. For gravitational stability, we will also study combined effects of roughness and shape, and investigate synergistic effects.
2. A full study of the structural evolution of systems in (1) will be investigated by 4D confocal rheology, with an emphasis on understanding the yielding transition.
3. To understand the role of non-central forces we would intensify the measurements of local scale mechanics using AFM (to characterize static friction) and then go to the micro mechanics of model aggregates (using optical tweezers).
4. we propose to also study these systems in 2D as this also has application to engineer strong interfaces or understand what happens in protein solutions, as a model system for lock and key interactions. The 2D nature of these systems makes them also a stepping stone for doing the micromechanics not immediately on the 3D systems.
5. we propose to continue the investigation of simplified industrial dispersion by industrial partners especially in light of systems with roughness and shape variations.

Project Phases

In the first phase of this project (2019 – 2023), three types of grinding aid additives in their pure form (n-Heptanoic acid, Diethylene glycol, and 1-Hexanol), which promote material bulk properties to various levels, were selected. The research aimed to assess the influence of these grinding aids by diverse dosages on both, grinding in ball mills and size classification in dynamic air classifiers. The focus was placed on determining how the grinding aid additives influence the grinding and classification process environment and on modifying selected models from literature for both, ball mills and deflector wheel classifiers. The models should account for the presence of grinding aids during simulating a dry-operated grinding plant in a flowsheet simulation.

Second Phase

During the second phase of the project (2023 – 2026), the research is focusing on identifying appropriate powder macroscopic bulk properties that accurately reflect both, the characteristics of particles and the presence of a particular type and dosage of grinding aid additives, as illustrated in Figure 1. In addition, the study aims to establish correlations between important microscopic particles properties, such as particle size, specific surface area, and particles specific surface energy, and bulk behavior of the powder. These correlations can be used to account for the impact of grinding aids within modeling grinding processes. Moreover, the bulk properties of the powder influence specific process characteristics, such as the discharge rate that can be achieved, the quantity of material hold-up in the grinding drum, and the residence time within the mill. Further, the knowledge about the material hold-up and residence time is required for modeling continuous grinding processes. These factors subsequently affect the quality of the final product (see Figure 1).

Experimental Approach

In order to understand the relationship between the powder’s bulk properties, the respond of the process in terms of resulting process characteristics, and the outcome of the grinding process, dry grinding experiments in an open-circuit continuous tumbling ball mill were performed. The trials were conducted until a stable operational state was reached. The outcomes of this series of trials provided data on the hold-up mass, discharge rate, and samples from product as well as hold-up material in the grinding drum. The gained samples underwent measurement to evaluate the characteristics of the particles and the powder and to correlate it to the system response. Based on this series of tests, couple of tests were selected for measuring residence time distribution. The results demonstrated that Diethylene glycol (DEG) led to a higher material hold-up compared to the product that did not contain grinding aid by the same feed rate. However, DEG resulted in a shorter median residence time with the highest maximum residence time and much finer product than that without grinding aid. On the other hand, Hexanol produced a product size and powder-to-void-ratio of almost 1 similar to that of the product without grinding aids, but this was achieved at a higher feed rate than that of the product without grinding aids. The comparison of the experimental data regarding residence time measurements with the results obtained from the one-dimensional axial dispersion model provided a reliable approximation, especially up to 80 % of the cumulative residence time distribution, showing slight deviations for all product formulations. The influence of grinding aids on the macroscopic properties of powder, as well as their incorporation into flowsheet modeling for a grinding plant, has revealed a dependable correlation between the powder flowability index (ffc) and the specific surface area. This correlation, which illustrate the effects of various grinding aids, can be represented by a power function. This function can be used in the ball mill model to predict dynamically changes in powder flowability as the particle size evolves during the grinding process.