Particle Formation

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.

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.

The objective of this research project is to assess and enhance the ability of a recently-advanced high-fidelity modeling framework for spray formation to model complex liquid break-up and predict drop size distributions in high viscosity and non-Newtonian liquid atomization systems, such as found in spray drying applications. This framework, dubbed enhanced Volume of Fluid (eVOF), was developed by the PI’s research group and hinges on two key components:

1. a fully conservative Eulerian interface capturing technique with the ability to capture sub-grid scale liquid features such as thin films and thin ligaments, known to be of critical importance in the break-up of viscous and non-Newtonian fluids, and
2. simple physics-based break-up models to convert these thin liquid features into spray droplets that can be tracked in a Lagrangian fashion.

In the first year of the project, non-Newtonian constitutive models were implemented and tested in the PI’s research flow solver, and shown to influence spray formation in simple flow configurations. Moreover, a simple pressure-swirl configuration was explored to demonstrate the ability of eVOF to preserve thin liquid films and virtually eliminate numerical break-up. In year 2, the non-Newtonian constitutive models were further refined and validated against bubble rise experiments. A realistic pressure-swirl nozzle was selected for study based on availability of nozzle geometry and drop size measurements. Despite the complexity of the resulting flow, eVOF was again shown to preserve sub-grid scale liquid films successfully. Advances were made on sub-grid scale modeling of film and ligament break-up, allowing preliminary comparisons of drop sizes against experiments to be shown.

Going forward, the sub-grid scale modeling of film and ligament break-up will be further improved, in particular in the limit of high-viscosity liquids, and a more comprehensive comparison of drop sizes will be made against experiments.

The main objective of this project is to apply a pneumatic nozzle design, the Air-Core-Liquid-Ring (ALCR)-nozzle, for spray-drying of highly viscous liquids and pastes. The project is divided into three main working packages (WP). WP 1 aims to validate the ACLR atomizer technology to enable spraying of highly viscous liquids, using both experimental measurements and CFD simulations. WP 2 aims to evaluate the impact of the composition and morphology of the atomized droplets on the drying kinetics, for highly concentrated feeds. WP 3 aims to join the results of both packages to investigate the applicability of the ACLR nozzle for spray-drying of highly viscous liquids. The followings findings were achieved in the present funding period.

WP 1: Atomization with the ACLR nozzle

• The ACLR can achieve stable atomization with feed viscosities as high as 3 Pa·s, at relatively low pressures (7 bar) and low air-to-liquid ratios (0.8).
• The internal flow and the external spray instabilities can be directly correlated with each other.
• A CFD model was successfully adapted in STAR-CCM+ v.2206 to predict the internal flow of non-Newtonian maltodextrin solutions being atomized with an ACLR nozzle. In general, the predicted ALRs from the simulations agree with what was observed in experiments. Additionally, the liquid lamella thickness inside the nozzle follows the same trend in the simulations as what is observed in experiment: A smaller internal lamella variation is observed as the ALR increases.
• The possibility of using simulations to evaluate operating conditions outside of experimental capabilities was evidenced. The lamella variation can be severely reduced by increasing the operating pressure to 15 bar, which is still far below the 50-250 bar that is common in pressure swirl nozzles.

WP 2: Evaluation of the impact of the composition and morphology on the drying kinetics and model development by single droplet drying

• A method for the analysis of the mass data and calculation of the drying kinetics was developed.
• Experiments were conducted to evaluate the impact of initial solids concentrations of up to 45 wt%. The results for the particle size, mass and drying kinetics showed good agreement with theoretical considerations.
• The impact of the drying temperature was evaluated. While the impact of the drying temperature on the drying time agrees well with expectation, its influence on the drying kinetics showed no apparent trend.

WP 3: Proof-of-concept of industrial applicability of the ACLR nozzle for spray-drying of highly viscous liquids

The simulation plan to optimize the geometrical design of the nozzle has been formulated, and it is currently being carried out.

The presence of moisture in powders and grains drastically changes the mechanical properties of the materials. Inter-particle cohesion due to capillary bridges, causes grains to agglomerate into clumps of sizes much larger than the size of the constituent particles. Besides lacking a complete understanding of the effects of inter-particle cohesion on granular mechanics, the agglomeration of granules makes the processing of such materials challenging, in particular during drying under agitation 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.

The project 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, we hope to shed some light on the mechanical behavior of agglomerates to develop models at agglomerate scales. In particular, we consider the breakup of model agglomerates, with an application to more efficient drying of powders. Besides causing trouble in the processing of such materials, agglomerates can also sustain humidity within them, reducing the overall ability to dry such bulk materials.

During the first year of the project, different experimental tools were developed and tested with model particles - spherical glass beads - and without considering heat exchange and drying. We developed an oscillating system consisting of a mechanical shaker and a quasi-2D transparent box allowing us to observe the agglomerates. Preliminary tests with model glass beads and water have been performed to probe the role of acceleration and amplitude of oscillation on the agglomerate sizes. A second system, relying on an agitation provided by a turbulent airflow has been designed and led to some first results. Finally, we initiated model experiments consisting of the impact of isolated agglomerates on a solid surface to probe their mechanical properties and fragmentation.

The project brief included the following objectives:

• Identification of appropriate test powders and characterization of their relevant physical and chemical properties.
• Establishment of a test method to quantify material adhesion on compaction tooling over an industrially relevant range of process and environmental conditions.
• Identification of key factors affecting the amount and/or rate of powder adhesion on
• compaction tooling such as: molecular, crystal, surface, and mechanical properties of the powder, surface finish and chemistry (including coated surfaces), process conditions (e.g., pressure/stress) and environmental conditions (temperature, relative humidity)
• Establish predictive criteria for the propensity of adhesion given a set of molecular/crystal properties and process/environmental conditions.

The sticking behaviour was characterized for the following materials: Ibuprofen, Acetylsalicylic Acid (Aspirin), Acetaminophen (Paracetamol), Mannitol (Pearlitol), Sorbitol (Neosorb), Maize Starch B and Microcrystalline cellulose (Microcel) which was used as a reference non-sticking material.

In addition to standard compaction studies, two new test methods were developed: heated die and high-rate compaction. The experimental conditions for a diagnostic test were established.

The key factors controlling sticking were determined as: compaction pressure, compaction rate, temperature and relative humidity.

The team at Leicester conceived a predictive method that uses machine learning to determine the sticking probability of sticking of any existing or new chemical entity from molecular information as follows. The chemical formula together with the structure of the molecule is encoded in SMILES (Simplified Molecular Input Line Entry System), for which molecular descriptors are calculated (Mordred). Machine learning tools including linear discriminant analysis (to rank the descriptors), feature engineering (to balance the data set), principal component analysis (to determine weighting for the descriptors), and support vector machine (to classify sticking and assign probability).

The experimental data generated in the project was used to train the algorithm, together with known sticking and non-sticking materials from the literature. The sticking probability was determined for the materials published in the Handbook of Pharmaceutical Excipients and molecules proposed by the industrial partners.

The focus of this project is to understand the physical mechanisms that lead to defect formation – pitting, cracking, and delamination – during pharmaceutical tableting. A leading hypothesis among IFPRI members is that trapped interstitial air leads to high pore pressures that tend to fracture adhered particle interfaces after removal of the confining pressure. The project objective is to explore this problem through coupled numerical methods including:

1. continuum mixture models
2. the discrete element method (DEM) coupled with a fluid solver.

The primary barrier to using these methods is that fact that the behavior of cohesive powders is not well understood, with neither a generally accepted constitutive relation nor contact model in existence.

To address this, the project has emphasized developing a reliable cohesive powder contact model for usage in DEM. This is the natural progression, since a powder DEM model will be indispensable in determining a constitutive relation for continuum simulations. In particular, we have concentrated on creating a mechanically-derived contact model for adhesive elastic-perfectly plastic particles.

In year one of the project, the majority of the theoretical framework for the contact model was developed, but a number of issues remained. The JKR-type adhesion of the contact model needed to be validated once significant plastic deformation had occurred and the scheme to respect plastic incompressibility required an overhaul. The contact model was limited to simple symmetric loadings of a single particle, necessitating adaptation to many-particle interactions. Additionally, the model, initially coded in Matlab, needed implementation in an established software like LIGGGHTS or LAMMPS, with a reliable fluid-solid coupling strategy.

In year two, the theoretical framework was completed by validating the adhesive model within the fully-plastic regime and correcting the plastic incompressibility scheme. The completed contact model was published in the premier solid mechanics journal, Journal of Mechanics and Physics of Solids, as a two part series. E↵orts have extended to modeling many-particle interactions, a necessary step to allow simulation of full-scale industrial applications. Implementation into LIGGGHTS is underway and preliminary simulations show promise in replicating compaction simulator data. In the upcoming phase, we are working directly with Sandia National Laboratories to create a LAMMPS implementation. In addition to greater computational e ciency and formal support for the model, LAMMPS provides the advantage of allowing immediate coupling with a multi-particle collision dynamics fluid solver, capable of simulating a compressible gas phase.

In summary, the project has made substantial progress on the front of creating a reliable powder DEM model and we are now poised at an exciting place where beginning to understand defect formation during pharmaceutical tableting is tangible. Because the model is mechanically-derived, it can also be trusted to assist in the future development of a continuum constitutive relation. Finally, because of the planned open-source nature of the implementation into LAMMPS, a familiar software to most IFPRI members, the powder DEM model can be used for industrial applications extending beyond tableting.

The following report is split into three chapters. Chapter 1 gives a high level update of the project, without detailed technical explanations and equations. Chapter 2 and 3 are both papers of the two part series published in the Journal of Mechanics and Physics of Solids. These papers contain detailed explanations regarding the theoretical background of the contact model in addition to validations made against finite element simulations. Throughout Chapter 1, references to the two papers are made directing the reader to pertinent information to supplement understanding, however, Chapter 1 was written with the intention that it could be understood without reference to the papers.

This project was a continuation of our previous work on developing atomization model. The goals of this work were to understand the breakup of ligament of highly viscous, rheologically complex fluid under given stretch rate and to predict the droplet size distribution from the ligament breakup. We divided the work in three stages: i) breakup of ligament, ii) breakup of ligament in air crossflow and iii) application of ligament breakup model to spray. The current report is on the first stage of the work.

We have completed a set of experiments on the breakup of polymeric ligaments by generating a liquid bridge between two rods. We found that the evolution of the liquid bridge can be studied in two stages, each with certain substages:

• Formation of a beads-on-string structure at equilibrium
  • First-generation beads form due to surface wave described by Rayleigh-Plateau instability.
  • Second-generation and higher generation beads form due to the pressure difference between the beads and string region.
  • Beads will slide along the string until they reach their equilibrium positions.
  • Unequal end drop sizes can create a liquid flow from small end drop to large one. This will generate a fresh, undisturbed ligament near small end drop. Later, a reverse liquid flow will be generated after the stopper bead formed at the large end drop side.
    • The initial liquid flow (from small to large end drop) delays the formation of first-generation beads.
    • The reverse liquid flow (from large to small end drop) will let a segment of the liquid bridge be absorbed by small end drop, while the rest is non-uniformly stretched.
  • Beads have multiple sizes at the equilibrium state.
• Breakup of liquid bridge from the equilibrium stage
  • Tension in strings starts to relax. This makes the string thinner and longer. The tension force in the string reduces. This process starts with two end strings.
  • Distances between the beads get closer, causing the smaller beads to move towards locally large beads and merge together.
  • Number of beads largely decreases at the time string breaks, generating multiple large beads.