Using AI/ML to predict blending performance and process sensitivity for Continuous Direct Compression (CDC).

Utilising three artificial intelligence (AI)/machine learning (ML) tools, this study explores the prediction of fill level in inclined linear blenders at steady state by mapping a wide range of bulk powder characteristics to processing parameters. Predicting fill levels enables the calculation of blade passes (strain), known from existing literature to enhance content uniformity. We present and train three AI/ML models, each demonstrating unique predictive capabilities for fill level. These models collectively identify the following rank order of feature importance: RPM, Mixing Blade Region (MB) size, Wall Friction Angle (WFA), and Feed Rate (FR). Random Forest Regression, a machine learning algorithm that constructs a multitude of decision trees at training time and outputs the mode of the classes (classification) or mean prediction (regression) of the individual trees, develops a series of individually useful decision trees. but also allows the extraction of logic and breakpoints within the data. A novel tool which utilises smart optimisation and symbolic regression to model complex systems into simple, closed-form equations, is used to build an accurate reduced-order model. Finally, an Artificial Neural Network (ANN), though less interrogable emerges as the most accurate fill level predictor, with an r2 value of 0.97. Following training on single-component mixtures, the models are tested with a four-component powdered paracetamol formulation, mimicking an existing commercial drug product. The ANN predicts the fill level of this formulation at three RPMs (250, 350 and 450) with a mean absolute error of 1.4%. Ultimately, the modelling tools showcase a framework to better understand the interaction between process and formulation. The result of this allows for a first-time-right approach for formulation development whilst gaining process understanding from fewer experiments. Resulting in the ability to approach risk during product development whilst gaining a greater holistic understanding of the processing environment of the desired formulation.

Application of Positron Emission Particle Tracking (PEPT) for the evaluation of powder behaviour in an incline linear blender for Continuous Direct Compression (CDC).

Positron Emission Particle Tracking (PEPT) is a non-invasive measurement technique which offers the ability to track the motion of individual particles with high temporal and spatial resolution, and thus build up an understanding of the bulk behaviour of a system from its microscopic (particle level) dynamics. Using this measurement technique, we have developed a series of novel metrics to better understand the behaviours of powders during the steady-state operation of a continuous blender system. Results are presented concerning the response of particle motion to processing parameters (mixing blade configuration and RPM), quantifying the motion in terms of predicted mixing performance. It was found that both increasing rpm and increasing hold-up mass (by selecting fewer transport blades and more mixing blades) provided improved mixing conditions. Interestingly, under specific conditions, there is evidence of convection-like mixing occurring at the interface of the transport and mixing region. This suggests the existence of a potential 'folding region' whereby powder is transported up the barrel (and away from the powder bulk bed) before being reconstituted back into the bulk mass. The results also provide valuable experimental data for the development, calibration and validation of future Discrete Element Method (DEM) simulations.

Recent advances in positron emission particle tracking: a comparative review.

Positron emission particle tracking (PEPT) is a technique which allows the high-resolution, three-dimensional imaging of particulate and multiphase systems, including systems which are large, dense, and/or optically opaque, and thus difficult to study using other methodologies. In this work, we bring together researchers from the world's foremost PEPT facilities not only to give a balanced and detailed overview and review of the technique but, for the first time, provide a rigorous, direct, quantitative assessment of the relative strengths and weaknesses of all contemporary PEPT methodologies. We provide detailed explanations of the methodologies explored, including also interactive code examples allowing the reader to actively explore, edit and apply the algorithms discussed. The suite of benchmarking tests performed and described within the document is made available in an open-source repository for future researchers.

Impact in granular matter: Force at the base of a container made with one movable wall.

In geotechnics as well as in planetary science, it is important to find a means by which to protect a base from impacts of micrometeoroids. In the moon, for example, covering a moon base with regolith, and housing such regolith by movable bounding walls, could work as a stress-leaking shield. Using a numerical model, by performing impacts on a granular material housed in a rectangular container made with one movable sidewall, it is found that such wall mobility serves as a good means for controlling the maximum force exerted at the container's base. We show that the force exerted at the container's base decreases as the movable wall decreases in mass, and it follows a Janssen-like trend. Moreover, by making use of a dynamically defined redirecting coefficient K(X), proposed by Windows-Yule et al. [Phys. Rev. E 100, 022902 (2019)2470-004510.1103/PhysRevE.100.022902], which depends on the container's width X, we propose a model for predicting the maxima measured at the container's base. The model depends on the projectile and granulate properties, and the container's geometry.

Positron Emission Particle Tracking of Granular Flows.

Positron emission particle tracking (PEPT) is a noninvasive technique capable of imaging the three-dimensional dynamics of a wide variety of powders, particles, grains, and/or fluids. The PEPT technique can track the motion of particles with high temporal and spatial resolution and can be used to study various phenomena in systems spanning a broad range of scales, geometries, and physical states. We provide an introduction to the PEPT technique, an overview of its fundamental principles and operation, and a brief review of its application to a diverse range of scientific and industrial systems.

Positron emission particle tracking using machine learning.

We introduce a new approach to positron emission particle tracking based on machine learning algorithms, demonstrating novel methods for particle location, tracking, and trajectory separation. The method allows radioactively labeled particles to be located, in three-dimensional space, with high temporal and spatial resolution, requiring no prior knowledge of the number of tracers within the system and can successfully distinguish multiple particles separated by distances as small as 2 mm. The technique's spatial resolution is observed to be invariant with the number of tracers used, allowing large numbers of particles to be tracked simultaneously, with no loss of data quality.

Janssen effect in dynamic particulate systems.

The Janssen model of stress redistribution within laterally bounded particulate assemblies is a longstanding and valuable theoretical framework, widely used in the design of industrial systems. However, the model relies on the assumption of a static packing of particles and has never been tested in a truly dynamic regime nor for a constraining system whose geometry is dynamically altered. In this paper, we explore the pressure distributions of granular beds housed within a container possessing a laterally mobile sidewall, allowing the depth, height, and cross-sectional areas of the systems studied to be dynamically altered, thus, inducing particle rearrangements and flow in the particulate system constrained thereby. We demonstrate that the systems studied can be successfully described by the Janssen model across a wide range of system expansion rates, including those for which liquidlike flow is clearly observed and propose an extension to the model allowing for an improved characterization of constrained dynamic systems.

New Insight into Pseudo-Thermal Convection in Vibrofluidised Granular Systems.

Utilising a combination of experimental results obtained via positron emission particle tracking (PEPT) and numerical simulations, we study the influence of a system's geometric and elastic properties on the convective behaviours of a dilute, vibrofluidised granular assembly. Through the use of a novel, 'modular' system geometry, we demonstrate the existence of several previously undocumented convection-inducing mechanisms and compare their relative strengths across a broad, multi-dimensional parameter space, providing criteria through which the dominant mechanism within a given system - and hence its expected dynamics - may be predicted. We demonstrate a range of manners through which the manipulation of a system's geometry, material properties and imposed motion may be exploited in order to induce, suppress, strengthen, weaken or even invert granular convection. The sum of our results demonstrates that boundary-layer effects due to wall (in)elasticity or directional impulses due to 'rough' boundaries exert only a secondary influence on the system's behaviour. Rather, the direction and strength of convective motion is predominantly determined by the energy flux in the vicinity of the system's lateral boundaries, demonstrating unequivocally that pseudo-thermal granular convection is decidedly a collective phenomenon.

Energy decay in a tapped granular column: Can a one-dimensional toy model provide insight into fully three-dimensional systems?

The decay of energy within particulate media subjected to an impulse is an issue of significant scientific interest, but also one with numerous important practical applications. In this paper, we study the dynamics of a granular system exposed to energetic impulses in the form of discrete taps from a solid surface. By considering a one-dimensional toy system, we develop a simple theory, which successfully describes the energy decay within the system following exposure to an impulse. We then extend this theory so as to make it applicable also to more realistic, three-dimensional granular systems, assessing the validity of the model through direct comparison with discrete particle method simulations. The theoretical form presented possesses several notable consequences; in particular, it is demonstrated that for suitably large systems, effects due to the bounding walls may be entirely neglected. We also establish the existence of a threshold system size above which a granular bed may be considered fully three dimensional.

Modifying self-assembly and species separation in three-dimensional systems of shape-anisotropic particles.

The behaviors of large, dynamic assemblies of macroscopic particles are of direct relevance to geophysical and industrial processes and may also be used as easily studied analogs to micro- or nano-scale systems, or model systems for microbiological, zoological, and even anthropological phenomena. We study vibrated mixtures of elongated particles, demonstrating that the inclusion of differing particle "species" may profoundly alter a system's dynamics and physical structure in various diverse manners. The phase behavior observed suggests that our system, despite its athermal nature, obeys a minimum free energy principle analogous to that observed for thermodynamic systems. We demonstrate that systems of exclusively spherical objects, which form the basis of numerous theoretical frameworks in many scientific disciplines, represent only a narrow region of a wide, multidimensional phase space. Thus, our results raise significant questions as to whether such models can accurately describe the behaviors of systems outside this highly specialized case.

Forced axial segregation in axially inhomogeneous rotating systems.

Controlling segregation is both a practical and a theoretical challenge. Using a novel drum design comprising concave and convex geometry, we explore, through the application of both discrete particle simulations and positron emission particle tracking, a means by which radial size segregation may be used to drive axial segregation, resulting in an order of magnitude increase in the rate of separation. The inhomogeneous drum geometry explored also allows the direction of axial segregation within a binary granular bed to be controlled, with a stable, two-band segregation pattern being reliably and reproducibly imposed on the bed for a variety of differing system parameters. This strong banding is observed to persist even in systems that are highly constrained in the axial direction, where such segregation would not normally occur. These findings, and the explanations provided of their underlying mechanisms, could lead to radical new designs for a broad range of particle processing applications but also may potentially prove useful for medical and microflow applications.

Maximizing energy transfer in vibrofluidized granular systems.

Using discrete particle simulations validated by experimental data acquired using the positron emission particle tracking technique, we study the efficiency of energy transfer from a vibrating wall to a system of discrete, macroscopic particles. We demonstrate that even for a fixed input energy from the wall, energy conveyed to the granular system under excitation may vary significantly dependent on the frequency and amplitude of the driving oscillations. We investigate the manner in which the efficiency with which energy is transferred to the system depends on the system variables and determine the key control parameters governing the optimization of this energy transfer. A mechanism capable of explaining our results is proposed, and the implications of our findings in the research field of granular dynamics as well as their possible utilization in industrial applications are discussed.

Competition between geometrically induced and density-driven segregation mechanisms in vibrofluidized granular systems.

The behaviors of granular systems are sensitive to a wide variety of particle properties, including size, density, elasticity, and shape. Differences in any of these properties between particles in a granular mixture may lead to segregation, or "demixing," a process of great industrial relevance. Despite the known influence of particle geometry in granular systems, a considerable fraction of research into these systems concerns only uniformly spherical particles. We address, for the case of vertically vibrated granular systems, the important question of whether the introduction of differing particle geometries entirely invalidates our existing knowledge based on purely spherical granulates, or whether current models may simply be adapted to account for the effects of particle shape. We demonstrate that while shape effects can indeed influence the dynamical and segregative behaviors of a granular system, the segregative mechanisms associated with particle geometry are decidedly secondary to those related to particle density. The relevant control parameters determining the extent of geometrically induced segregation are established. Finally, a manner in which shape effects may be accounted for in simulations utilizing purely spherical particles is proposed.

Influence of thermal convection on density segregation in a vibrated binary granular system.

Using a combination of experimental results and discrete particle method simulations, the role of buoyancy-driven convection in the segregative behavior of a three-dimensional, binary granular system is investigated. A relationship between convective motion and segregation intensity is presented, and a qualitative explanation for this behavior is proposed. This study also provides an insight into the role of diffusive behavior in the segregation of a granular bed in the convective regime. The results of this work strongly imply the possibility that, for an adequately fluidized granular bed, the degree of segregation may be indirectly controlled through the adjustment of the system's driving parameters, or the dissipative properties of the system's side-boundaries.

Center of mass scaling in three-dimensional binary granular systems.

Using a combination of experimental results acquired through positron emission particle tracking and simulational results obtained via the discrete particle method, we determine a scaling relationship for the center of mass height of a vibrofluidized three-dimensional, bidisperse granular system. We find the scaling to be dependent on the characteristic velocity with which the system is driven, the depth of the granular bed, and the elasticities of the particles involved, as well as the degree of segregation exhibited by the system and the ratio of masses between particle species. The scaling is observed to be robust over a significant range of system parameters.

Effects of packing density on the segregative behaviors of granular systems.

We present results concerning the important role of system packing in the processes of density- and inelasticity-induced segregation in vibrofluidized binary granular beds. Data are acquired through a combination of experimental results acquired from positron emission particle tracking and simulations performed using the discrete particle method. It is found that segregation due to inelasticity differences between particle species is most pronounced in moderately dense systems, yet still exerts a significant effect in all but the highest density systems. Results concerning segregation due to disparities in particles' material densities show that the maximal degree to which a system can achieve segregation is directly related to the density of the system, while the rate at which segregation occurs shows an inverse relation. Based on this observation, a method of minimizing the time and energy requirements associated with producing a fully segregated system is proposed.

Energy non-equipartition in strongly convective granular systems.

Using positron emission particle tracking, the effects of convective motion and the resulting segregative behaviour on the partition of kinetic energy between the components of a bidisperse granular system are, for the first time, systematically investigated. It is found that the distribution of energy between the two system components, which are equal in size but differ in their material properties, is strongly dependent on the degree of segregation observed in the granular bed. The results obtained demonstrate that the difference in energy obtained by dissimilar particle species is not an innate property of the materials in question, but can in fact be altered through variation of the relevant system parameters. The existence of a relationship between the convective and segregative properties of a granular system and the degree of energy equipartition within the system implies the possibility of extending existing theory into the convective regime. Thus, our findings represent an incremental step towards the definition of a granular analogy to temperature that can be applied to more generalised systems and, through this, an improved understanding of inhomogeneous granular systems in general.

Low-frequency oscillations and convective phenomena in a density-inverted vibrofluidized granular system.

Low-frequency oscillations (LFOs) are thought to play an important role in the transition between the Leidenfrost and convective states of a vibrated granular bed. This work details the experimental observation of LFOs, which are found to be consistently present for a range of driving frequencies and amplitudes, with particles of varying material and using containers of differing material properties. The experimentally acquired results show a close qualitative and quantitative agreement with both theory and simulations across the range of parameters tested. Strong agreement between experimental and simulation results was also observed when investigating the influence of sidewall dissipation on LFOs and vertical density profiles. This paper additionally provides evidence of two phenomena present in the Leidenfrost state: a circulatory motion over extended time periods in near-crystalline configurations, and a Leidenfrost-like state in which the dense upper region displays an unusual inverse thermal convection.

Thermal convection and temperature inhomogeneity in a vibrofluidized granular bed: the influence of sidewall dissipation.

Using a vertically vibrated, fully three-dimensional granular system, we investigate the impact of dissipative interactions between the particles in the system and the vertical sidewalls bounding it. We find that sidewall dissipation influences various properties of the bed including, but not limited to, the spatial distribution of granular temperatures, the functional form of velocity distributions, and the strength of convection. Simple, monotonic relationships are observed for all the aforementioned properties, including a striking linear relationship between convection strength and wall dissipation. We conclude that sidewall effects are not limited to the vicinity of the walls themselves, but extend into the bulk of the system and hence must be considered even in relatively wide, three-dimensional systems. We also propose the possibility of using the alteration of sidewall material as a method of "tuning" certain system parameters in situations where changing the bulk properties or driving parameters of a granular system may be undesirable.

Boltzmann statistics in a three-dimensional vibrofluidized granular bed: idealizing the experimental system.

The importance of the method of energy injection into a vertically vibrated granular bed was investigated using positron emission particle tracking. A comparison was made between two experimental systems. The first was driven by a flat base, the second by a base comprising a monolayer of spheres, each free to move in three dimensions but constrained to the bottom of the system, effectively randomizing energy transfer into the bed. The latter system exhibited more Gaussian velocity distributions, a more isotropic temperature, and a better approximation of molecular chaos than the former, behavior more akin to the idealized situation of white noise forcing than is generally observed in an experimental system.