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A bi-directional coupling between the Discrete Element Method (DEM) and Population Balance Modelling (PBM) is suggested to model the failure of pharmaceutical tablets under abrasive conditions such as bulk flow of impact. DEM provides the description of kinetics and permits the extraction of collision energy distributions. Representation of the primary shape of the tablets is achieved by using the multi-sphere approach, a rigid assembly of systematically connected spheres to resemble non-spherical shape. Based on the collision energy distribution and the abrasion characteristics of the tablets by solving the PBM equations, the mass loss of tablets according to their mechanical resistance, as well as the fragment size distribution progeny can be computed. For the description of the abrasive failure characteristics, a multi-stage calibration procedure for the empirical breakage kernels of Vogel and Peukert as well as of Ghadiri and Zhang is also applied. The novelty of the presented approach is the bi-directional coupling: tablet and fragment distribution masses are dynamically updated for subsequent time steps in DEM by the particle replacement method according to the stress history of the system. The outcome of this methodology helps to get a deeper understanding of the process-property relationships, to evaluate the effect of any process or geometry modifications in processing operations, such as drum coating, and to reduce the requirements of experimental investigations.

Fine grinding in wet stirred media mills is a key operation in numerous industrial processes. During wet milling, grinding beads (typically millimetre scale) collide with each other under rapid agitation. These collisions transfer energy into the surrounding medium, a feed stream comprising a premixed slurry (a suspension of micron-sized particles), leading to a reduced particle size. Numerical simulation provides an opportunity to gain mechanistic insight by modelling the influences of grinding media, agitator speed and slurry rheology on the breakage. The multiphase nature of wet milling necessitates models that account for both the solid grinding beads and the slurry feed. Established fluid-particle coupled methods are in principle capable of doing this, but the need to resolve the large hydrodynamic lubrication forces between near-contacting beads demands extremely high fluid field resolution, leading to proliferating simulation size and cost. To address this challenge, a Discrete Element Method (DEM) simulation for a lab scale mill is presented in which the bead-bead interaction includes pairwise hydrodynamic lubrication in addition to frictional contact forces. The model accounts for multiphase effects in a simplified yet physically well-motivated way, circumventing the computational cost of a fully fluid-resolved model. A systematic model calibration against the laboratory mill is presented, and thereafter the model provides a good estimation for the empirical power draw across the full range of rotation speeds and considered feed viscosities. The differences in energy dissipation modes and the local distribution of collisions along the mill chamber are examined for the extreme viscosity condition, revealing that most energy dissipation is due to inter-particle forces acting tangentially (shearing and rolling) while highly energetic collisions (impact and torsion), relying on free flows and inter-bead mobility, are relatively unimportant.

Processability of powders in high load compaction constitutes a challenge due to particle rearrangement, compression and breakage occurring simultaneously. Although tableting is a central operation in pharmaceutical technology, a better understanding of the link between the macroscopic powder behaviour and its micro-mechanical properties is still required. In the present study, a dual focus on the powder compaction behaviour and the quality properties of final tablets using a compaction simulator is presented. Tableting has been performed for a wide size range of limestone powders from 10 to 400 MPa, in order to understand and compare the powder compaction behaviour at both low and high confining stresses. Compactibility of limestone, the relation between porosity and stress, has been assessed with both the classical (logarithmic) Heckel model and the newly proposed (double logarithmic) Wunsch model, confirming the improvement of the latter to enhance the description of the porosity change during compaction, as well as the model robustness towards non-pharmaceutical powders. The qualitative effect of particle size and thus cohesion on the bulk density at high pressure compaction is found to be very similar to the low pressure regime. However, the geometrical interlocking influence of large size powders found in a previous study becomes irrelevant at such high pressures. For d 50 10 μm, the tablet tensile strength remains almost insensitive to the size variation. However, for the coarsest grades, the tensile strength decreases with increasing d 50 at all compaction stresses. In addition, the tablet tensile strength is found to follow a non-monotonic trend with median particle size.

Finishing and transport operations of pharmaceutical tablets such as coating and conveying processes can qualitatively be improved with a better understanding of the interplay of process parameters and product quality attributes. This study provides a first step towards the simulation of these processes with the calibration of the motion modelling of uniaxial-compressed cylindrical tablets using the multi-sphere approach (MS) within the Discrete Element Method (DEM). Only high accuracy in the representation of cylindrical tablet shape, especially regarding edges, yields a good agreement between simulated and experimental packing fraction. Sensitivity regarding model parameter calibration was evaluated based on tumbling drum tests which are of wide occurrence in the industry and the so-called pouring experiment extracting static and dynamic angles of repose, identified sliding and rolling friction as the most sensitive parameters. These were successfully calibrated by an iterative crossed analysis in tumbling drum and pouring tests. Additionally, a complete determination and subsequent calibration strategy is provided for Coefficient of Restitution and Young's modulus. Results of the final numerical modelling are qualitative and quantitative in agreement with experimental test case experiments. A final validation is performed through the simulation of an attrition tester with a single baffle, highlighting one of the main limitations of DEM: the problem-targeted nature of the operation of calibration.

The bulk properties of powders depend on material characteristics and size of the primary particles. During storage and transportation processes in the powder processing industry, the material undergoes various modes of deformation and stress conditions, e.g., due to compression or shear. In many applications, it is important to know when powders are yielding, i.e. when they start to flow under shear; in other cases it is necessary to know how much stress is needed to keep them flowing. The measurement of powder yield and flow properties is still a challenge and will be addressed in this study. In the framework of the collaborative project T-MAPPP, a large set of shear experiments using different shear devices, namely the Jenike shear tester, the ELE direct shear tester, the Schulze ring shear tester and the FT4 powder rheometer, have been carried out on eight chemically-identical limestone powders of different particle sizes in a wide range of confining stresses. These experiments serve two goals: i) to test the reproducibility/consistency among different shear devices and testing protocols; ii) to relate the bulk behaviour to microscopic particle properties, focusing on the effect of particle size and thus inter-particle cohesion. The experiments show high repeatability for all shear devices, though some of them show more fluctuations than others. All devices provide consistent results, where the FT4 powder rheometer gives lower yield/steady state stress values, due to a different pre-shearing protocol. As expected, the bulk cohesion decreases with increasing particle size (up to 150 μm), due to the decrease of inter-particle cohesion. The bulk friction, characterized in different ways, is following a similar decreasing trend, whereas the bulk density increases with particle size in this range. Interestingly, for samples with particle sizes larger than 150 μm, the bulk cohesion increases slightly, while the bulk friction increases considerably—presumably due to particle interlocking effects—up to magnitudes comparable to those of the finest powders. Furthermore, removing the fines from the coarse powder samples reduces the bulk cohesion and bulk density, but has a negligible effect on the bulk friction. In addition to providing useful insights into the role of microscopically attractive, van der Waals, gravitational and/or compressive forces for the macroscopic bulk powder flow behaviour, the experimental data provide a robust database of cohesive and frictional fine powders for industrially relevant designs such as silos, as well as for calibration and validation of models and computer simulations.