The Effect of Particle Shape on the Compaction of Realistic Non-Spherical Particles—A Multi-Contact DEM Study

Abstract

The purpose of this study was to investigate the deformation behavior of non-spherical particles during high-load compaction using the multi-contact discrete element method (MC-DEM). To account for non-spherical particles, the bonded multi-sphere method (BMS), which incorporates intragranular bonds between particles, and the conventional multi-sphere (CMS), where overlaps between particles are allowed to form a rigid body, were used. Several test cases were performed to justify the conclusions of this study. The bonded multi-sphere method was first employed to study the compression of a single rubber sphere. This method’s ability to naturally handle large elastic deformations is demonstrated by its agreement with experimental data. This result was validated further through detailed finite element simulations (multiple particle finite element method (MPFEM)). Furthermore, the conventional multi-sphere (CMS) approach, in which overlaps between particles are allowed to form a rigid body, was used for the same objective, and revealed the limitations of this method in successfully capturing the compression behavior of a single rubber sphere. Finally, the uniaxial compaction of a microcrystalline cellulose-grade material, Avicel^® PH 200 (FMC BioPolymer, Philadelphia, PA, USA), subjected to high confining conditions was studied using the BMS method. A series of simulation results was obtained with realistic non-spherical particles and compared with the experimental data. For a system composed of non-spherical particles, the multi-contact DEM showed very good agreement with experimental data.

Introduction

Granular materials are unique in that they can behave as either solids or liquids. Sand, for instance, is composed of dissipative grains that interact with one another via repulsive and frictional contact forces. Despite their simplicity, the physics of granular materials is still poorly understood, leaving many open questions in a variety of fields, such as physics, process engineering, material science and geotechnical engineering. Cundall and Strack [1] pioneered the discrete element method (DEM) to model their physical behavior. The DEM numerically represents granular materials as a collection of particles rather than a continuum, and the bulk behavior of granular materials is determined by collective interactions among individual particles.

However, modeling the mechanical behavior of granular assemblies when subjected to high loads, such as mineral processing [2], soil compaction [3], and pharmaceutical tablets [4], is a difficult issue strongly affected by the shape of the individual particles. In reality, and in the vast majority of applications, the particle shape is non-spherical, but it may be reformed into a sphere by the spheronization [5] process. Due to the time required for contact detection and resolution, particle shape consideration is a computationally costly operation in DEM; hence, an ideal spherical particle approximation is frequently used as a fast alternative. Adjusting the rolling friction parameters to mimic the particle shape effects is one way to compensate for the lack of accuracy that is caused by ideal spherical representations [6]. However, this approach still does not allow for a thorough investigation of the impact of particle shape.

Nonetheless, general agreement on the need for sophisticated particle shape representations has resulted in techniques that allow for shape consideration within DEM. Approaches that are now available include sphere clusters, superquadrics, and polyhedra. Two distinct approaches may be found in sphere clusters: (a) the multi-sphere (hereinafter referred to as the conventional multi-sphere) and (b) the bonded multi-sphere [7,8]. In the conventional multi-sphere (CMS) [9,10], many particles are “linked together” by overlapping particles experiencing multiple contacts [11] to resemble a rigid, unbreakable non-spherical particle.

The bonded multi-sphere approach (BMS) [12], on the other hand, uses non-overlapping particles that are “touching” each other and bonded together with intragranular bonds to represent arbitrary particle shapes. The bonded multi-sphere model, which was first developed to simulate fracture initiation and evolution across mineral grains in rock [12], may also be used to approximate individual particles with complex shapes. The main advantage of this approach is that, by adjusting the bond parameters, the particles may behave both rigidly and deformably, and their breaking behavior can be simulated [8]. In contrast, ellipsoids and other quadric shapes can be constructed by employing superquadrics [13] and adjusting the shape parameters in the mathematical formulation. A comparison [10] of the conventional multi-sphere approach with superquadrics shows that using superquadrics saves computation time when simulating non-spherical particles, particularly blocky particles. Polyhedral particle models allow for the use of sharp corners and edges that may be used to create a variety of random particles [14]. Polyhedral particles can be used in a variety of applications [15,16], including crushing [17]. Nevertheless, these techniques have the problem of high computing costs, especially when compared to the use of solely spherical particles. For example, the neighbor search and contact resolution processing time that is necessary to investigate the interactions of thousands of non-spherical particles may render the study impractical. This limitation may arise when large numbers of particles need to be simulated.

The objective of this study was to investigate the impact of the particle shape on compaction profiles using the MC-DEM method. Due to computational time constraints, the simulations were limited to a small number of particles. The accuracy of the MC-DEM method had previously been validated by demonstrating its ability to model the compressibility properties of two pharmaceutical materials (Avicel® PH 200 (FMC BioPolymer) and Pharmacel® 102 (DFE Pharma)), assuming that the particles were spherical [4]. This study aimed to extend the MC-DEM method to include realistic non-spherical particles by combining it with BMS. The outcomes of both spherical and non-spherical particle simulations were compared to experimental data.

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Giannis, K.; Kwade, A.; Finke, J.H.; Schilde, C. The Effect of Particle Shape on the Compaction of Realistic Non-Spherical Particles—A Multi-Contact DEM Study. Pharmaceutics 2023, 15, 909. https://doi.org/10.3390/pharmaceutics15030909

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