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1. The 'Signature' of Particle Geometry - DEM Modelling Perspective

   https://doi.org/10.23967/particles.2021.033  

   Lee, S.; Lee, C.; Shin, M.; Tripathi, P. (February 2022, PARTICLES 2021 – VII International Conference on Particle-based Methods, Hamburg, Germany, October 4-6, 2021)

   Wriggers, Peter; Bischoff, Manfred; Oñate, Eugenio; Düster, Alexander; Zohdi, Tarek (Ed.)

   This study evidences that the particle surface-area-to-volume ratio (A/V) and the particle volume (V) have the key information of particle geometry and the ‘signature’ is realized by a power-law relationship between A/V and V in a form of V = (A/V)^α × β. We find that the power value α is influenced by the shape-size relationship while the β* term (β evaluated with a fixed value of α = -3) informs the average particle shape of a granular material regarding the overall angularity. This study also discusses how the particle shape can be retrieved in terms of Wadell’s true sphericity using the A/V and V. This concept is linked to another shape index M that interprets the particle shape as a function of surface area A, volume V, and size L. This paper explains the analytical aspects of geometric ‘signature’ and examines the idea using the example particles to address the DEM modelling-related questions. 

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2. A New Paradigm Integrating the Concepts of Particle Abrasion and Breakage

   https://doi.org/10.1061/9780784485309.028  

   Tripathi, Priya; Lee, Seung Jae; Shin, Moochul; Lee, Chang Hoon (February 2024, American Society of Civil Engineers)

   Evans, T Matthew; Stark, N; Chang, S (Ed.)

   This paper introduces a new paradigm that integrates the concepts of particle abrasion and breakage. Both processes can co-occur under loading as soil particles are subjected to friction as well as collisions between particles. Therefore, the significance of this integrating paradigm lies in its ability to address both abrasion and breakage in a single framework. The new paradigm is mapped out in a framework called the particle geometry space. The x-axis corresponds to the surface-area-to-volume ratio (A/V), while the y-axis represents volume (V). This space facilitates a holistic characterization of the four-particle geometry features, that is, shape (β) and size (D) as well as surface area (A) and volume (V). Three distinct paths (abrasion, breakage, and equally occurring abrasion and breakage processes), three limit lines (breakage line, sphere line, and average shape-conserving line), and five different zones are defined in the particle geometry space. Consequently, this approach enables us to systematically relate the extent of co-occurring abrasion and breakage to the particle geometry evolution. 

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3. The structural, vibrational, and mechanical properties of jammed packings of deformable particles in three dimensions

   https://doi.org/10.1039/d1sm01228b  

   Wang, Dong; Treado, John D.; Boromand, Arman; Norwick, Blake; Murrell, Michael P.; Shattuck, Mark D.; O'Hern, Corey S. (November 2021, Soft Matter)

   We investigate the structural, vibrational, and mechanical properties of jammed packings of deformable particles with shape degrees of freedom in three dimensions (3D). Each 3D deformable particle is modeled as a surface-triangulated polyhedron, with spherical vertices whose positions are determined by a shape-energy function with terms that constrain the particle surface area, volume, and curvature, and prevent interparticle overlap. We show that jammed packings of deformable particles without bending energy possess low-frequency, quartic vibrational modes, whose number decreases with increasing asphericity and matches the number of missing contacts relative to the isostatic value. In contrast, jammed packings of deformable particles with non-zero bending energy are isostatic in 3D, with no quartic modes. We find that the contributions to the eigenmodes of the dynamical matrix from the shape degrees of freedom are significant over the full range of frequency and shape parameters for particles with zero bending energy. We further show that the ensemble-averaged shear modulus 〈 G 〉 scales with pressure P as 〈 G 〉 ∼ P β , with β ≈ 0.75 for jammed packings of deformable particles with zero bending energy. In contrast, β ≈ 0.5 for packings of deformable particles with non-zero bending energy, which matches the value for jammed packings of soft, spherical particles with fixed shape. These studies underscore the importance of incorporating particle deformability and shape change when modeling the properties of jammed soft materials. 

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4. Evaluation of Particle Size Distribution Metrics to Estimate the Relative Contributions of Different Size Fractions Based on Measurements in Arctic Waters

   https://doi.org/10.1029/2020JC016218  

   Runyan, Hugh; Reynolds, Rick A.; Stramski, Dariusz (June 2020, Journal of Geophysical Research: Oceans)

   Abstract The size distribution of suspended particles influences several processes in aquatic ecosystems, including light propagation, trophic interactions, and biogeochemical cycling. The shape of the particle size distribution (PSD) is commonly modeled as a single‐slope power law in oceanographic studies, which can be used to further estimate the relative contributions of different particle size classes to particle number, area, and volume concentration. We use a data set of 168 high size‐resolution PSD measurements in Arctic oceanic waters to examine variability in the shape of the PSD over the particle diameter range 0.8 to 120 μm. An average value of −3.6 ± 0.33 was obtained for the slope of a power law fitted over this size range, consistent with other studies. Our analysis indicates, however, that this model has significant limitations in adequately parameterizing the complexity of the PSD, and thus performs poorly in predicting the relative contributions of different size intervals such as those based on picoplankton, nanoplankton, and microplankton size classes. Similarly, median particle size was also generally a poor indicator of these size class contributions. Our results suggest that alternative percentile diameters derived from the cumulative distribution functions of particle number, cross‐sectional area, and volume concentration may provide better metrics to capture the overall shape of the PSD and to quantify the contributions of different particle size classes. 

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5. Multi-Size Proppant Pumping Schedule of Hydraulic Fracturing: Application to a MP-PIC Model of Unconventional Reservoir for Enhanced Gas Production

   https://doi.org/10.3390/pr8050570  

   Siddhamshetty, Prashanth; Mao, Shaowen; Wu, Kan; Kwon, Joseph Sang-Il (May 2020, Processes)

   Slickwater hydraulic fracturing is becoming a prevalent approach to economically recovering shale hydrocarbon. It is very important to understand the proppant’s transport behavior during slickwater hydraulic fracturing treatment for effective creation of a desired propped fracture geometry. The currently available models are either oversimplified or have been performed at limited length scales to avoid high computational requirements. Another limitation is that the currently available hydraulic fracturing simulators are developed using only single-sized proppant particles. Motivated by this, in this work, a computationally efficient, three-dimensional, multiphase particle-in-cell (MP-PIC) model was employed to simulate the multi-size proppant transport in a field-scale geometry using the Eulerian–Lagrangian framework. Instead of tracking each particle, groups of particles (called parcels) are tracked, which allows one to simulate the proppant transport in field-scale geometries at an affordable computational cost. Then, we found from our sensitivity study that pumping schedules significantly affect propped fracture surface area and average fracture conductivity, thereby influencing shale gas production. Motivated by these results, we propose an optimization framework using the MP-PIC model to design the multi-size proppant pumping schedule that maximizes shale gas production from unconventional reservoirs for given fracturing resources. 

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