This study introduces a mathematical model to predict the dynamic angle of repose exhibited by granular materials in a rotating drum. The model accounts for the effect of particle properties, particularly sliding and rolling friction, as well as process conditions, i.e., the Froude number. We show that the effects of particle properties can be modeled independently of the process conditions, resulting in a multiplicative model. The model is validated using experimental data taken at different Froude numbers, yielding favorable agreement between the predicted dynamic angle of repose and the experimental observations. The findings of this study hold significant implications for engineering disciplines, as they provide crucial insights for optimizing processes involving granular materials in various engineering applications.@en

In this paper we introduce the open-source code MercuryDPM: a code for simulating discrete particles. The paper discusses software and management issues that may be interesting for the developers of other open-source codes. Then we review the new features that have been added since the last publication: an improved Hertz-Mindlin model; a new liquid bridge model of Lian and Seville; a droplet-spray model; better support for re-creating complex, measured particle size distributions; a new implementation of rigid clumps; an implementation of elastic membranes; a wear model for walls; a soft-kill feature and a cloud-deployment interface for AWS.

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We introduce the open-source package MercuryDPM, which we have been developing over the last few years. MercuryDPM is a code for discrete particle simulations. It simulates the motion of particles by applying forces and torques that stem either from external body forces, (gravity, magnetic fields, etc.) or particle interactions. The code has been developed extensively for granular applications, and in this case these are typically (elastic, plastic, viscous, frictional) contact forces or (adhesive) short-range forces. However, it could be adapted to include long-range (molecular, self-gravity) interactions as well. MercuryDPM is an object-oriented algorithm with an easy-to-use user interface and a flexible core, allowing developers to quickly add new features. It is parallelised using MPI and released under the BSD 3-clause licence. Its open-source developers’ community has developed many features, including moving and curved walls; state-of-the-art granular contact models; specialised classes for common geometries; non-spherical particles; general interfaces; restarting; visualisation; a large self-test suite; extensive documentation; and numerous tutorials and demos. In addition, MercuryDPM has three major components that were originally invented and developed by its team: an advanced contact detection method, which allows for the first time large simulations with wide size distributions; curved (non-triangulated) walls; and multicomponent, spatial and temporal coarse-graining, a novel way to extract continuum fields from discrete particle systems. We illustrate these tools and a selection of other MercuryDPM features via various applications, including size-driven segregation down inclined planes, rotating drums, and dosing silos. Program summary: Program Title: MercuryDPM Program Files doi: http://dx.doi.org/10.17632/n7jmdrdc52.1 Licensing provisions: BSD 3-Clause Programming language: C++, Fortran Supplementary material: http://mercurydpm.org Nature of problem: Simulation of granular materials, i.e. conglomerations of discrete, macroscopic particles. The interaction between individual grains is characterised by a loss of energy, making the behaviour of granular materials distinct from atomistic materials, i.e. solids, liquids and gases. Solution method: MercuryDPM (Thornton et al., 2013, 2019; Weinhart et al., 2016, 2017, 2019) is an implementation of the Discrete Particle Method (DPM), also known as the Discrete Element Method (DEM) (Cundall and Strack, 1979). It simulates the motion of individual particles by applying forces and torques that stem either from external forces (gravity, magnetic fields, etc.) or from particle-pair and particle–wall interactions (typically elastic, plastic, dissipative, frictional, and adhesive contact forces). DPM simulations have been successfully used to understand the many unique granular phenomena – sudden phase transitions, jamming, force localisation, etc. – that cannot be explained without considering the granular microstructure. Unusual features: MercuryDPM was designed ab initio with the aim of allowing the simulation of realistic geometries and materials found in industrial and geotechnical applications. It thus contains several bespoke features invented by the MercuryDPM team: (i) a neighbourhood detection algorithm (Krijgsman et al., 2014) that can efficiently simulate highly polydisperse packings, which are common in industry; (ii) curved walls (Weinhart et al., 2016) making it possible to model real industrial geometries exactly, without triangulation errors; and (iii) MercuryCG (Weinhart et al., 2012, 2013, 2016; Tunuguntla et al., 2016), a state-of-the-art analysis tool that extracts local continuum fields, providing accurate analytical/rheological information often not available from experiments or pilot plants. It further contains a large range of contact models to simulate complex interactions such as elasto-plastic deformation (Luding, 2008), sintering (Fuchs et al., 2017), melting (Weinhart et al., 2019), breaking, wet and dry cohesion (Roy et al., 2016, 2017), and liquid migration (Roy et al., 2018), all of which have important industrial applications.

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This paper aims to understand the effect of different particle/contact properties like friction, softness and cohesion on the compression/dilation of sheared granular materials. We focus on the local volume fraction in steady state of various non-cohesive, dry cohesive and moderate to strong wet cohesive, frictionless-to-frictional soft granular materials. The results from (1) an inhomogeneous, slowly sheared split-bottom ring shear cell and (2) a homogeneous, stress-controlled simple shear box with periodic boundaries are compared. The steady state volume fractions agree between the two geometries for a wide range of particle properties. While increasing inter-particle friction systematically leads to decreasing volume fractions, the inter-particle cohesion causes two opposing effects. With increasing strength of cohesion, we report an enhancement of the effect of contact friction i.e. even smaller volume fraction. However, for soft granular materials, strong cohesion causes an increase in volume fraction due to significant attractive forces causing larger deformations, not visible for stiff particles. This behaviour is condensed into a particle friction—Bond number phase diagram, which can be used to predict non-monotonic relative sample dilation/compression.

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We focus on the main new developments underway in MercuryDPM. New features include deformable clusters (agglomerates), experimental coarse-graining, melting particles, particle-solid interactions, multi-resolution particle-fluid coupling, pressurecontrolled Lees-Edwards boundaries, better hybrid openMP-MPI parallelisation, and more advanced STL/STEP readers for reading in industrial geometries. Some of these new features will be demonstrated for industrial relevant examples, such as industrial mixers, selective laser sintering, and a tunnel boring machine.@en

MercuryDPM is a particle-simulation software developed open-source by a global network of researchers. It was designed ab initio to simulate realistic geometries and materials, thus it contains several unique features not found in any other particle simulation software. These features have been discussed in a companion paper published in the DEM7 conference proceedings; here we present several challenging setups implemented in MercuryDPM . Via these setups, we demonstrate the unique capability of the code to simulate and analyse highly complex geotechnical and industrial applications. The setups implemented include complex geometries such as (i) a screw conveyor, (ii) steady-state inflow conditions for chute flows, (iii) a confined conveyor belt to simulate a steady-state breaking wave, and (iii) a quasi-2D cylindrical slice to efficiently study shear flows. MercuryDPM is also parallel, which we showcase via a multi-million particle simulations of a rotating drum. We further demonstrate how to simulate complex particle interactions, including: (i) deformable, charged clay particles; and (ii) liquid bridges and liquid migration in wet particulates, (iii) non-spherical particles implemented via superquadrics. Finally, we show how to analyse and complex systems using the unique micro-macro mapping (coarse-graining) tool MercuryCG.

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