Granular flow through vertical slots: analysis of a general formula

United States

Currently, very little is known about reliable phenomelogical correlations to estimate the gravity-driven mass flow rate, of dry non-cohesive granular material, outflowing from thin thickness slots in vertical sidewalls of rectangular silos. Here, we validate a simple and general formula that fits pretty well data published elsewhere, including the cases of vertically and horizontally elongated slots.

Powders &amp; Grains 2021

[EPJ Web of Conferences, Volume 249 (2021)](https://www.epj-conferences.org/articles/epjconf/abs/2021/03/contents/contents.html)

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Powders & Grains 2021

Powders & Grains 2021 will be held in Buenos Aires (Argentina, VIRTUAL) July 5, 13, 21, 29 and Aug 6, 2021. The aim of the conference is to give an up-to-date picture of the broad research field of granular media, powders and grains. Contributions from experts around the world will focus on research topics that cover a wide range of open problems in the field.

poster

A Contact Dynamics algorithm is applied to simulate the failure of 2-dimensional granular steps. Focussing on one single value for both the adhesive force threshold and the contact friction, we track the signature of the failure in the cumulative displacement of the grains. The introduction of a displacement threshold allows for the identification of the onset of a rapid failure and the formation of the corresponding shear band. The latter gives access to an estimation of the failure orientation. 
The robustness of the measure thus performed for one single run is assessed by carrying out a series of 10 additional simulations, showing a fairly reproducible behaviour.

Capturing the failure of a cohesive granular step

The frictional behaviour of a series of numerical 2D granular mass flows down a model topography is analysed. Effective friction coefficients estimated from final deposits are compared with data from documented natural geophysical flows, and show a consistent behaviour as far as run-out distances are concerned. The latter is used to estimate effective friction coefficients which capture well the frictional behaviour derived from the computation of micro-mechanical stress tensors near the gravity centre. Distinguishing between the different parts of the mass while spreading, we show that the downstream part of the flow exhibits a much larger friction than the core and the tail. A dependence between friction and flow volume is however observed 
in each region.


Mobilisation of friction in unstationary flows down a model topography

The outflow characteristics of hard grains from containers with narrow basal openings have been extensively studied. Recently, it was shown that soft, low-frictional grains can behave qualitatively different from rigid grains. We compare experimentally the discharge of monodisperse hard spheres, soft spheres and mixtures of both from a quasi-twodimensional (2D) silo. The experiments
demonstrate their remarkable differences in discharge behavior and clogging statistics. The flow field of a 50/50 mixture is already very similar to a pure hard bead system, while its clogging behaviour is fill height dependent, like in a pure low friction soft particle system.

Discharge of soft and hard grains and their mixtures from 2D silos

The effect of boundary roughness on dense granular flows

Passages of people or cattle through narrow entrances or exits occur in manifold situations. They are difficult to study experimentally, because one has to carefully separate objective, physical parameters from subjective, individual motivations, manners and temperament. Mechanically excited physical model systems can help to discriminate some of these classes of parameters. We characterize active and passive particles of equal shape and mass on a vibrating plate and study their bottleneck passage dynamics. They show fundamentally different scaling behavior.

Mechanically driven active and passive grains as models for egress dynamics

Granular media consist of a large number of discrete particles interacting mostly through contact forces that, being dissipative, jeopardizes a classical statistical equilibrium approach based on energy. Instead, two independent equilibrium statistical descriptions have been proposed: the Volume Ensemble and the Force Network Ensemble. Hereby, we propose a procedure to join them into a single description, using Discrete Element simulations of a granular medium of monodisperse spheres in the limit state of isotropic compression as testing ground. By classifying grains according to the number of faces of the Voronoï cells around them, our analysis establishes an empirical relationship between that number of faces and the number of contacts on the grain. In addition, a linear relationship between the number of faces of each Voronoï cell and the number of elementary cells proposed by T. Aste and T. Di Matteo in 2007 is found. From those two relations, an expression for the total entropy (volumes plus forces) is written in terms of the contact number, an entropy that, when maximized, gives an equation of state connecting angoricity (the temperature-like variable for the force network ensemble) and compactivity (the temperature-like variable for the volume ensemble). So, the procedure establishes a microscopic connection between geometry and mechanics and, constitutes a further step towards building a complete statistical theory for granular media in equilibrium.

A procedure to join the force and volume ensemble statistical descriptions of granular media

Magnetic forces are used to heat up thousands of spherical particles under low-gravity. This longrange external excitation, combined with the induced particle-particle interactions, results in a homogeneousspatial distribution of the particles. Comparisons with predictions of kinetic theories can hence be carried out.Haff’s cooling law is verified qualitatively, while the measured cooling time scale is quantitatively differentfrom the prediction. The high velocity tail of the velocity distribution during homogeneous cooling state (HCS)is measured, while the expected cluster formation after HCS can not be verified by our experiment.

Magnetically heated granular gas in a low-gravity environment

Inthepresenceofviscousandcohesiveinteractionsbetweenparticles,agranularflowisgoverned by several characteristic time and stress scales that determine its rheological properties (shear stress, packing fraction, e↵ective viscosities). In this paper, we revisit and extend the scaling arguments used previously for dry cohesionless granular flows and suspensions. We show that the rheology can be in principle described by a single dimensionless control parameter that includes all characteristic times. We also briefly present simulation results for 2D sheared suspensions and 3D wet granular flows where the e↵ective friction coecient and packing fraction are consistently described as functions of this unique control parameter.

Time scales and rheology of visco-cohesive granular flows

A spiral jet mill was simulated using Discrete Element Method modelling and Computational
Fluid Dynamics. The particle behavior and fluid motion were analysed as a function of hold-up and
grinding pressure. The particle collision energy was predicted to be prevalent along the bed surface and in front
of the grinding jets, as shown through the collision data recorded. The bed itself affects the fluid flow field,
as momentum is transferred to the particles. Increasing the grinding pressure does not result in a proportional
increase in the kinetic energy of the particle system, as the high-pressure jets begin to penetrate the bed with
greater ease. The particle bed moves as ‘plug-flow’, with the layers of the bed closest to the chamber wall.

Analysis of hold-up and grinding pressure in a spiral jet mill using CFD-DEM

To prevent texture defects in powder-based processes, the sintering time needs to be adjusted such that a certain amount of coalescence is achieved. However, predicting the required sintering time is extremely challenging to assess in materials such as polymers because the kinetics exhibit both elastic and viscous characteristics when undergoing deformation. The present work introduces a computational approach to model the viscoelastic effect in the sintering of particles. The model contains three stages, three different mechanisms driven by adhesive inter-surface forces and surface tension, which describes the non-linear sintering behaviour. Experimental data from the binary coalescence of Polystyrene (PS), Polyamide (PA) 12 and PEEK 450PF particles are employed to calibrate the contact model, as implemented in MercuryDPM, an open-source software package. Using machine learning-based Bayesian calibration, good agreement is obtained between the experimental data and the numerical results. The findings will be used in future studies to predict densification rates in powder-based processes.

Granular flow through vertical slots: analysis of a general formula

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