Granular impacts: how far the Boussinesq model can go?

United States

Stress propagation in granular impacts is a key problem in physics and many other related disciplines, particularly in civil engineering. However, this topic has been poorly addressed in the literature so far, motivating the present study where the pressure distribution was measured at the bottom of a sandy bed, impacted by a rigid sphere. Exploring different bed thicknesses and intruder’s dropping height, we have found that the structure of this distribution is very similar to the Boussinesq model, initially proposed for a static point-force acting over an isotropic-elastic medium. This surprising result opens up many challenging questions that could help validate or refute this model in other scenarios.

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.

technical paper

The macro-scale behavior of granular materials is strongly influenced by grain kinematics. The mobility of the grains in turn is affected by grain morphology which needs to be comprehensively characterized. Initially, morphological descriptors were determined by manual processes which were tedious and cumbersome. But with the help of image processing techniques and computational geometry, this problem can be handled with ease. The long-established descriptors such as sphericity and roundness can be estimated by operating over the grain boundary obtained from 2D images of the particle. The main objective of this study is to quantify these descriptors in a computationally effective way. The roundness quantification in previous studies involves the sequence of processes such as removing the noise, corner identification and fitting circles. This paper details the necessary modifications to the quantification process required to reduce the cost of time for a single particle. Further, the influence of different smoothing techniques and a new corner identification method will be detailed.

Computationally efficient approach to quantify 2D particle morphological descriptors

The experiments involving a slider moving on top of granular media consisting of photoelastic parti- cles in two dimensions have uncovered elaborate dynamics that may vary from continuous motion to crackling, periodic motion, and stick-slip type of behavior. We establish that there is a clear correlation between the slider dynamics and the response of the force network that spontaneously develop in the granular system. This correla- tion is established by application of the persistence homology that allows for formulation of objective measures for quantification of time-dependent force networks. We find that correlation between the slider dynamics and the force network properties is particularly strong in the dynamical regime characterized by well-defined stick-slip type of dynamics.

Correlating the force network evolution and dynamics in slider experiments

The growth dynamics of polyacrylamide hydrogel beads due to liquid absorption under geometric confinement is studied. First, the behavior of individual hydrogel beads is investigated and, subsequently, the growth dynamics is analyzed in the presence of several interacting beads of the same material. In both, individual and collective studies, the magnitude of the geometric confinement is varied, in order to investigate the effect that the stress applied on the particles has on their hydration kinetics.

Swelling of a granular hydrogel medium under confinement: individual and collective dynamic

Particle shape can significantly affect the bubble dynamics of bubbling fluidized beds (BFB). In this paper, findings obtained from simulations using CFD-DEM are summarized to discuss the effect of particle shape on bubble dynamics and bubble properties such as bubble size, shape and velocity at a single orifice and uniform fluidized bed. Particles with aspect ratios at 0.5 (oblate), 1 (spherical) and 2 (prolate) are employed to represent disc-like, spherical and rod-like particles, respectively. Both single jet and uniform fluidized bed simulations demonstrate that the bubble forming/rising regions, bubble coalescence locations, and bubble splitting phenomena are significantly influenced by particle shape. The CFD-DEM results for bubble size and bubble velocity show good agreement with literature correlations.


Effect of particle shape on bubble dynamics in bubbling fluidized bed

Whereas the original Boltzmann's $H$-theorem applies to elastic collisions, its rigorous generalization to the inelastic case is still lacking. Nonetheless, it has been conjectured in the literature that the relative entropy of the velocity distribution function with respect to the homogeneous cooling state (HCS) represents an adequate nonequilibrium entropy-like functional for an isolated freely cooling granular gas. In this work, we present molecular dynamics results reinforcing this conjecture and rejecting the choice of the Maxwellian over the HCS as a reference distribution. These results are qualitatively predicted by a simplified theoretical toy model. Additionally, a Maxwell-demon-like velocity-inversion simulation experiment highlights the microscopic irreversibility of the granular gas dynamics, monitored by the relative entropy, where a short ``anti-kinetic'' transient regime appears for nearly elastic collisions only.

Relative entropy of freely cooling granular gases. A molecular dynamics study

Particle fracture, the formation of small particles as the result of the breakage of large ones, and aggregation, the formation of large particles as the result of the combination of small ones, have important implications in industry (e.g. food processing, pharmaceutical production) and geophysics (e.g., snow avalanches and rock debris flows). Also, the presence of particles of different size that result from fracture and aggregation can induce segregation, resulting in the migration of large and small particles to different regions of the flow. Here, we formulate simple models for fracture and agglomeration and analyze the evolution of measures of the relative concentration of two sizes of spheres due the combined effects of fracture, aggregation, and segregation in dense, dry, granular flows. Particle breakage and combination is influenced by the frequency of collisions, by the local number density of the spheres, and by the particle kinetic energy. Segregation is predicted using a kinetic theory proposed by Larcher & Jenkins (J. Fluid Mech. 782, 405, 2015).

Fracture, aggregation and segregation in dry, granular flows

The implementation of a conveyor belt below the orifice of a granular silo allows to
control the grains discharge velocities. By this way, we were able to separate the
geometrical and kinematic contributions to the clogging process. In particular, the
reduction of grains velocities to the limit leads to a clogging probability increment of
almost two orders of magnitude. Exploring the contribution of both variables (outlet
size and grains velocity) we propose a modification of a previous model to describe
the experimental data using only two parameters: one is related with the geometry of
the problem, and the other with the grains kinematics. Additionally, the expression we
proposed allowed us to demonstrate that the placement of an obstacle above the
orifice prevents clogging via two mechanisms. The first is related with an alteration of
the kinematics in the region of the outlet and the second with an anisotropy in the
distribution of interparticle contacts.


Non-monotonic dependence of avalanche durations on particle velocities in the discharge of a silo

Characterization of soil cohesion is crucial for the understanding of geomechanical phenomena such as erosion, excavation, or sediment transport. Moreover, cohesive granular flows occur in many industrial processes ranging from agriculture to pharmaceutical. In the present study, we experimentally investigated cohesion of artificially bonded granular materials made of spherical glass beads cemented by solid paraffin bridges. By means of laboratory tests designed and carried out for investigation at different scales, we measured the tensile yield strength for solid bonds both at the inter-particle micro-scale and at the meso-scale of a cemented sample.

Multi-scale cohesion force measurements for cemented granular materials

Controlling the powder flow by the surface properties of the particles as well as understanding their flowability under different processing dynamics is amongst the major challenges of the powder industry. Indeed, handling large quantities needs powders with good flowability, adequate compressibility, and few electrostatic charges. We have performed a chemical treatment in order to obtain hydrophobic glass bead and its bulk behavior has been compared with raw glass bead. We characterized flow properties under different processing conditions. Both powders presented similar flow behavior in the free fall measurement, however,
hydrophobic glass bead showed lower flow behavior under flow with a rotating drum. Also, hydrophobic glass bead presented negative and raw glass bead almost zero electrostatic charges.

Hydrophobic and raw glass beads flow behavior under different processing conditions

We perform numerical simulations of a two-dimensional frictional granular system under oscillatory shear confined by constant pressure. We found that the system undergoes dilatancy as the strain increases. We confirmed that compaction also takes place at an intermediate strain amplitude for a small mutual friction coefficient between particles. We also found that compaction depends on the confinement pressure while dilatancy little depends on the pressure.

Granular impacts: how far the Boussinesq model can go?

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Computationally efficient approach to quantify 2D particle morphological descriptors

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Granular impacts: how far the Boussinesq model can go?

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Next from Powders & Grains 2021

Computationally efficient approach to quantify 2D particle morphological descriptors

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Aerodynamic and impact thresholds for cohesive mixture of sand and non-volatile liquid

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CONFERENCES

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RESOURCES

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