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

United States

Whereas the original Boltzmann&#39;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&#39;&#39; transient regime appears for nearly elastic collisions only.

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.

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.

poster

In this work, we will use SedFOAM (sedFoam project, copyright © Cyrille Bonamy and contributors, 2015–2020; https://sedfoam.github.io) and FLOW-3D® (Version 12.0; 2019; https://www.flow3d.com; Flow Science, Inc.) to simulate a case scenario of a hydro-sedimentary canal proposed by Martino et al. in 2019. Benchmarking will be done based on the experimental study of Martino et al. (2019) on the development of a scour and mound formation due to a water jet in a confined canal. For a certain flow rate, a digging and refilling cycle of the sediments inside the scour is observed. The objective of this work is to be able to reproduce numerically the same cycle of digging and refilling and to be able to conclude the phenomena behind this type of sediment erosion cycle by comparing the experimental data with the numerical results.


Modelling of scour formation using SedFoam, continuum approach

We revisit the Critical State (CS) in a dynamic perspective at a mesoscopic scale to enrich the classical view of the critical state as a steady state. The dynamics of mesostructures has been characterized by recording generating and vanishing processes in discrete element simulations. Our results suggest that mesostructures have a short but regular lifespan at the critical state along a biaxial compression loading path.

Dynamic view of critical state regime in granular materials: a mesoscale perspective

We first phrase a boundary-value problem for a dense, steady, fully-developed, gravitational flow of identical inelastic spheres over in inclined bumpy base in the absence of sidewalls. We then obtain approximate analytical solutions for the profiles of the solid volume fraction, the strength of the velocity fluctuations, and the mean velocity of the flow. We compare these with those obtained in numerical solutions of the exact equations.

Analytical solutions for dense, inclined, granular flow over a rigid, bumpy base

We investigate numerically high speed granular flows down an incline and focus our attention on the influence of the restitution coefficient e of binary collisions on the nature of the flow regimes. We show in particular that e plays a major role in rapid flows. Decreasing e leads in general to denser flows but also quicker flows. The increase of the mean flow velocity with decreasing e is explained as the result of the clustering instability which produces a dense and cold core moving very fast as a plug.

Effect of dissipation in rapid-gravitational granular flows

Granular assemblies can experience complex failure patterns along a given loading path, with adistribution of ephemeral inertial events marked by local outbursts in kinetic energy. However, investigatingsuch mechanisms appears to be necessary to understand how a certain failure mode develops in a granularmaterial. Using a discrete element method, this study highlights several microstructure reorganizationsbefore the specimen reaches a proper failure state. Meso structures have proven to be efficient to understand the elementary mechanisms responsible for these outbursts in kinetic energy. Strain–like and stress-like quantities are thus defined at a mesoscale and they are used to characterize the nucleation and propagation of these local microstructural events.

Mesoscale inertial transition in granular materials

We have developed and employed a 3D particle stress tensor and contact force inference technique that employs synchrotron X-ray tomography and di↵raction with an optimization algorithm. We have used this technique to study stress and force heterogeneity, particle fracture mechanics, contact-level energy dissipation, and the origin of wave phenomena in 3D granular media for the past five years. Here, we review the technique, describe experimental and numerical sources of uncertainty, and use experimental data and discrete element method simulations to study the method’s accuracy. We find that inferred forces in the strong force network of a 3D granular material are accurately determined even in the presence of noisy stress measurements.

Stress and force measurement uncertainties in 3D granular materials

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.


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

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