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Vega Reyes F, Rodríguez-Rivas Á, González-Saavedra JF, López-Castaño MA. Diffusion and Velocity Correlations of the Phase Transitions in a System of Macroscopic Rolling Spheres. ENTROPY (BASEL, SWITZERLAND) 2022; 24:1684. [PMID: 36421539 PMCID: PMC9689610 DOI: 10.3390/e24111684] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/20/2022] [Revised: 10/31/2022] [Accepted: 11/11/2022] [Indexed: 06/16/2023]
Abstract
We study an air-fluidized granular monolayer composed of plastic spheres which roll on a metallic grid. The air current is adjusted so that the spheres never lose contact with the grid and so that the dynamics may be regarded as pseudo two dimensional (or two dimensional, if the effects of the sphere rolling are not taken into account). We find two surprising continuous transitions, both of them displaying two coexisting phases. Moreover, in all the cases, we found the coexisting phases display a strong energy non-equipartition. In the first transition, at a weak fluidization, a glass phase coexists with a disordered fluid-like phase. In the second transition, a hexagonal crystal coexists with the fluid phase. We analyze, for these two-phase systems, the specific diffusive properties of each phase, as well as the velocity correlations. Surprisingly, we find a glass phase at a very low packing fraction and for a wide range of granular temperatures. Both phases are also characterized by strong anticorrelated velocities upon a collision. Thus, the dynamics observed for this quasi two-dimensional system unveil phase transitions with peculiar properties, very different from the predicted behavior in well-know theories for their equilibrium counterparts.
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Affiliation(s)
- Francisco Vega Reyes
- Departamento de Física, Universidad de Extremadura, 06071 Badajoz, Spain
- Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, 06071 Badajoz, Spain
| | - Álvaro Rodríguez-Rivas
- Department of Physical, Chemical and Natural Systems, Pablo de Olavide University, 41013 Sevilla, Spain
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Xiao H, Liu AJ, Durian DJ. Probing Gardner Physics in an Active Quasithermal Pressure-Controlled Granular System of Noncircular Particles. PHYSICAL REVIEW LETTERS 2022; 128:248001. [PMID: 35776474 DOI: 10.1103/physrevlett.128.248001] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/06/2021] [Revised: 03/22/2022] [Accepted: 05/24/2022] [Indexed: 06/15/2023]
Abstract
To search for experimental signals of the Gardner crossover, an active quasithermal granular glass is constructed using a monolayer of air-fluidized star-shaped particles. The pressure of the system is controlled by adjusting the tension exerted on an enclosing boundary. Velocity distributions of the internal particles and the scaling of the pressure, density, effective temperature, and relaxation time are examined, demonstrating that the system has key features of a thermal system. Using a pressure-based quenching protocol that brings the system into deeper glassy states, signals of the Gardner crossover are detected via cage size and separation order parameters for both particle positions and orientations, offering experimental evidence of Gardner physics for a system of anisotropic quasithermal particles in a low spatial dimension.
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Affiliation(s)
- Hongyi Xiao
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia 19104, Pennsylvania, USA
| | - Andrea J Liu
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia 19104, Pennsylvania, USA
| | - Douglas J Durian
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia 19104, Pennsylvania, USA
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Escobar A, Donado F, Moctezuma RE, Weeks ER. Direct observation of crystal nucleation and growth in a quasi-two-dimensional nonvibrating granular system. Phys Rev E 2021; 104:044904. [PMID: 34781520 DOI: 10.1103/physreve.104.044904] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2021] [Accepted: 09/28/2021] [Indexed: 11/07/2022]
Abstract
We study a quasi-two-dimensional macroscopic system of magnetic spherical particles settled on a shallow concave dish under a temporally oscillating magnetic field. The system reaches a stationary state where the energy losses from collisions and friction with the concave dish surface are compensated by the continuous energy input coming from the oscillating magnetic field. Random particle motions show some similarities with the motions of atoms and molecules in a glass or a crystal-forming fluid. Because of the curvature of the surface, particles experience an additional force toward the center of the concave dish. When decreasing the magnetic field, the effective temperature is decreased and diffusive particle motion slows. For slow cooling rates we observe crystallization, where the particles organize into a hexagonal lattice. We study the birth of the crystalline nucleus and the subsequent growth of the crystal. Our observations support nonclassical theories of crystal formation. Initially a dense amorphous aggregate of particles forms, and then in a second stage this aggregate rearranges internally to form the crystalline nucleus. As the aggregate grows, the crystal grows in its interior. After a certain size, all the aggregated particles are part of the crystal and after that crystal growth follows the classical theory for crystal growth.
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Affiliation(s)
- A Escobar
- Instituto de Ciencias Básicas e Ingeniería de la Universidad Autónoma del Estado de Hidalgo-AAMF, Pachuca 42184, Pachuca, México
| | - F Donado
- Instituto de Ciencias Básicas e Ingeniería de la Universidad Autónoma del Estado de Hidalgo-AAMF, Pachuca 42184, Pachuca, México
| | - R E Moctezuma
- CONACYT-Instituto de Física "Manuel Sandoval Vallarta," Universidad Autónoma de San Luis Potosí, Alvaro Obregón 64, 78000 San Luis Potosí, San Luis Potosí, México
| | - Eric R Weeks
- Physics Department, Emory University, Atlanta, Georgia 30322, USA
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Rinkinen O, Viitanen L, Mac Intyre JR, Koivisto J, Puisto A, Alava M. Vibration controlled foam yielding. SOFT MATTER 2020; 16:9028-9034. [PMID: 32842140 DOI: 10.1039/d0sm00439a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
In rheological terms, foams are time independent yield stress fluids, displaying properties of both solid and liquid materials. Here we measure the propagation of a 2D dry foam in a radially symmetric Hele-Shaw cell forcing local yielding. The yield rate is manipulated by mechanical vibration with frequencies from 0 to 150 Hz. The flow speed is then extracted from the video stream and analyzed using digital image correlation software. The data are modeled analytically by a Guzman-Arrhenius type of energy landscape where the local yielding of foam correlates with the number of oscillations, i.e. attempts to cross the energy barrier. The model is confirmed in an auxiliary experiment where the vibrated foam stays in its flowing state at the same small driving pressures, where the flow of the unvibrated foam ceases. We conclude that the yield stress behaviour of foams under an external perturbation can be summarized using a simple energy landscape model. The vibration affects the films causing the stress to occasionally and locally exceed the yield threshold. This, thus, prevents the foam from jamming as in a static configuration even when the global driving is below the yield point of the foam.
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Affiliation(s)
- Oona Rinkinen
- Aalto University, School of Science, Department of Applied Physics, P.O. Box 11100, 00076 Aalto, Finland.
| | - Leevi Viitanen
- Aalto University, School of Science, Department of Applied Physics, P.O. Box 11100, 00076 Aalto, Finland.
| | - Jonatan R Mac Intyre
- Aalto University, School of Science, Department of Applied Physics, P.O. Box 11100, 00076 Aalto, Finland.
| | - Juha Koivisto
- Aalto University, School of Science, Department of Applied Physics, P.O. Box 11100, 00076 Aalto, Finland.
| | - Antti Puisto
- Aalto University, School of Science, Department of Applied Physics, P.O. Box 11100, 00076 Aalto, Finland.
| | - Mikko Alava
- Aalto University, School of Science, Department of Applied Physics, P.O. Box 11100, 00076 Aalto, Finland.
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Sakaï N, Moulinet S, Lechenault F, Adda-Bedia M. Experimental Evidence of Thermal-Like Behavior in Dense Granular Suspensions. PHYSICAL REVIEW LETTERS 2019; 122:168001. [PMID: 31075033 DOI: 10.1103/physrevlett.122.168001] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/04/2018] [Indexed: 06/09/2023]
Abstract
We experimentally investigate the statistical behavior of a model two-dimensional granular system undergoing stationary sedimentation. Buoyant cylindrical particles are rotated in a liquid-filled drum, thus confined in a harmonic centripetal potential with tunable curvature, which competes with gravity to produce various stationary states: though heterogeneous, the packing fraction of the system can be tuned from fully dispersed to crystallized as the rotation rate is increased. We show that this dynamical system is in mechanical equilibrium in the confining potential and exhibits a thermal-like behavior, where the granular pressure and the packing fraction are related through an equation of state. We obtain an expression of the equation of state allowing us to probe the nature of the hydrodynamic interactions between the particles. This description is valid in the whole range of the physical parameters we investigated and reveals a buoyant energy scale that we interpret as an effective temperature. We finally discuss the behavior of our system at high packing fractions and the relevance of the equation of state to the liquid-solid phase transition.
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Affiliation(s)
- Nariaki Sakaï
- Laboratoire de Physique de l'Ecole Normale Supérieure, PSL Research University, Sorbonne University, CNRS, F-75231 Paris, France
| | - Sébastien Moulinet
- Laboratoire de Physique de l'Ecole Normale Supérieure, PSL Research University, Sorbonne University, CNRS, F-75231 Paris, France
| | - Frédéric Lechenault
- Laboratoire de Physique de l'Ecole Normale Supérieure, PSL Research University, Sorbonne University, CNRS, F-75231 Paris, France
| | - Mokhtar Adda-Bedia
- Université de Lyon, Ecole Normale Supérieure de Lyon, Université Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France
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Farhadi S, Machaca S, Aird J, Torres Maldonado BO, Davis S, Arratia PE, Durian DJ. Dynamics and thermodynamics of air-driven active spinners. SOFT MATTER 2018; 14:5588-5594. [PMID: 29882572 DOI: 10.1039/c8sm00403j] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We report on the collective behavior of active particles in which energy is continuously supplied to rotational degrees of freedom. The active spinners are 3D-printed disks, 1 cm in diameter, that have an embedded fan-like structure, such that a sub-levitating up-flow of air forces them to spin. Single spinners exhibit Brownian motion with a narrow Gaussian velocity distribution function, P(v), for translational motion. We study the evolution of P(v) as the packing fraction and the average single particle spin speeds are varied. The interparticle hydrodynamic interaction is negligible, and the dynamics is dominated by hyperelastic collisions and dissipative forces. As expected for nonequilibrium systems, P(v) for a collection of many spinners deviates from Gaussian behavior. However, unlike translationally active systems, phase separation is not observed, and the system remains spatially homogeneous. We then search for a near-equilibrium counterpart for our active spinners by measuring the equation of state. Interestingly, it agrees well with a hard-sphere model, despite the dissipative nature of the single particle dynamics.
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Le Guen L, Piton M, Hénaut Q, Huchet F, Richard P. Heat convection and radiation in flighted rotary kilns: A minimal model. CAN J CHEM ENG 2016. [DOI: 10.1002/cjce.22659] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Affiliation(s)
- Laurédan Le Guen
- LUNAM Université, GPEM, IFSTTAR, site de Nantes, Route de Bouaye; CS4 44344 Bouguenais Cedex France
| | - Maxime Piton
- LUNAM Université, GPEM, IFSTTAR, site de Nantes, Route de Bouaye; CS4 44344 Bouguenais Cedex France
| | - Quentin Hénaut
- LUNAM Université, GPEM, IFSTTAR, site de Nantes, Route de Bouaye; CS4 44344 Bouguenais Cedex France
| | - Florian Huchet
- LUNAM Université, GPEM, IFSTTAR, site de Nantes, Route de Bouaye; CS4 44344 Bouguenais Cedex France
| | - Patrick Richard
- LUNAM Université, GPEM, IFSTTAR, site de Nantes, Route de Bouaye; CS4 44344 Bouguenais Cedex France
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Lieou CKC, Langer JS. Nonequilibrium thermodynamics in sheared hard-sphere materials. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:061308. [PMID: 23005087 DOI: 10.1103/physreve.85.061308] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/16/2012] [Indexed: 06/01/2023]
Abstract
We combine the shear-transformation-zone (STZ) theory of amorphous plasticity with Edwards' statistical theory of granular materials to describe shear flow in a disordered system of thermalized hard spheres. The equations of motion for this system are developed within a statistical thermodynamic framework analogous to that which has been used in the analysis of molecular glasses. For hard spheres, the system volume V replaces the internal energy U as a function of entropy S in conventional statistical mechanics. In place of the effective temperature, the compactivity X=∂V/∂S characterizes the internal state of disorder. We derive the STZ equations of motion for a granular material accordingly, and predict the strain rate as a function of the ratio of the shear stress to the pressure for different values of a dimensionless, temperature-like variable near a jamming transition. We use a simplified version of our theory to interpret numerical simulations by Haxton, Schmiedeberg, and Liu, and in this way are able to obtain useful insights about internal rate factors and relations between jamming and glass transitions.
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Affiliation(s)
- Charles K C Lieou
- Department of Physics, University of California, Santa Barbara, California 93106, USA
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