Particle Dynamics at the Onset of the Granular Gas-Liquid Transition

Non-equilibrium coexistence between a fluid and a hotter or colder crystal of granular hard disks

Non-equilibrium phase coexistence is commonly observed in both biological and artificial systems, yet understanding it remains a significant challenge. Unlike equilibrium systems, where free energy provides a unifying framework, the absence of such a quantity in non-equilibrium settings complicates their theoretical understanding. Granular materials, driven out of equilibrium by energy dissipation during collisions, serve as an ideal platform to investigate these systems, offering insights into the parallels and distinctions between equilibrium and non-equilibrium phase behavior. For example, the coexisting dense phase is typically colder than the dilute phase, a result usually attributed to greater dissipation in denser regions. In this article, we demonstrate that this is not always the case. Using a simple numerical granular model, we show that a hot solid and a cold liquid can coexist in granular systems. This counterintuitive phenomenon arises because the collision frequency can be lower in the solid phase than in the liquid phase, consistent with equilibrium results for hard-disk systems. We further demonstrate that kinetic theory can be extended to accurately predict phase temperatures even at very high packing fractions, including within the solid phase. Our results highlight the importance of collisional dynamics and energy exchange in determining phase behavior in granular materials, offering new insights into non-equilibrium phase coexistence and the complex physics underlying granular systems.

Trajectories of a magnetic sphere in a shaken three-dimensional granular bed under low gravity

This present investigation employs an advanced magnetic particle tracking method to trace the trajectories of an intruder within a vibration-driven granular medium under artificial low-gravity conditions. The experiments are carried out within the centrifuge of the Chinese Space Station, encompassing six distinct low-gravity environments. Trajectories under various vibration modes are captured and analysed for each gravity level. This paper offers an exhaustive account of data collection and algorithms used for data processing, ensuring the dependability and precision of the datasets obtained. Additionally, we make the raw magnetic field data, processing scripts, and visualization tools accessible to the public. This research contributes a comprehensive dataset that is instrumental in exploring the mechanisms of granular segregation under low gravity and aids in the verification of novel physical models for understanding intruder dynamics in granular systems under such conditions.

Onsager variational principle for granular fluids

Granular fluids, as defined by a collection of moving solid particles, is a paradigm of a dissipative system out of equilibrium. Inelastic collisions between particles is the source of dissipation, and is the origin of a transition from a gas to a liquidlike state. This transition can be triggered by an increase of the solid fraction. Moreover, in compartmentalized systems, this condensation is driving the entire granular fluid into a Maxwell demon phenomenon, localizing most of the grains into a specific compartment. Classical approaches fail to capture these phenomena, thus motivating many experimental and numerical works. Herein, we demonstrate that the Onsager variational principle is able to predict accurately the coexistence of gas-liquid states in granular systems, opening ways to model other phenomena observed in such dissipative systems like segregation or the jamming transition.

Platonic solids bouncing on a vibrating plate

The energy transfer between bouncing particles and rigid boundaries during impacts is crucially influenced not only by restitution coefficients of the material but also by particle shapes. This is particularly important when such particles are mechanically agitated with vibrating plates. Inertial measurement units are able to measure all acceleration and rotational velocity components of an object and store these data for subsequent analysis. We employ them to measure the dynamics of cubes and icosahedra on vibrating plates to study the efficiency of energy transfer into the individual degrees of freedom (DOFs) of the excited object. The rotational DOFs turn out to be much less excited than the vertical translational motion. Most remarkably, there is only little difference between the two Platonic solids in both the absolute energies and the energy partition ratios.

Enskog kinetic theory of binary granular suspensions: Heat flux and stability analysis of the homogeneous steady state

The Enskog kinetic theory of multicomponent granular suspensions employed previously [Gómez González, Khalil, and Garzó, Phys. Rev. E 101, 012904 (2020)2470-004510.1103/PhysRevE.101.012904] is considered further to determine the four transport coefficients associated with the heat flux. These transport coefficients are obtained by solving the Enskog equation by means of the application of the Chapman-Enskog method around the local version of the homogeneous state. Explicit forms of the heat flux transport coefficients are provided in steady-state conditions by considering the so-called second Sonine approximation to the distribution function of each species. Their quantitative variation on the control parameters of the mixture (masses and diameters, coefficients of restitution, concentration, volume fraction, and the background temperature) is demonstrated and the results show that in general the dependence of the heat flux transport coefficients on inelasticity is clearly different from that found in the absence of the gas phase (dry granular mixtures). As an application of the general results, the stability of the homogeneous steady state is analyzed by solving the linearized Navier-Stokes hydrodynamic equations. The linear stability analysis (which holds for wavelengths long compared with the mean free path) shows that the transversal and longitudinal modes are always stable with respect to long-enough wavelength excitations. This conclusion agrees with previous results derived for monocomponent and (dilute) bidisperse granular suspensions but contrasts with the instabilities found in previous works in dry (no gas phase) granular mixtures.

High-energy velocity tails in uniformly heated granular materials

We experimentally investigate the velocity distributions of quasi-two-dimensional granular materials uniformly heated by an electromagnetic vibrator, where the translational velocity and the rotation of a single particle are Gaussian and independent. We observe the non-Gaussian distributions of particle velocity, with the density-independent high-energy tails characterized by an exponent of β=1.50±0.03 for volume fractions of 0.111≤ϕ≤0.832, covering a wide range of structures and dynamics. Surprisingly, our results are not only in excellent agreement with the prediction of the kinetic theories of granular gas but also hold for an extremely high-volume fraction of ϕ=0.832 where the granular material forms a crystalline solid and the kinetic theory of granular gas fails fantastically. Our experiment suggests that the density-independent high-energy velocity tails of β=1.50 are a characteristic of uniformly heated granular matter.

Geometry-controlled phase transition in vibrated granular media

We report experiments on the dynamics of vibrated particles constrained in a two-dimensional vertical container, motivated by the following question: how to get the most out of a given external vibration to maximize internal disorder (e.g. to blend particles) and agitation (e.g. to absorb vibrations)? Granular media are analogs to classical thermodynamic systems, where the injection of energy can be achieved by shaking them: fluidization arises by tuning either the amplitude or the frequency of the oscillations. Alternatively, we explore what happens when another feature, the container geometry, is modified while keeping constant the energy injection. Our method consists in modifying the container base into a V-shape to break the symmetries of the inner particulate arrangement. The lattice contains a compact hexagonal solid-like crystalline phase coexisting with a loose amorphous fluid-like phase, at any thermal agitation. We show that both the solid-to-fluid volume fraction and the granular temperature depend not only on the external vibration but also on the number of topological defects triggered by the asymmetry of the container. The former relies on the statistics of the energy fluctuations and the latter is consistent with a two-dimensional melting transition described by the KTHNY theory.

Wave spectroscopy in a driven granular material

Driven granular media constitute model systems in out-of-equilibrium statistical physics. By assimilating the motions of granular particles to those of atoms, by analogy, one can obtain macroscopic equivalent of phase transitions. Here, we study fluid-like and crystal-like two-dimensional states in a driven granular material. In our experimental device, a tunable magnetic field induces and controls remote interactions between the granular particles. We use high-speed video recordings to analyse the velocity fluctuations of individual particles in stationary regime. Using statistical averaging, we find that the particles self-organize into collective excitations characterized by dispersion relations in the frequency-wavenumber space. These findings thus reveal that mechanical waves analogous to condensed matter phonons propagate in driven granular media. When the magnetic coupling is weak, the waves are longitudinal, as expected for a fluid-like phase. When the coupling is stronger, both longitudinal and transverse waves propagate, which is typically seen in solid-like phases. We model the dispersion relations using the spatial distribution of particles and their interaction potential. Finally, we infer the elastic parameters of the granular assembly from equivalent sound velocities, thus realizing the spectroscopy of a granular material.