Observing the evaporation transition in vibro-fluidized granular matter

By shaking a sand box the grains on the top start to jump giving the picture of evaporating a sand bulk, and a gaseous transition starts at the surface granular matter (GM) bed. Moreover the mixture of the grains in the whole bed starts to move in a cooperative way which is far away from a Brownian description. In a previous work we have shown that the key element to describe the statistics of this behavior is the exclusion of volume principle, whereby the system obeys a Fermi configurational approach. Even though the experiment involves an archetypal non-equilibrium system, we succeeded in defining a global temperature, as the quantity associated to the Lagrange parameter in a maximum entropic statistical description. In fact in order to close our approach we had to generalize the equipartition theorem for dissipative systems. Therefore we postulated, found and measured a fundamental dissipative parameter, written in terms of pumping and gravitational energies, linking the configurational entropy to the collective response for the expansion of the centre of mass (c.m.) of the granular bed. Here we present a kinetic approach to describe the experimental velocity distribution function (VDF) of this non-Maxwellian gas of macroscopic Fermi-like particles (mFp). The evaporation transition occurs mainly by jumping balls governed by the excluded volume principle. Surprisingly in the whole range of low temperatures that we measured this description reveals a lattice-gas, leading to a packing factor, which is independent of the external parameters. In addition we measure the mean free path, as a function of the driving frequency, and corroborate our prediction from the present kinetic theory.Comment: 6 pages, 4 figures, submitted for publication September 1st, 200

Defining Temperatures of Granular Powders Analogously with Thermodynamics to Understand the Jamming Phenomena

For the purpose of applying laws or principles originated from thermal systems to granular athermal systems, we may need to properly define the critical temperature concept in granular powders. The conventional environmental temperature in thermal systems is too weak to drive movements of particles in granular powders and cannot function as a thermal energy indicator. For maintaining the same functionality as in thermal systems, the temperature in granular powders is defined analogously and uniformly in this article. The newly defined granular temperature is utilized to describe and explain one of the most important phenomena observed in granular powders, the jamming transition, by introducing jamming temperature and jamming volume fraction concepts. The predictions from the equations of the jamming volume fractions for several cases like granular powders under shear or vibration are in line with experimental observations and empirical solutions in powder handlings. The goal of this article is to establish similar concepts in granular powders, allowing granular powders to be described with common laws or principles we are familiar with in thermal systems. Our intention is to build a bridge between thermal systems and granular powders to account for many similarities already found between these two systems.Comment: 34 pages,15 figure

What is the temperature of a granular medium?

In this paper we discuss whether thermodynamical concepts and in particular the notion of temperature could be relevant for the dynamics of granular systems. We briefly review how a temperature-like quantity can be defined and measured in granular media in very different regimes, namely the glassy-like, the liquid-like and the granular gas. The common denominator will be given by the Fluctuation-Dissipation Theorem, whose validity is explored by means of both numerical and experimental techniques. It turns out that, although a definition of a temperature is possible in all cases, its interpretation is far from being obvious. We discuss the possible perspectives both from the theoretical and, more importantly, from the experimental point of view

Microscopic origin of self-similarity in granular blast waves

The self-similar expansion of a blast wave, well-studied in air, has peculiar counterparts in dense and dissipative media such as granular gases. Recent results have shown that, while the traditional Taylor-von Neumann-Sedov (TvNS) derivation is not applicable to such granular blasts, they can nevertheless be well understood via a combination of microscopic and hydrodynamic insights. In this article, we provide a detailed analysis of these methods associating Molecular Dynamics simulations and continuum equations, which successfully predict hydrodynamic profiles, scaling properties and the instability of the self-similar solution. We also present new results for the energy conserving case, including the particle-level analysis of the classic TvNS solution and its breakdown at higher densities.Comment: 47 pages, 9 figures Supplementary Materials: 2 appendices, 3 figure

Wave propagation across interfaces induced by different interaction exponents in ordered and disordered Hertz-like granular chains

We study solitary wave propagation in 1D granular crystals with Hertz-like interaction potentials. We consider interfaces between media with different exponents in the interaction potential. For an interface with increasing interaction potential exponent along the propagation direction we obtain mainly transmission with delayed secondary transmitted and reflected pulses. For interfaces with decreasing interaction potential exponent we observe both significant reflection and transmission of the solitary wave, where the transmitted part of the wave forms a multipulse structure. We also investigate impurities consisting of beads with different interaction exponents compared to the media they are embedded in, and we find that the impurities cause both reflection and transmission, including the formation of multipulse structures, independent of whether the exponent in the impurities is smaller than in the surrounding media. We explain wave propagation effects at interfaces and impurities in terms of quasi-particle collisions. Next we consider wave propagation along Hertz-like granular chains of beads in the presence of disorder and periodicity in the interaction exponents present in the Hertz-like potential, modelling, for instance, inhomogeneity in the contact geometry between beads in the granular chain. We find that solitary waves in media with randomised interaction exponents (which models disorder in the contact geometry) experience exponential decay, where the dependence of the decay rate is similar to the case of randomised bead masses. In the periodic case of chains with interaction exponents alternating between two fixed values, we find qualitatively different propagation properties depending on the choice of the two exponents. In particular, we find regimes with either exponential decay or stable solitary wave propagation with pairwise collective behaviour.Comment: 33 pages, 28 figure

Applying GSH to a Wide Range of Experiments in Granular Media

Granular solid hydrodynamics (GSH) is a continuum-mechanical theory for granular media, the range of which is shown in this paper. Simple, frequently analytic solutions are related to classic observations at different shear rates, including: (i)~static stress distribution, clogging; (ii)~elasto-plastic motion: loading and unloading, approach to the critical state, angle of stability and repose; (iii)~rapid dense flow: the $\mu$-rheology, Bagnold scaling and the stress minimum; (iv)~elastic waves, compaction, wide and narrow shear band. Less conventional experiments have also been considered: shear jamming, creep flow, visco-elastic behavior and nonlocal fluidization. With all these phenomena ordered, related, explained and accounted for, though frequently qualitatively, we believe that GSH may be taken as a unifying framework, providing the appropriate macroscopic vocabulary and mindset that help one coming to terms with the breadth of granular physics.Comment: arXiv admin note: substantial text overlap with arXiv:1207.128

Velocity statistics in excited granular media

We present an experimental study of velocity statistics for a partial layer of inelastic colliding beads driven by a vertically oscillating boundary. Over a wide range of parameters (accelerations 3-8 times the gravitational acceleration), the probability distribution P(v) deviates measurably from a Gaussian for the two horizontal velocity components. It can be described by P(v) ~ exp(-|v/v_c|^1.5), in agreement with a recent theory. The characteristic velocity v_c is proportional to the peak velocity of the boundary. The granular temperature, defined as the mean square particle velocity, varies with particle density and exhibits a maximum at intermediate densities. On the other hand, for free cooling in the absence of excitation, we find an exponential velocity distribution. Finally, we examine the sharing of energy between particles of different mass. The more massive particles are found to have greater kinetic energy.Comment: 27 pages, 13 figures, to appear in Chaos, September 99, revised 3 figures and tex