From the granular Leidenfrost state to buoyancy-driven convection

Grains inside a vertically vibrated box undergo a transition from a density-inverted and horizontally homogeneous state, referred to as the granular Leidenfrost state, to a buoyancy-driven convective state. We perform a simulational study of the precursors of such a transition and quantify their dynamics as the bed of grains is progressively fluidized. The transition is preceded by transient convective states, which increase their correlation time as the transition point is approached. Increasingly correlated convective flows lead to density fluctuations, as quantified by the structure factor, that also shows critical behavior near the transition point. The amplitude of the modulations in the vertical velocity field are seen to be best described by a quintic supercritical amplitude equation with an additive noise term. The validity of such an amplitude equation, and previously observed collective semiperiodic oscillations of the bed of grains, suggests a new interpretation of the transition analogous to a coupled chain of vertically vibrated damped oscillators. Increasing the size of the container shows metastability of convective states, as well as an overall invariant critical behavior close to the transition

Discrete and continuum descriptions of shaken granular matter

The subject of this thesis is the dynamics of granular materials. Granular matter is defined as collections of macroscopic, dissipative particles. The size of the individual particles (grains) must be large enough so that thermal fluctuations may be ignored. The loss of kinetic energy at every grain-grain collision implies the need of an external energy source to keep grains in movement. This thesis centres on a specific energy injection method: vibrated systems, where the grains container is shaken such that particles gain energy through collisions with the walls. As farfrom-equilibrium dissipative systems, vibrated granular matter presents many distinct out-of-equilibrium stable states and complex transitions between them. In this thesis both particle simulations and different continuum models are used to investigate further the relation between discrete and continuum descriptions of particle systems, a subject of fundamental scientific interest. A collective, semi-periodic movement of the grains inside vertically vibrated containers is for the first time identified and characterized. A simulational study of these oscillations is presented in Chapter 2, and Chapter 3 mainly describes an experimental observation of it. The oscillations take place in density-inverted states, such as the granular Leidenfrost effect, where grains separate in a high temperature region near the moving bottom wall and a dense region on top. The quasiperiodic movement is usually orders of magnitude slower than the energy injection shaking frequency, thus they are named low-frequency oscillations (LFOs). Furthermore, from the equations of mass and momentum conservation in continuum media an expression for the typical natural oscillation frequency is derived, in good agreement with both simulations and experiments in the high energy injection limit. Increasing the energy input and system size takes the system from the granular Leidenfrost state to a buoyancy-driven convective state. Chapter 4 presents an indepth study of this transition, revealing the existence of fluctuating convective flows far before the transition, as also suggesting a reinterpretation of the dynamics that includes the influence of LFOs. The characteristic length and time-scales of precursory fluctuations are measured, and the amplitude of the critical mode is observed to be consistent with a quintic supercritical amplitude equation. The last two chapters of this thesis study the granular Leidenfrost to convection transition using granular hydrodynamics. Chapter 5 deals directly with the relation of discrete and continuum descriptions of granular systems. A methodology is proposed to quantify the finite-number effects on fluctuations, involving scalings that leave the granular hydrodynamic equations invariant while varying the total number of particles. This method allows us to conclude that LFOs are a finite-number, discretization phenomena, although the mode of oscillation is seen to be a macroscopically determined quantity. In Chapter 6 the granular hydrodynamic equations are numerically solved, and the solutions compared with particle simulations. Deviations of the continuum model due to finite-size and higher order effects are discussed. Finally, it is observed that to first order the transition can be understood as a Rayleigh-Bernard instability described by Navier-Stokes-like equations in the Boussinesq approximation

Characterization of the energy bursts in vibrated shallow granular systems

We study the recently reported energy bursts that take place in a granular system confined to a vertically vibrated shallow box containing two types of grains of equal size but different mass (Rivas in Phys Rev Lett 106:088001–1–088001–4, 2011). In a quasi one dimensional configuration, it is possible to characterize the propagating fronts. The rapid expansion and the subsequent compression of the energy bursts take place at roughly constant velocities. The expansion velocity is 40 times larger than the compression velocity. Starting from an initially segregated configuration it is possible to determine the instants at which the energy bursts begin and the mechanisms that trigger them. Two mechanisms are identified: an oblique collision of a heavy grain with a light one in contact with one of the horizontal walls and a slow destabilization produced by light grains that are surrounded by heavy ones

From soft and hard particle simulations to continuum theory for granular flows

One challenge of today’s research is the realistic simulation of disordered many particle systems in static and dynamic/flow situations. Examples are particulate and granular materials like sand, powders, ceramics or composites, with applications in particle-technology and geo-technical/physical systems. The inhomogeneous microstructure of such materials makes it very difficult to model them with continuum methods, which typically assume homogeneity on the microscale and scale separation between the constituents and the macroscopic fields. As an alternative, discrete particle methods can be applied, since they intrinsically take the micro-structure into account. The ultimate challenge is to bridge the gap between both approaches by using particlesimulations to obtain appropriate constitutive relations for continuum theories, and work with those on the macro-scale. Here, soft and hard particle simulation methods are introduced as well as the micro-macro transition to obtain the continuum fields from the particle data. Two application examples discussed in detail concern the flow of particle down an incline, as relevant for geo-flows, as well as a vibrated granular system as relevant for highly agitated transport or conveying processes