In this paper we report measurements of collisional properties of spheres using high-speed video analysis. These results agree with a simple collision operator. We study the size and velocity dependences of the coefficient of restitution in the normal direction. The experimental data are compared with the relevant models of energy dissipation and show the existence of two dissipation regimes. For large impact velocities a plastic deformation model is in good agreement with our measurements, while for smaller velocities a model of viscoelastic dissipation gives qualitative agreement.
Segregation of particulate mixtures is a problem of great consequence in industries involved with the handling and processing of granular materials in which homogeneity is generally required. While there are several factors that may be responsible for segregation in bulk solids, it is well accepted that nonuniformity in particle size is a fundamental contributor. When the granular material is exposed to vibrations, the question of whether or not convection is an essential ingredient for size segregation is addressed by distinguishing between the situation where vibrations are not sufficiently energetic to promote a mean flow of the bulk solid, and those cases where a convective flow does occur. Based on experimental and simulation results in the literature, as well as dynamical systems analysis of a recent model of a binary granular mixture, it is proposed that "void-filling" beneath large particles is a universal mechanism promoting segregation, while convection essentially provides a means of mixing enhancement.
Three-dimensional granular dynamics simulations are carried out to investigate macroscopic behavior of granular materials subjected to vibrations. Particles, idealized as smooth inelastic, uniform spheres, are gravitationally loaded into a rectangular periodic cell having an open top and plane floor. Vibrations to the bed are subsequently imposed through the sinusoidally oscillated floor. Significant differences in the character of the bed are found, depending on the strength of the applied floor accelerations Γ=aω2, even if the boundary input energy is fixed. At high acceleration values, a dense upper region is supported on a fluidized low-density region near the floor. The temperature is maximum at the floor and monotonically attenuates upward, while the solids fraction profile peaks at some intermediate depth. When lower accelerations are applied, the granular temperature no longer decreases monotonically from the bottom to the top and the solids fraction depth profile bulges at approximately three diameters from the floor. The surface of the bed appears chaotic and fluidized, where a low solids fraction and high temperature occurs. The bed height, which remains almost constant below 1.2g, undergoes a pronounced expansion when 1.2g≤Γ≤2.0g, and subsequently flattens out at Γ≂2.8g. Computed granular temperature and solids fraction depth profiles are in good agreement with recent kinetic theory predictions when the acceleration is large enough, while bed expansion at lower accelerations is quantitatively consistent with existing experimental data.
We report experiments on the rise time T of a single large sphere within a sinusoidally vibrated bed (amplitude a) of uniform particles (diameter d). At fixed acceleration, we identify three distinct behavioral regimes both from visual observations and from the typical increase of T with frequency f. We observe two convective regimes separated by a critical frequency and, for low a and high f, a "nonconvective" regime. In the latter, the bed crystallizes and a size dependent rise is evidenced. We show the relevance of the nondimensional parameter a͞d and deduce a scaling law of the form f~d 21͞2 . [S0031-9007 (97)02305-3] PACS numbers: 46.10.+z, 83.70.FnOver approximately the last ten years, significant attention has been given to the phenomenon of size segregation in granular mixture. This is motivated in part by the fact that size segregation is often an undesirable outcome of handling and/or processing operations of bulk solids [1]. In a vibrated bed of monodisperse dry granular material, behaviors (e.g., heaping [2,3], compaction [4], convection [5][6][7][8], fluidization [9][10][11], surface waves [12][13][14], or arching [15]) are highly dependent on the level and form of the external vibration, and are likely to influence the process of size segregation in a polydisperse bed.In general, a large ball placed at the bottom of a vibrated bed will rise to the surface [16]. Depending on the properties of the system (e.g., ball size), the ball may be trapped on the surface or may reenter the bed [7,17]. If trapping occurs, the primary components of a mixture may eventually separate according to their size. In order to understand why a large ball (or intruder) rises, experiments and simulations have aimed at identifying possible mechanisms. Two main driving processes have been proposed. One is the formation of a bulk convective flow of the bed particles which, at the same time, carry the intruder [7,[17][18][19][20][21]. The other is related to local rearrangements under gravity of the bed geometry, as supported by numerical simulations [22][23][24], and is possibly controlled by collective effects like arching [25] or bridges [26]. Experimentally, a "nonconvective" and size-dependent rising has been observed, but only in a two-dimensional bed [18,25]. In all cases, the time dependence of the phenomenon is not understood.In this paper we report the influence of the macroscopic behavior of a monodisperse bed on the rise time T of a single large sphere. Three rise regimes are identified from the specific relationship between T and the frequency f. Our results show the distinct features of two convective flows: one where heaping occurs and the other where heaping is not present. For the first time, we observe in a three-dimensional bed a dependence of T on the intruder size. This occurs when the bed becomes so compact that it crystallizes. Finally, we emphasize the relevance of the dimensionless amplitude a͞d which allows us to predict the rapid increase of T with frequency at high accelerations.The experimental syst...
Using a combination of experimental techniques and discrete particle method simulations, we investigate the resonant behaviour of a dense, vibrated granular system. We demonstrate that a bed of particles driven by a vibrating plate may exhibit marked differences in its internal energy dependent on the specific frequency at which it is driven, even if the energy corresponding to the oscillations driving the system is held constant and the acceleration provided by the base remains consistently significantly higher than the gravitational acceleration, g. We show that these differences in the efficiency of energy transfer to the granular system can be explained by the existence of resonances between the bed's bulk motion and that of the oscillating plate driving the system. We systematically study the dependency of the observed resonant behaviour on the system's main, controllable parameters and, based on the results obtained, propose a simple empirical model capable of determining, for a given system, the points in parameter space for which optimal energy transfer may be achieved. been demonstrated [15] that, for relatively shallow, strongly fluidized systems, this assumption does not necessarily hold true; rather, the dynamic properties of a vertically vibrated granulate are additionally sensitive to the specific combinations of f and A used to produce a given v, S or Γ. In other words, two systems vibrated with the same input energy achieved using two differing combinations of f and A may exhibit strongly disparate properties. Similarly, it is found that two systems driven with markedly different S and/or Γ values may possess near-identical internal energies, in direct contradiction of the monotonic relations one might expect.Specifically, for dilute systems such as those described in [15], it was found that an increase in A at fixed S resulted in an increase in the total energy possessed by the excited granulate. This greater energy transfer from the vibrating system to the granular bed at large driving amplitudes was attributed to the observed increase in the particle-base collision rate with increasing A. In other words, the lack of a simple, monotonic relationship between a granulate's kinetic and/or potential energy and any of the individual parameters v S , or Γ can be explained by the fact that such parameters do not provide sufficient information regarding certain key variables, in this case the particle-base collision rate within the system. As such, in order to accurately characterize the steady-state of such a system, one requires a pair of driving variables, f and A-in addition, of course, to a knowledge of the system's depth and dissipative properties.Recent works by Pugnaloni et al [16,17] have similarly challenged the assumption that a system's steady state may be adequately defined by a single parameter, in this instance for the case of a granular bed excited by a series of discrete taps, as opposed to continuous vibration. Specifically, it was, until recently, a generally held belief [18,19] that ...
The density relaxation phenomenon is modeled using both Monte Carlo and discrete element simulations to investigate the effects of regular taps applied to a vessel having a planar floor filled with monodisperse spheres. Results suggest the existence of a critical tap intensity which produces a maximum bulk solids fraction. We find that the mechanism responsible for the relaxation phenomenon is an evolving ordered packing structure propagating upwards from the plane floor.
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