Rise-Time Regimes of a Large Sphere in Vibrated Bulk Solids

Abstract

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...

Hydrodynamic model for particle size segregation in granular media

“…In this case, both intruder and the small particles are driven up along the middle of the cell, and while the smaller particles are carried down in a convection roll near the walls the intruder remains trapped on the top. In experiments performed by Vanel et al, in three dimensions, they observed two convective regimes separated by a critical frequency [7]. The first regime is associated with heaping and the second regime is similar to the one observed in Ref.…”

“…A series of experiments [3][4][5][6][7][8][9] and computer simulations [2,[10][11][12][13][14][15][16][17] have elucidated different size segregation mechanisms, including vibration frequency and amplitude [3][4][5][6][7][8]10,15]; particle size [3,5,6,10,11,13,14,17] and size distribution [12,15]; particle shape [16]; and other properties such as density [9,13,17] and elastic modulus [15].…”

Crystallization of non-Brownian Spheres under Horizontal Shaking

“…Owe Berg et al [12] carried out experiments on the packing of spheres obtained under different shaking processes and concluded that "three dimensional shaking" (shaking with an horizontal component) can lead to a crystallization. More recently, Vanel et al [13] obtained a regular packing of steel beads by vertically vibrating the container. However, all these experiments deal with a very small number of particles and the thickness of the crystal does not exceed 20 particles.…”

The theory of gradient vibratory segregation effect as applied to screening process

“…They did not find evidence for the intruder motion through the small particles via local grain rearrangement. Experiments by Duran et al [84] and Vanel et al [85] have found convective as well as non-convective regimes where rise-times were dominated by mean flow. Poschel and Herrmann [41] performed MD simulations and found that convection can be triggered by the motion of the large particle.…”

“…Such experiments have been performed in two dimensions by Duran et al [84], and in three dimensions by Vanel et al [85]. In these experiments, a 'non-convective' regime was found for appropriate driving frequencies and amplitudes.…”