Particle size segregation in a two-dimensional bed undergoing vertical vibration

Cooke, William J.; Warr, Stephen; Huntley, Jonathan M.; Ball, Robin C.

doi:10.1103/physreve.53.2812

Cited by 104 publications

(65 citation statements)

References 23 publications

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“…A large steel ball bearing buried in fine sand, for example, will upon shaking migrate to the surface. This is also observed in simply vibrating or shaking a column of large and small particles (Jullien et al 1992;Cooke et al 1996), which leads to a form of granular convection (Knight et al 1993). In shear flows, both normally graded and inversely graded beds can be laid down due to flow timing and deposition.…”

Section: Granular Processesmentioning

confidence: 99%

On some fundamentals of igneous petrology

Marsh

2013

Contrib Mineral Petrol

135

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The age-old process of crystal fractionation leading to the diversity of the igneous rocks and Earth itself is an exceedingly well-understood chemical process in magmatism and physical chemistry. But the broader physical aspects of this and related processes have proven elusive on many fronts, especially in its relation to the spatial variations in rock composition, texture, and macroscopic features like layering. Magmatic systems, be they volcanic, dikes, sills, or plutons, are generally analyzed with a problem at hand and an end result in mind. The processes invoked to solve these problems, which are most often purely chemical, are often unique to each problem with few if any general principles emerging that are central to understanding the wider perspective of magmatic processes and problems. An attempt is made at the outset to provide a list of inviolate Magmatic First Principles that are relevant to analyzing most magmatic problems. These involve: initial conditions; critical crystallinity; solidification fronts; transport and emplacement fluxes; phenocrysts, xenocrysts, primocrysts; crystal size; layering and crystal sorting; thermal convection; magmatic processes are physical. Along with these principles, two reference magmatic systems are suggested where the initial conditions and outcome are unequivocal: the Sudbury impact melt sheet and the Hawaiian lava lakes. Sudbury formed in *5 min by superheated magma crystallized to a near uniform sequence, while the tiny lava lakes, formed of crystal-laden slurries, form a highly differentiated layered sequence. The major difference is in the initial conditions of formation, especially the nature of the input materials. The challenge is to construct and analyze magmatic systems (i.e., magma chambers, sills, dikes, and lavas) using these reference end members and the suggested principles. The Hawaiian 500,000 year volcanic record exhibits what can be expected as input materials, namely a highly varied output of magma of an overall composition reflecting the abundance of entrained olivine primocrysts. The provenance of these crystals is varied, and within any single sample, the population may be highly heterogeneous in composition from crystal to crystal, yet the overall pattern of chemical fractionation is exceedingly regular and well defined. If similar inputs go to form large intrusions, these systems will undoubtedly be dominated by crystal-rich slurries, which provide a vast set of physical processes promoting exotic layering and, at the same time, given the effects of annealing and continued crystal growth, a final chemical record adhering to all the time-honored effects of crystal fractionation. The long assumed initial condition of instantaneously emplaced crystal-free magmas cannot reasonably produce the observed rock records.

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Section: Granular Processesmentioning

confidence: 99%

On some fundamentals of igneous petrology

Marsh

2013

Contrib Mineral Petrol

135

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“…From the definition of granular temperature, the change of the granular temperature depends on the mean kinetic energy of the particles. A volume change dV is related to a temperature change dT g by the equation of state (6).…”

Section: Energy Equipartition Breakdownmentioning

confidence: 99%

“…This provoked some controversy [18][19][20][21] and this threshold may be an artifact of the simulation model based on the "steepest descent algorithm" [10]. Experiments in Helle Shaw cells [3,5,6] observed an intruder size dependent behavior, where the segregation rate increases with the size ratio between the intruder and the surrounding particles. Duran et al, formulated a geometrical theory for segregation based on the arching effect [3].…”

Section: Introductionmentioning

confidence: 99%

“…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].…”

Section: Introductionmentioning

confidence: 99%

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Hydrodynamic model for particle size segregation in granular media

Trujillo

Herrmann

2003

Physica A: Statistical Mechanics and its Applications

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We present a hydrodynamic theoretical model for "Brazil nut" size segregation in granular materials. We give analytical solutions for the rise velocity of a large intruder particle immersed in a medium of monodisperse fluidized small particles. We propose a new mechanism for this particle size-segregation due to buoyant forces caused by density variations which come from differences in the local "granular temperature". The mobility of the particles is modified by the energy dissipation due to inelastic collisions and this leads to a different behavior from what one would expect for an elastic system. Using our model we can explain the size ratio dependence of the upward velocity.

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“…In other words, an aspect ratio between width and height (w/h) of the container used for each case: the w/h ratio for D l /D s = 2.0 > the w/h ratio for D l /D s = 3.0 and 4.0 > the w/h ratio for D l /D s = 1.2. A difference of the container size may cause a different intensity of bulk convection motion, which is one of main mechanisms behind segregation phenomena [6,12,13]. …”

Section: The Effect Of the Dimensionless Accelerationmentioning

confidence: 99%

Experimental study of particle size segregation in 2D granular materials under vertical vibrations

2017

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Abstract. The influence of particle size on segregation phenomena in two-dimensional binary granular mixtures with a similar solid fraction under vertical vibrations is experimentally investigated in this study. Four different particle size ratios (D l /D s ) are varied. The granular mixtures are subjected to vertical vibrations under six different dimensionless accelerations (ī = 1-6), with constant vibrational amplitude of 5 mm. The vertical segregation coefficient (H) is here introduced to analyse the degree of segregation of the mixtures. We found that the Brazil nut effect, where the larger particle rises to the top, is observed for all the tests whenever the segregation is occurred. The degree of segregation of the mixtures is a function of the coefficient H, which can be divided into 3 zones: a compaction zone with particle mixing (0.0 < H 0.2), a partially segregated zone (0.2 < H 0.4), and an apparently segregated zone (0.4 < H 1.0). The segregation begins when ī 2 and then tends to increase when ī is increased. In addition, the segregation is quite clearly found when D l /D s 3 and ī 3.

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Particle size segregation in a two-dimensional bed undergoing vertical vibration

Cited by 104 publications

References 23 publications

On some fundamentals of igneous petrology

On some fundamentals of igneous petrology

Hydrodynamic model for particle size segregation in granular media

Experimental study of particle size segregation in 2D granular materials under vertical vibrations

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