Hydrodynamic model for particle size segregation in granular media

Trujillo, Leonardo; Herrmann, Hans J.

doi:10.1016/s0378-4371(03)00621-6

Cited by 29 publications

(19 citation statements)

References 62 publications

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“…Furthermore, in Figure 2, one sees that the larger the size of the impurities is, the larger is their speed for rising or sinking at t ′ < 600; this should account for the size grading. It is known that impurities are subjected to a granular viscous force from randomly moving matrix particles when the impurities move relative to matrix particles [ Zik et al , 1992], and that the viscous force is a function of the impurity size [ Albert et al , 1999; Trujillo and Herrmann , 2003]. Therefore, the dependence in the rising‐ and sinking‐speeds on the size of the impurities is expected to be caused by the granular viscous force.…”

Section: Discussionmentioning

confidence: 99%

Density and size segregation in deposits of pyroclastic flow

Mitani

Matuttis

Kadono

2004

Geophysical Research Letters

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[1] The main portion in the deposits of pyroclastic flow shows various characteristic features such as density and size segregation of large fragments in the vertical direction. To understand the mechanism which produces these features, we numerically study granular flows on an inclined rough surface with impurities that are different in density and size from the matrix particles. The simulation shows the occurrence of density and size segregation of large impurities, and the impurities finally concentrate at the top and the bottom. Based on these results, we discuss the mechanism of the segregation. It is found that the behavior of impurities is governed by gravity, buoyancy and the viscosity of the randomly moving matrix.

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Section: Discussionmentioning

confidence: 99%

Density and size segregation in deposits of pyroclastic flow

Mitani

Matuttis

Kadono

2004

Geophysical Research Letters

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“…[117]. This way, the validity of the pair correlation functions can be extended to higher densities They can be used to predict mixing and segregation of two species [124,[214][215][216][217][218].…”

Section: Particle Size-distributionsmentioning

confidence: 99%

Towards dense, realistic granular media in 2D

Luding¹

2009

Nonlinearity

133

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The development of an applicable theory for granular matter -with both qualitative and quantitative value -is a challenging prospect, given the multitude of states, phases and (industrial) situations it has to cover. Given the general balance equations for mass, momentum, and energy, the limiting case of dilute and almost elastic granular gases, where kinetic theory works perfectly well, is the starting point.In most systems, low density coexists with very high density, where the latter is an open problem for kinetic theory. Furthermore, many additional non-linear phenomena and material properties are important in realistic granular media, involving, e.g.: (i) multi-particle interactions and elasticity (ii) strong dissipation, (iii) friction, (iv) long-range forces and wet contacts (v) wide particle size-distributions, and (vi) various particle shapes. Note that, while some of these issues are more relevant for high density, others are important for both low and high densities; some of them can be dealt with by means of kinetic theory, some can not. This paper is a review of recent progress towards more realistic models for dense granular media in 2D, even though most of the observations, conclusions, and corrections given are qualitatively true also in 3D. Starting from an elastic, frictionless and monodisperse hard sphere gas, the (continuum) balance equations of mass, momentum and energy are given. The equation of state, the (Navier-Stokes level) transport coefficients and the energy-density dissipation rate are considered. Several corrections are applied to those constitutive material laws -one by one -in order to account for the realistic physical effects and properties listed above.

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“…More recently, new behavior was discovered for the limit of very small bed particles ("dust"), in particular the sinking of light intruders [6,7], and a non-monotonic dependence of the rise time on density [8,9,10]. A number of theory and experimental papers explored different aspects of this surprising behavior [11,12,13,14,15,16], but so far there has been no consensus about either the underlying mechanisms or the relative importance of various system parameters in driving the intruder motion.Here we present results from a systematic investigation of both the intruder motion and the bed particle flow. Our central finding is that there is a phase diagram which delineates rising and sinking behavior of the intruder as a function of interstitial gas pressure, intruder density, and initial intruder height within the container.…”

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confidence: 99%

“…As a consequence, our findings directly contrast with the mechanisms proposed in Refs. [6,10,14,16] that neglect interstitial gas flow.We placed granular material inside an acrylic cylinder (inner diameter 8.2 cm) mounted on a shaker and used individual, well-spaced sine wave cycles ("taps") of frequency f and amplitude A to vibrate the vessel vertically. The cell could be evacuated to a gas pressure, P .…”

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confidence: 99%

Intruders in the Dust: Air-Driven Granular Size Separation

et al. 2004

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Using MRI and high-speed video we investigate the motion of a large intruder particle inside a vertically shaken bed of smaller particles. We find a pronounced, non-monotonic density dependence, with both light and heavy intruders moving faster than those whose density is approximately that of the granular bed. For light intruders, we furthermore observe either rising or sinking behavior, depending on intruder starting height, boundary condition and interstitial gas pressure. We map out the phase boundary delineating the rising and sinking regimes. A simple model can account for much of the observed behavior and show how the two regimes are connected by considering pressure gradients across the granular bed during a shaking cycle.PACS numbers: 45.70. Mg, 64.75.+g, 83.80.Fg Unlike thermal systems which favor mixing to increase entropy, granular systems tend to separate under an external driving mechanism such as vibrations [1,2]. This is commonly known as the Brazil Nut Effect, in which a large particle, the "intruder", rises to the top of a bed of smaller background particles [3,4,5]. More recently, new behavior was discovered for the limit of very small bed particles ("dust"), in particular the sinking of light intruders [6,7], and a non-monotonic dependence of the rise time on density [8,9,10]. A number of theory and experimental papers explored different aspects of this surprising behavior [11,12,13,14,15,16], but so far there has been no consensus about either the underlying mechanisms or the relative importance of various system parameters in driving the intruder motion.Here we present results from a systematic investigation of both the intruder motion and the bed particle flow. Our central finding is that there is a phase diagram which delineates rising and sinking behavior of the intruder as a function of interstitial gas pressure, intruder density, and initial intruder height within the container. Our results lead to a physical model that provides a unifying framework to describe both rising and sinking regimes. In this way, the work presented here connects previously disjointed pieces of a puzzle that pointed to the importance of pressure gradients [7,8,9] but approached the two regimes as separate phenomena. As a consequence, our findings directly contrast with the mechanisms proposed in Refs. [6,10,14,16] that neglect interstitial gas flow.We placed granular material inside an acrylic cylinder (inner diameter 8.2 cm) mounted on a shaker and used individual, well-spaced sine wave cycles ("taps") of frequency f and amplitude A to vibrate the vessel vertically. The cell could be evacuated to a gas pressure, P . Both smooth and rough cells (created by gluing glass beads to the interior walls of an otherwise smooth cell) were used to study the effect of wall friction. A large intruder sphere of diameter D was buried in the bed of background spheres (diameter d) at a height h s measured from the vessel bottom to the intruder top (See Fig. 1(a)). A range of diameter ratios D/d, shaking parameters, and bac...

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Hydrodynamic model for particle size segregation in granular media

Cited by 29 publications

References 62 publications

Density and size segregation in deposits of pyroclastic flow

Density and size segregation in deposits of pyroclastic flow

Towards dense, realistic granular media in 2D

Intruders in the Dust: Air-Driven Granular Size Separation

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