Surface properties and the flow of granular material in a two-dimensional rotating-drum model

Granular materials exhibit several regimes of behavior: plastic, inertial, fluidized, and entrained flow, but not all materials can pass through all of these states. Our concern is with the criteria that determine the transition from one regime to another and with the boundaries to the various flow regimes that these criteria define. Experimentally we have focused on fine, cohesive powders, where the interparticle cohesive force dominates over gravitational force and where entrained air can cause moving powder to become fluidized. [S0031-9007(98)08339-2] PACS numbers: 45.70.Mg, 81.20.Ev, 83.70.Fn The past decade has witnessed a strong interest in granular materials by the physics community, but there is an important class of granular materials that has been largely ignored in spite of its commercial importance; these materials can be classified as fine cohesive powders. In these powders, with particle diameters less than about 30 3 10 26 m, interparticle cohesive effects are dominant, and ambient gas plays an important role in the behavior of the powder. Granular materials display four different flow regimes: plastic behavior, inertial flow, fluidized flow, and entrained flow. Particle size, particle density, cohesivity, and gas flow determine which of these types of behavior occur.(i) The plastic regime is characterized by a small spacing between neighboring particles. Velocities are small or zero and the stresses are independent of velocity for simple geometries. Plastic behavior determines the stability of heaps and slopes and there is an extensive literature on the subject because of its importance in civil engineering.(ii) In the inertial regime the stresses are due to the transport of momentum by interparticle collisions. The spacing between particles is much smaller than the particle size but greater than in the plastic regime. In everyday life granular materials such as sand, sugar, and ground coffee exhibit the transition from plastic solid to inertial flow when the limit of plastic stability is reached. We note that the interstitial fluid plays no part in inertial flow.(iii) Powders are capable of being fluidized by gas flow provided their cohesivity is not too great. In this regime the interparticle distance is of the same order of magnitude as the particle size. The interstitial fluid is the agent of transfer of momentum between particles, and fluid velocity determines the stresses in the material. The best known example of this situation is the fluidized bed, in which gas is forced through a bed of particles and the gas flow causes a pressure drop across the powder. When the pressure drop is sufficient to support the weight of the powder and to overcome the interparticle cohesive forces, the bed expands and becomes fluidized. The powder then takes on many of the properties of liquid, its upper surface remaining horizontal when the container is tilted.(iv) A fourth regime is that of entrainment, or suspension of the particles by the gas. In this case the distance between particles is much greater ...

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“…2(a)]. This type of behavior is widely reported [10][11][12][13] for coarse, granular materials ͑d p . 10 24 m͒.…”

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confidence: 92%

Flow Regimes in Fine Cohesive Powders

et al. 1999

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“…Modeling studies have used numerical methods to calculate the position, velocity and interactions of particles in a rotating drum. Such a study of monodisperse granular material demonstrated almost perfect temporal periodicity in surface¯ow [7]. The introduction of a second size particle into the simulation destroyed the periodic behavior.…”

Section: Introductionmentioning

confidence: 96%

Signal Processing and Analysis Applied to Powder Behavior in a Rotating Drum

Crowder

Sethuraman

Fields³

et al. 1999

Part. Part. Syst. Charact.

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Previous studies of the¯ow of granular materials in a rotating drum have described the observed time sequences of angle of repose or time to avalanche. The time between avalanches approach has been incorporated into a commercially available powder¯ow analysis tool. In the present study, the time to avalanche analysis was complemented with a Fourier Transform power spectrum and phase space analysis of the angle of repose time series and avalanche size variability determination. The avalanche size variability approach was found to most readily differentiate between the¯ow properties of powders across material types. A model was constructed to provide an explanation for the utility of this method.

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“…[9,10,12,16]). Some others fix their attention in models for which particular mechanisms of interaction seem to be relevant [13][14][15]18,21,28].In the present work we propose a representation of the avalanche process in sandpiles as a percolation in a Bethe lattice, capturing the essential features of the avalanche phenomenon and simultaneously taking into account the nature of the sandpile, in order to reproduce the experimental results.The image of an avalanche as an initial object that consecutively drags another resembles a branching process for which the Bethe lattice representation seems to be natural. This branching process was proposed in [22], showing good possibilities to describe the change of behavior of fragment size distribution in fragmentation phenomena.…”

mentioning

confidence: 93%

“…[9,10,12,16]). Some others fix their attention in models for which particular mechanisms of interaction seem to be relevant [13][14][15]18,21,28].…”

Section: Introductionmentioning

confidence: 99%

“…In this experiment, small sandpiles seemed to exhibit SOC. Besides, an apparent disagreement has emerged between the results reported in [5] and [6] but, as we will show in this paper, these results are essentially the same.Though many other theoretical and experimental works were performed [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28], some of the later proposed models were devoted to the problem of SOC in a more general fashion than the sole application to sandpiles (e.g. [9,10,12,16]).…”

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confidence: 99%

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Bethe lattice representation for sandpiles

1999

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Avalanches in sandpiles are represented throughout a process of percolation in a Bethe lattice with a feedback mechanism. The results indicate that the frequency spectrum and probability distribution of avalanches resemble more to experimental results than other models using cellular automata simulations. Apparent discrepancies between experiments are reconciled. Critical behavior is here expressed throughout the critical properties of percolation phenomena.PACS numbers: 64.60 Fr, 64.90 +b, 84.90 +n INTRODUCTIONThe idea of self-organized criticality (SOC) proposed by Bak, Tang and Wiesenfeld [1,2] triggered a lot of experimental as well as theoretical work on relaxation processes in granular materials. Sandpiles seem to be the simplest systems to test self-organized behavior. The importance of its study comes from the fact that SOC has been suggested as a possible explanation for the power law behavior seen in many systems: earthquakes, [3] mass distribution in the Universe, star flickers, etc. [4] Experiments on sandpiles were designed and performed in [5,6]. In [5], avalanche sizes were recorded in rotating drum experiments, finding that avalanches, instead of being distributed over all sizes obeying a power law distribution as predicted in [1,2], occurred quite regularly in size and time, in an almost periodic pattern (See also [7,8]).In [6], mass fluctuations in an evolving sandpile were studied, showing that for small enough sandpiles, the observed mass fluctuations are scale invariant, and probability distribution of avalanches shows finite size scaling whereas large sandpiles do not. In this experiment, small sandpiles seemed to exhibit SOC. Besides, an apparent disagreement has emerged between the results reported in [5] and [6] but, as we will show in this paper, these results are essentially the same.Though many other theoretical and experimental works were performed [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28], some of the later proposed models were devoted to the problem of SOC in a more general fashion than the sole application to sandpiles (e.g. [9,10,12,16]). Some others fix their attention in models for which particular mechanisms of interaction seem to be relevant [13][14][15]18,21,28].In the present work we propose a representation of the avalanche process in sandpiles as a percolation in a Bethe lattice, capturing the essential features of the avalanche phenomenon and simultaneously taking into account the nature of the sandpile, in order to reproduce the experimental results.The image of an avalanche as an initial object that consecutively drags another resembles a branching process for which the Bethe lattice representation seems to be natural. This branching process was proposed in [22], showing good possibilities to describe the change of behavior of fragment size distribution in fragmentation phenomena. Another branching process representation was proposed in [12,26] in an attempt to obtain analytical solutions for avalanche processes, and in [23,24], a...

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Surface properties and the flow of granular material in a two-dimensional rotating-drum model

Cited by 61 publications

References 19 publications

Flow Regimes in Fine Cohesive Powders

Flow Regimes in Fine Cohesive Powders

Signal Processing and Analysis Applied to Powder Behavior in a Rotating Drum

Bethe lattice representation for sandpiles

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