Fundamental powder mixing mechanisms

Bridgwater, J.

doi:10.1016/0032-5910(76)80051-4

Cited by 292 publications

(134 citation statements)

References 20 publications

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“…In industrial applications, rotating cylinders are primarily used for mixing different components [2]. But it is well known that particles of different sizes or density show radial segregation on small time scales and axial segregation on large time scales which compete against the mixing process [2][3][4][5][6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Shape dynamics of interfacial front in rotating cylinders

Ristow

Nakagawa

1999

Phys. Rev. E

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Section: Introductionmentioning

confidence: 99%

Shape dynamics of interfacial front in rotating cylinders

Ristow

Nakagawa

1999

Phys. Rev. E

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“…The results are confirmed numerically. We suggest that the same mechanism may contribute to the formation of stripes in experiments on horizontally oscillated granular mixtures.Binary systems subject to an oscillatory driving force are often found to phase segregate and form patterned structures [1,2]. Often this segregation can have important practical applications.…”

mentioning

confidence: 99%

“…Binary systems subject to an oscillatory driving force are often found to phase segregate and form patterned structures [1,2]. Often this segregation can have important practical applications.…”

mentioning

confidence: 99%

Stripe Formation in Differentially Forced Binary Systems

Pooley¹,

Yeomans²

2004

Phys. Rev. Lett.

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We consider pattern formation in periodically forced binary systems. In particular we focus on systems in which the two species are differentially forced, one being accelerated with respect to the other. Using a continuum model consisting of two isothermal ideal gases which interact via a frictional force we demonstrate analytically that stripes form spontaneously above a critical forcing amplitude. The wavelength of the stripes is found to be close to the wavelength of sound in the limit of small viscosity. The results are confirmed numerically. We suggest that the same mechanism may contribute to the formation of stripes in experiments on horizontally oscillated granular mixtures.Binary systems subject to an oscillatory driving force are often found to phase segregate and form patterned structures [1,2]. Often this segregation can have important practical applications. For example it may provide a useful way of separating two mixed species, or conversely, it may be undesirable in an industrial process [3]. The phenomenon is well documented experimentally but a full theoretical understanding is still missing with different mechanisms for the pattern formation being proposed in the literature.Sanchez et al.[4] have carried out experiments and parallel simulations on granular mixtures immersed in water. For sufficiently large amplitudes of vibration a mixture of equal sized glass and bronze particles were found to separate into a striped pattern. Sanchez et al. proposed that the differential fluid drag on the two components of the mixture is the mechanism responsible for the segregation.Mullin et al. [5,6,7] have performed a series of experiments in which they horizontally oscillate a quasi-2 dimensional layer of bronze spheres and poppy seeds. The species are again observed to segregate into a striped pattern. However they propose a different explanation for the stripes: the effective excluded volume interactions which occur because of the different size of the shaken particles [8].Therefore our aim in this Letter is to investigate possible mechanisms for binary phase segregation by providing an approximate analytic solution to a one-dimensional isothermal continuum model describing the physics of a binary mixture of two ideal fluids. We find that if the components are differentially forced stripes are formed in the concentration above a critical forcing amplitude. The wavelength of the stripes is controlled by the velocity of sound and standing wave oscillations in the total density pay a crucial role in the stripe formation.We then relate our results more closely to experiments on granular mixtures through a simple particle model. We find that differential forcing of the two types of particle is enough to cause stripe formation even if the particles have the same mass and volume.We consider two ideal fluids, labeled A and B, which are coupled by a frictional force proportional to the difference in their velocities. The physical origin of this force is from collisions between the A and B particles which tend to...

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“…This can sometimes be desirable, such as in mining and stone crushing, and can be exploited to separate the grains [1], but it is often a source of great frustration that can significantly degrade the quality and the safety of a product [2]. A considerable amount of early work was therefore performed by engineers who sought to understand the fundamental size segregation mechanisms and learn how to control their effects [3,4,5]. Geologists and sedimentologists were also early pioneers who were quick to identify inversely (or reverse) graded deposits, in which the grain size population coarsens upwards, and use this as an indicator of ancient granular avalanches on dunes, in dense pyroclastic flows and debris flows [e.g.…”

Section: Introductionmentioning

confidence: 99%

A hierarchy of particle-size segregation models: From polydisperse mixtures to depth-averaged theories

Gray¹

2013

AIP Conference Proceedings

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Numerical study on the axial segregation dynamics of a binary-size granular mixture in a three-dimensional rotating drum Physics of Fluids 29, 103302 (2017) Abstract.Particle size segregation in granular avalanches occurs due to inter-particle percolation and squeeze expulsion. The general theory for a polydisperse mixture yields a segregation equation for each grain size class. For a three constituent mixture of large, small and medium sized particles there are three segregation equations, one of which can be eliminated, since the concentrations of all the species necessarily sums to unity. The remaining two coupled parabolic equations can be solved using a standard Galerkin finite element method. Numerical solutions show that small particles percolate to the base of the avalanche, large particles are squeezed to the surface and the medium sized grains are sandwiched in between. For certain choices of the segregation parameters it is possible to generate instabilities that lead to saw-tooth segregation in the threephase mixture, but these die off as the grains separate into bi-disperse sub-mixtures. In general, all the grains contribute to the segregation process and develop an inversely graded particle size distribution, that coarsens upwards. This is known as reverse distribution grading. Sometimes, however, the fine particles may not segregate readily, leading to reverse coarse tail grading. For a bi-disperse mixture, the general theory yields one independent segregation equation, which always seeks to drive the particles into an inversely graded state. However, when the bulk flow shears small particles over the top of large, a breaking size-segregation wave is created. Such waves are important close to flow fronts, because they allow large particles that are over-run to rise up to the surface again and be recirculated. Computing the evolving particle-size distribution in a three-dimensional flow is still a challenge. However, it is possible to obtain a simplified representation by integrating the segregation equation through the avalanche depth. This fits naturally into the depth-averaged framework of avalanche models and opens the door to fully couple calculations to study levee formation and segregation induced flow fingering.

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Fundamental powder mixing mechanisms

Cited by 292 publications

References 20 publications

Shape dynamics of interfacial front in rotating cylinders

Shape dynamics of interfacial front in rotating cylinders

Stripe Formation in Differentially Forced Binary Systems

A hierarchy of particle-size segregation models: From polydisperse mixtures to depth-averaged theories

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