Boundary conditions on continuum theories of granular flow

Gutt, Gary; Haff, P. K.

doi:10.1016/0301-9322(91)90028-2

Cited by 17 publications

(7 citation statements)

References 12 publications

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“…0148-0227/90/89JB-03623 $05.00 dependence of the normal and shear stresses in collisional flows. Realization that the kinetic theory of gases [Maxwell, 1866;Boltzmann, 1896] might be modified to describe collisional grain flows spurred an outpouring of theoretical work [e.g., Goldreich and Tremaine, 1978;Jenkins and Savage, 1983;Haft, 1983;Savage, 1983;Lun et al, 1984;Hui et al, 1984;Jenkins and Richman, 1985a, b;Araki and Tremaine, 1986;Lun and Savage, 1987;Gutt, 1987;Gutt and Haft, 1988] that has, to date, significantly outpaced experimental developments. This new kinetic theory paradigm has drastically shifted the focus of research away from general flows in which both collisional and frictional effects are important to purely collisional flows to which the kinetic theory can be applied.…”

Section: Introductionmentioning

confidence: 99%

Structural features in granular flows

Drake¹

1990

J. Geophys. Res.

179

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High-speed motion pictures document a series of essentially two-dimensional, free-surface flows of 6-mm diameter plastic spheres generated in an inclined glass-walled chute 3.7 m long and 6.7 mm wide. Flows exhibit a diverse suite of structural features, depending on particle flux, chute inclination, and geometry of the fixed bed. Flows at sufficiently low inclination or high particle flux can generally be divided into frictional and collisional regions. In the frictional region, intergranular momentum transfer occurs by enduring, frictional contacts; kinetic theories of granular flow do not apply. The frictional region typically consists of a quasi-static zone extending up from the fixed bed and an overlying block-gliding zone, in which coherent blocks of grains move parallel to the bed. The collisional region overlies the contact region in sufficiently deep flows; otherwise it extends to the bed. In it, momentum transfer is dominated by collisions. It typically consists of three zones: a lower grain-layer-gliding zone, in which grains appear to slide over one another; a middle chaotic zone, in which grain motions are highly random, as in a dense gas; and an overlying saltational zone, in which grains trace long, curved paths. Zones grade smoothly into one another, and some are missing in certain flows. In none of the flows does a frictional region overlie a collisional region. Zone thicknesses and block dimensions are previously unrecognized length scales in granular flows. The no-slip velocity boundary condition applies only when a frictional region adjoins a geometrically rough fixed bed, otherwise significant slip occurs (up to 50% of the mean flow velocity). Binary collisions dominate only in the collisional region and there perhaps only in the chaotic and saltational zones. Because many collision-dominated geophysical flows start from friction-dominated ones and end by reverting to the frictional regime as the energy supply diminishes, kinetic theories of granular flow, which unanimously employ the binary-collision assumption, can at best describe only a portion of the phenomena. Microstructural descriptions of the relatively slow, compact, and frictional regions evident in most geophysical flows are required to complement existing kinetic theories. ß ß i chaotic ß i grain-layer ß gilding aone ß ß ß ß block gliding zone mltatlonal chaotic zone ,4. ß 4. ß ß ß ß ß ß ß ß ß !

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Section: Introductionmentioning

confidence: 99%

Structural features in granular flows

Drake¹

1990

J. Geophys. Res.

179

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“…Meanwhile, it is also a popular test case for validating the constitutive relations postulated in the earlier years (Gutt & Haff, 1991;Johnson & Jackson, 1987;Lun et al, 1984;Savage, 1984;Tardos et al, 2003).…”

Section: Granular Flow In Couette Configurationmentioning

confidence: 99%

Assessment of the kinetic–frictional model for dense granular flow

Ding

Ghadiri

2008

Particuology

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“…The thickness of this boundary layer is not yet defined. However, in this layer two processes must occur: the inelastic part of the collisions, including the sliding motion between the particles, will be converted to heat whereas the elastic part of the collision will be transformed into kinetic energy (Hui and others, 1984; Gutt and Haff, 1991; Jenkins, 1992). The transformation of collisional elastic strain energy to kinetic energy of the particles might extend over several diameters because of the closeness and enduring contacts of the particles.…”

Section: Constitutive Modelmentioning

confidence: 99%

Fluctuation-dissipation relations for granular snow avalanches

Bartelt¹,

Buser²,

Platzer³

2006

J. Glaciol.

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A fundamental problem in avalanche science is understanding the interaction between frictional processes taking place at the basal running surface and dissipative mechanisms within the avalanche body. In this paper, we address this question by studying how kinetic energy is dissipated into heat in snow avalanches. In doing so we consider the effect of random granular fluctuations and collisions in depth-averaged snow avalanche models. We show that relationships between the size of the granular fluctuations and the energy dissipated by granular collisions can be obtained by studying the energy input required to maintain steady-state flows. The energy input for granular fluctuations comes from mechanisms operating in the basal layer. The kinetic energy of the flow at the basal layer is converted to granular agitation energy, a random kinetic energy, which in turn is dissipated as heat by both viscous shearing and inelastic collisions at higher levels in the avalanche profile. Thus granular fluctuations play a crucial role in understanding the total dissipation process. We apply our theoretical considerations to develop a constitutive model for dense snow avalanches and are able to accurately model steady-state velocity profiles of both snow-chute experiments and field measurements.

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Boundary conditions on continuum theories of granular flow

Cited by 17 publications

References 12 publications

Structural features in granular flows

Structural features in granular flows

Assessment of the kinetic–frictional model for dense granular flow

Fluctuation-dissipation relations for granular snow avalanches

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