Extended kinetic theory for granular flow over and within an inclined erodible bed

Berzi, Diego; Jenkins, James T.; Richard, Patrick

doi:10.1017/jfm.2019.1017

Cited by 45 publications

(66 citation statements)

References 62 publications

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“…2(c): 3) and the fact that g can be rewritten as I=μ ffiffiffiffiffiffi 3Θ p , we obtain g ∼ constant. This plateau regime is in line with kinetic theory where g ¼ F 1 ðϕÞ= ffiffi ffi 3 p F 2 ðϕÞ becomes almost constant for ϕ ≳ 0.49 [20][21][22][23]47,49]. In the 1=3 regime, Θ cancels out in the expression g ¼ I=μ ffiffiffiffiffiffi 3Θ p upon applying Eq.…”

supporting

confidence: 84%

Power-Law Scaling in Granular Rheology across Flow Geometries

Kim

Kamrin

2020

Phys. Rev. Lett.

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Based on discrete element method simulations, we propose a new form of the constitutive equation for granular flows independent of packing fraction. Rescaling the stress ratio μ by a power of dimensionless temperature Θ makes the data from a wide set of flow geometries collapse to a master curve depending only on the inertial number I. The basic power-law structure appears robust to varying particle properties (e.g., surface friction) in both 2D and 3D systems. We show how this rheology fits and extends frameworks such as kinetic theory and the nonlocal granular fluidity model.

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confidence: 84%

Power-Law Scaling in Granular Rheology across Flow Geometries

Kim

Kamrin

2020

Phys. Rev. Lett.

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“…Opportunities for further study exist in the more comprehensive application of granular theory and for the investigation into the origins of the Gaussian profile in addition to the influence of size and physical properties of the grains and channel. Other theories may prove useful in understanding the present flows, such as nonlocal rheologies or kinetic theory 27,[56][57][58][59][60] . Future work may consider the modelling of dense Poiseuille-type flow of non-buoyant grains.…”

Section: Discussionmentioning

confidence: 99%

“…Depth velocity profiles akin to exponential decay have been observed in the flowing region in addition to a creep flow deeper in the packing with filling fractions increasing with depth 20,21 while dry grains too have been seen to exhibit similar such flow profiles 22,23 . Treatments of such geometries have also been carried out using theories of granular rheology including those relating to the viscous number and kinetic theory [24][25][26][27][28][29][30][31] . Study of Poiseuillestyle flow of grains on the other hand is somewhat limited to being either driven by gravity, for instance dry grains falling through a channel 32,33 , or in the complete absence of it, where pressure-driven density-matched grains in suspension exhibit Bingham-style plug flow velocity profiles similar to yield stress fluids 26,34,35 .…”

Section: Introductionmentioning

confidence: 99%

Self-similar velocity profiles and mass transport of grains carried by fluid through a confined channel

et al. 2020

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Confined fluid-driven granular flows are present in a plethora of natural and industrial settings yet even the most fundamental of these are not completely understood. While widely-studied grain flows such as bed load and density-matched Poiseuille flow have been observed to exhibit exponential and Bingham style velocity profiles respectively, this work finds that a fluid-driven bed of non-buoyant grains filling a narrow horizontal channel -confined both from the sides and above -exhibits self-similar Gaussian velocity profiles. As the imposed flow rate is increased and the grain velocity increases, the Gaussian flow profiles penetrate deeper into the packing of the channel. Filling fractions were observed to also be self-similar and qualitatively consistent with granular theory relating to the viscous number I, which at a given position on the self-similar Gaussian curve is found to be generally constant regardless of imposed flow rate or velocity magnitude. An empirical description of the flow is proposed, and local velocity and filling fraction measurements were used to obtain local grain flux and accurately recover a total grain flow rate.

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“…It consists in an inclined 3D cell (see Fig. 1) similar to those used in [2,9,10,[21][22][23]20]. The angle between the horizontal and the main flow direction (x−direction) is called θ.…”

Section: Laterally Confined Chute Flowmentioning

confidence: 99%

Influence of lateral confinement on granular flows: comparison between shear-driven and gravity-driven flows

et al. 2020

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The properties of confined granular flows are studied through discrete numerical simulations. Two types of flows with different boundaries are compared: (i) gravitydriven flows topped with a free surface and over a base where erosion balances accretion (ii) shear-driven flows with a constant pressure applied at their top and a bumpy bottom moving at constant velocity. In both cases we observe shear localization over or/and under a creep zone. We show that, although the different boundaries induce different flow properties (e.g. shear localization of transverse velocity profiles), the two types of flow share common properties like (i) a power law relation between the granular temperature and the shear rate (whose exponent varies from 1 for dense flows to 2 for dilute flows) and (ii) a weakening of friction at the sidewalls which gradually decreases with the depth within the flow.

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Extended kinetic theory for granular flow over and within an inclined erodible bed

Cited by 45 publications

References 62 publications

Power-Law Scaling in Granular Rheology across Flow Geometries

Power-Law Scaling in Granular Rheology across Flow Geometries

Self-similar velocity profiles and mass transport of grains carried by fluid through a confined channel

Influence of lateral confinement on granular flows: comparison between shear-driven and gravity-driven flows

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