Shear-induced diffusion in dense granular fluids

Rognon, Pierre; Macaulay, Matthew

doi:10.1039/d1sm00422k

“…In a dense flow regime, unlike its dilute counterpart, grains experience multiple and enduring contacts at all times without the possibility of free flights during an induced shear deformation. This leads the kinematic field of dense granular flows to exhibit complex spatiotemporal correlations and spontaneous formation of quasi-rigid clusters in the flow ( 6 , 7 ). The key to understanding the origins of such correlations is the characterization of interparticle force networks as the backbone of the stability and rigidity of amorphous materials.…”

Section: Introductionmentioning

confidence: 99%

Emergence of rigidity percolation in flowing granular systems

Dashti,

Saberi,

Rahbari

et al. 2023

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Jammed granular media and glasses exhibit spatial long-range correlations as a result of mechanical equilibrium. However, the existence of such correlations in the flowing matter, where the mechanical equilibrium is unattainable, has remained elusive. Here, we investigate this problem in the context of the percolation of interparticle forces in flowing granular media. We find that the flow rate introduces an effective long-range correlation, which plays the role of a relevant perturbation giving rise to a spectrum of varying exponents on a critical line as a function of the flow rate. Our numerical simulations along with analytical arguments predict a crossover flow rate γ ˙ c ≃ 1 0 − 5 below which the effect of induced disorder is weak and the universality of the force chain structure is shown to be given by the standard rigidity percolation. We also find a power-law behavior for the critical exponents with the flow rate γ ˙ > γ ˙ c .

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“…We focus on the dense granular flow regime, characterized by the inertial number ranging approximately from to , to avoid possible non-local effects for (Kim & Kamrin 2020) and the dilute, collisional flow regime for (Rognon & Macaulay 2021). To achieve this range of , we use s for Pa and s for Pa.…”

Section: Methodsmentioning

confidence: 99%

“…For dense granular flows, the velocity fluctuation (or, here, the square root of the granular temperature) follows a general scaling law, where is a system-dependent parameter (da Cruz et al. 2005; Kim & Kamrin 2020; Bancroft & Johnson 2021; Rognon & Macaulay 2021). Recent DEM simulations (Kim & Kamrin 2020; Bancroft & Johnson 2021) suggest for three-dimensional uniform shear flows, which approximately matches the slope of our uncontrolled (as well as weakly controlled) flow results in figure 10( a ).…”

Section: Figure 10mentioning

confidence: 99%

Drag force in granular shear flows: regimes, scaling laws and implications for segregation

Jing

¹

,

Ottino

²

,

Umbanhowar

³

et al. 2022

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The drag force on a spherical intruder in dense granular shear flows is studied using discrete element method simulations. Three regimes of the intruder dynamics are observed depending on the magnitude of the drag force (or the corresponding intruder velocity) and the flow inertial number: a fluctuation-dominated regime for small drag forces; a viscous regime for intermediate drag forces; and an inertial (cavity formation) regime for large drag forces. The transition from the viscous regime (linear force-velocity relation) to the inertial regime (quadratic force-velocity relation) depends further on the inertial number. Despite these distinct intruder dynamics, we find a quantitative similarity between the intruder drag in granular shear flows and the Stokesian drag on a sphere in a viscous fluid for intruder Reynolds numbers spanning five orders of magnitude. Beyond this first-order description, a modified Stokes drag model is developed that accounts for the secondary dependence of the drag coefficient on the inertial number and the intruder size and density ratios. When the drag model is coupled with a segregation force model for intruders in dense granular flows, it is possible to predict the velocity of gravity-driven segregation of an intruder particle in shear flow simulations.

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“…Plastic deformation of sediment around burrowing benthic organisms 39 , 40 is a possible BNE driving mechanism, because the deformation field includes a vertical gradient of horizontal displacement around burrow tips, which is analogous to the horizontal shearing used in many BNE experiments 6 , 41 . In this case, both the diffusivity and the segregation velocity are proportional to the shear rate 6 , 42 . Size segregation might also be driven by microbial-induced bubble formation in organic-rich sediments 43 .…”

Section: Microtektite Profilesmentioning

confidence: 99%

Multiscale Brazil nut effects in bioturbated sediment

Savranskaia

¹

,

Egli

²

,

Valet

³

2022

Sci Rep

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Size segregation in granular materials is a universal phenomenon popularly known as the Brazil nut effect (BNE), from the tendency of larger nuts to end on the top of a shaken container. In nature, fast granular flows bear many similarities with well-studied mixing processes. Instead, much slower phenomena, such as the accumulation of ferromanganese nodules (FN) on the seafloor, have been attributed to the BNE but remain essentially unexplained. Here we document, for the first time, the BNE on sub-millimetre particles in pelagic sediment and propose a size segregation model for the surface mixed layer of bioturbated sediments. Our model explains the size distribution of FN seeds, pointing to a uniform segregation mechanism over sizes ranging from < 1 mm to > 1 cm, which does not depend on selective ingestion by feeding organisms. In addition to explaining FN nucleation, our model has important implications for microfossil dating and the mechanism underlying sedimentary records of the Earth’s magnetic field.

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Shear-induced diffusion in dense granular fluids

Abstract: Granular materials are comprised of solid, athermal grains. Whilst immune to thermal motion, these grains move and diffuse when they undergo shear deformation. Here we introduce this process of shear-induced...

Cited by 14 publications

References 36 publications

Emergence of rigidity percolation in flowing granular systems

Emergence of rigidity percolation in flowing granular systems

Drag force in granular shear flows: regimes, scaling laws and implications for segregation

Multiscale Brazil nut effects in bioturbated sediment

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