Partially fluidized shear granular flows: Continuum theory and molecular dynamics simulations

Volfson, Dmitri; Tsimring, Lev S.; Aranson, Igor S.

doi:10.1103/physreve.68.021301

Cited by 102 publications

(126 citation statements)

References 38 publications

(92 reference statements)

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“…We hypothesize that to accurately capture the dynamics we have observed (including fluctuations and stopping acceleration), the physics of rapid fluidization and solidification must be included. Beyond discrete simulations [4], multi-phase modelling like that proposed in [28] might be applicable or perhaps such features will have to be captured by statistical models.…”

Section: Discussionmentioning

confidence: 99%

Scaling and dynamics of sphere and disk impact into granular media

2008

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Direct measurements of the acceleration of spheres and disks impacting granular media reveal simple power law scalings along with complex dynamics which bear the signatures of both fluid and solid behavior. The penetration depth scales linearly with impact velocity while the collision duration is constant for sufficiently large impact velocity. Both quantities exhibit power law dependence on sphere diameter and density, and gravitational acceleration. The acceleration during impact is characterized by two jumps: a rapid, velocity dependent increase upon initial contact and a similarly sharp, depth dependent decrease as the impacting object comes to rest. Examining the measured forces on the sphere in the vicinity of these features leads to a new experimentally based granular force model for collision. We discuss our findings in the context of recently proposed phenomenological models that capture qualitative dynamical features of impact but fail both quantitatively and in their inability to capture significant acceleration fluctuations that occur during penetration and which depend on the impacted material.

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Section: Discussionmentioning

confidence: 99%

Scaling and dynamics of sphere and disk impact into granular media

2008

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“…Recent theoretical models try to take into account the existence of this contact network through different approaches. Some models describe the flow as a mixture of solid and liquid phases [5] or try to account for the frictional contacts by adding a frictional term in collisional theories [6,7]. Other models consider the presence of arches in the flow [8,9] or account for some non local propagation of momentum through the contact network [10,11].…”

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confidence: 99%

Velocity Correlations in Dense Granular Flows

2004

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Velocity fluctuations of grains flowing down a rough inclined plane are experimentally studied. The grains at the free surface exhibit fluctuating motions, which are correlated over few grains diameters. The characteristic correlation length is shown to depend on the inclination of the plane and not on the thickness of the flowing layer. This result strongly supports the idea that dense granular flows are controlled by a characteristic length larger than the particle diameter.PACS numbers: 45.70.Mg, 83.50.Ax Dry cohesionless granular material can flow like a liquid, for example in an hourglass or on an inclined plane. However, the flow properties are not yet well understood and constitutive equations appropriate to describe the dense flow regime when particles are in close contact are still matter of debate [1,2]. One of the difficulty is that, in the dense regime, particles do not interact through binary collisions like in dilute and agitated granular gases [3,4]. They rather experience contact with several neighboring particles at the same time. The description of the multi-particles interactions is important in the development of constitutive equations. Recent theoretical models try to take into account the existence of this contact network through different approaches. Some models describe the flow as a mixture of solid and liquid phases [5] or try to account for the frictional contacts by adding a frictional term in collisional theories [6,7]. Other models consider the presence of arches in the flow [8,9] or account for some non local propagation of momentum through the contact network [10,11]. In this paper we will more specifically refer to a recent model proposed by Ertas and Halsey [12] to describe granular flows on an inclined plane. By introducing the idea of correlated motion of grains in clusters-like structures, they have been able by simple scaling arguments to recover some important results observed for flows down inclined plane. The experimental study presented in this paper is inspired by their approach, trying to evidence the existence of correlated motions in granular flows down inclined planes.The inclined plane configuration is obtained when a granular layer of thickness h flows down a rough surface inclined at an angle θ (Fig. 1). Experiments [1,13] and numerical simulations [14,15] have revealed two important results. First, for a given inclination θ, a minimum thickness h stop (θ) exists below which no flow is possible. This thickness is evidenced by the deposit remaining on the plane once the flow stops. Second, the variation of the depth averaged velocity u with the inclination θ and thickness h appears to be linked to the deposit function h stop (θ) through a flow rule:where g is gravity and β is a constant equal to 0.13 for spheres. The fact that the influence of θ on the flow velocity comes into play through the deposit function h stop (θ) is not straightforward and could be simply the result of a coincidence [7]. However, an interesting interpretation of relation 1 has been pro...

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“…In initial studies with weak dissipation and dynamic friction [26] near φ rcp , we found that t l is similar to that for systems with dissipation and no dynamic friction. However, more extensive studies of dynamic as well as static friction are required to make a definitive statement about the influence of friction on the long-time stability of nonlinear velocity profiles [11,12]. Second, most experimental studies of velocity profiles in granular systems are performed in (angular) Couette, not planar shear cells.…”

Section: Future Directionsmentioning

confidence: 99%

“…Thus, molecular dynamics simulations are often employed to study dense granular shear flows, for example in Refs. [10,11,12,13]. We choose a similar plan of attack and perform molecular dynamics simulations of model frictionless dense granular systems undergoing boundary-driven planar shear flow in 2D.…”

Section: Introductionmentioning

confidence: 99%

Stabilization of nonlinear velocity profiles in athermal systems undergoing planar shear flow

O’Hern

Kondic

2005

Phys. Rev. E

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We perform molecular dynamics simulations of model granular systems undergoing boundarydriven planar shear flow in two spatial dimensions with the goal of developing a more complete understanding of how dense particulate systems respond to applied shear. In particular, we are interested in determining when these systems will possess linear velocity profiles and when they will develop highly localized velocity profiles in response to shear. In previous work on similar systems we showed that nonlinear velocity profiles form when the speed of the shearing boundary exceeds the speed of shear waves in the material. However, we find that nonlinear velocity profiles in these systems are unstable at very long times. The degree of nonlinearity slowly decreases in time; the velocity profiles become linear when the granular temperature and density profiles are uniform across the system at long times. We measure the time t l required for the velocity profiles to become linear and find that t l increases as a power-law with the speed of the shearing boundary and increases rapidly as the packing fraction approaches random close packing. We also performed simulations in which differences in the granular temperature across the system were maintained by vertically vibrating one of the boundaries during shear flow. We find that nonlinear velocity profiles form and are stable at long times if the difference in the granular temperature across the system exceeds a threshold value that is comparable to the glass transition temperature in an equilibrium system at the same average density. Finally, the sheared and vibrated systems form stable shear bands, or highly localized velocity profiles, when the applied shear stress is lowered below the yield stress of the static part of the system.

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Partially fluidized shear granular flows: Continuum theory and molecular dynamics simulations

Cited by 102 publications

References 38 publications

Scaling and dynamics of sphere and disk impact into granular media

Scaling and dynamics of sphere and disk impact into granular media

Velocity Correlations in Dense Granular Flows

Stabilization of nonlinear velocity profiles in athermal systems undergoing planar shear flow

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