Velocity correlations in dense granular shear flows: Effects on energy dissipation and normal stress

Mitarai, Namiko; Nakanishi, Hiizu

doi:10.1103/physreve.75.031305

Cited by 79 publications

(97 citation statements)

References 48 publications

(63 reference statements)

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“…Building a theory based on first principles for flows of more realistic particles has proved a difficult task. Hence, ad hoc, but physically sound, modifications of classic kinetic theory have been proposed to take into account velocity correlation among the particles at large solid volume fractions [6][7][8][9][10][11][12], particle surface friction [13,14], and finite stiffness [15]. Recently [16,17], discrete element simulations on simple shear flows of cylinders at different solid volume fractions have been performed to study the influence of length-to-diameter (aspect) ratio, coefficient of collisional restitution, surface friction, and stiffness on the stresses, highlighting differences and similarities with the predictions of the kinetic theory for spheres.…”

Section: Introductionmentioning

confidence: 99%

Stresses and orientational order in shearing flows of granular liquid crystals

et al. 2016

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We perform discrete element simulations of homogeneous shearing of frictionless cylinders and show that the particles are characterized by orientational order and form a granular liquid crystal. For elongated and flat cylinders, the alignment is in the plane of shearing, while cylinders having an aspect ratio equal to 1 and 0.8 show no orientational order. We show that the particle pressure is insensitive to the cylinder aspect ratio and well predicted by the kinetic theory of granular gases, with a singularity in the radial distribution function at contact different from that for frictionless spheres. The numerical results quantitatively agree with physical experiments on different geometries. The particle shear stress is affected by orientational anisotropy. We postulate that, for frictionless cylinders, the viscosity is roughly due to the motion of the orientationally disordered fraction of the particles, and show that it is proportional, through the order parameter, to the expression of kinetic theory. Finally, we suggest that the orientational order is the result of the competing effects of the shear rate, which induces alignment, and the granular temperature, which ramdomizes.

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Section: Introductionmentioning

confidence: 99%

Stresses and orientational order in shearing flows of granular liquid crystals

et al. 2016

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“…Making various assumptions [14,66,67], the constitutive relations and transport coefficients (occurring within the macroscopic equations for mass, momentum, and energy balance) can be derived [14,67,68]. Among these assumptions are scale separation [66,69], molecular chaos [70,71] velocity correlations [72], isotropy and disorder [73,74], binary collisions [70,75,76], and many others, which will not be discussed in detail here.…”

Section: Hydrodynamicsmentioning

confidence: 99%

Towards dense, realistic granular media in 2D

Luding¹

2009

Nonlinearity

133

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The development of an applicable theory for granular matter -with both qualitative and quantitative value -is a challenging prospect, given the multitude of states, phases and (industrial) situations it has to cover. Given the general balance equations for mass, momentum, and energy, the limiting case of dilute and almost elastic granular gases, where kinetic theory works perfectly well, is the starting point.In most systems, low density coexists with very high density, where the latter is an open problem for kinetic theory. Furthermore, many additional non-linear phenomena and material properties are important in realistic granular media, involving, e.g.: (i) multi-particle interactions and elasticity (ii) strong dissipation, (iii) friction, (iv) long-range forces and wet contacts (v) wide particle size-distributions, and (vi) various particle shapes. Note that, while some of these issues are more relevant for high density, others are important for both low and high densities; some of them can be dealt with by means of kinetic theory, some can not. This paper is a review of recent progress towards more realistic models for dense granular media in 2D, even though most of the observations, conclusions, and corrections given are qualitatively true also in 3D. Starting from an elastic, frictionless and monodisperse hard sphere gas, the (continuum) balance equations of mass, momentum and energy are given. The equation of state, the (Navier-Stokes level) transport coefficients and the energy-density dissipation rate are considered. Several corrections are applied to those constitutive material laws -one by one -in order to account for the realistic physical effects and properties listed above.

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“…2. In this figure, we also plot the result of MD for hard spheres [8]. We find a remarkable agreement between MCT and MD for ϕ < 0.60 by using the shift of the density in MCT as ϕ → ϕ eff ≡ ϕ + ∆ϕ with ∆ϕ = 0.11.…”

Section: Numerical Calculationsmentioning

confidence: 69%

“…One of the remarkable achievements is the extension of the Boltzmann-Enskog kinetic theory to inelastic hard disks and spheres [5], which stimulated the following works [6,7]. However, it has been recognized that the kinetic theory breaks down at high densities with volume fraction ϕ > 0.5 [8,9], since there exists correlated motions of grains. Thus, a liquid theory which contains the effect of granular correlations is expected to be constructed for the regime 0.5 < ϕ < ϕ J .…”

Section: Introductionmentioning

confidence: 99%

Rheology of dense sheared granular liquids (Invited)

Suzuki¹,

Hayakawa²

2014

AIP Conference Proceedings

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Abstract. The rheology of dense sheared granular liquids is investigated based on the mode-coupling theory (MCT). This extended MCT includes correlations for the density-current mode as well as the density-density correlation mode, and a selfconsistent coupling equation for the energy balance condition. The extended MCT exhibits disappearance of the two-step relaxation of the density-density correlation function, and also successfully reproduces the density dependence of the shear viscosity for volume fractions between 0.50 and 0.60, if we shift the density. However, it predicts unphysical tendency for the granular temperature. The cause of this drawback and the possibilities of its amendment are discussed.

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Velocity correlations in dense granular shear flows: Effects on energy dissipation and normal stress

Cited by 79 publications

References 48 publications

Stresses and orientational order in shearing flows of granular liquid crystals

Stresses and orientational order in shearing flows of granular liquid crystals

Towards dense, realistic granular media in 2D

Rheology of dense sheared granular liquids (Invited)

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