Rheology of bidisperse granular mixtures via 
event-driven simulations

Alam, Meheboob; Luding, Stefan

doi:10.1017/s002211200200263x

Cited by 92 publications

(100 citation statements)

References 52 publications

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“…In addition to these effects, the shearing motion induces a strong anisotropy in the nor-mal stresses, namely P xx (t) > nT (t) > P zz (t) P yy (t). In other words, a breakdown of the energy equipartition occurs, whereby the "temperature" associated with the degree of freedom parallel to the fluid motion is significantly larger than that associated with the other two degrees of freedom, as already observed in previous studies [14,15,16,17,20,22,24,26,28,30,36,38].…”

Section: Discussionsupporting

confidence: 68%

“…The uniform (or simple) shear flow (USF) is perhaps the nonequilibrium state most widely studied, both for granular [6,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40] and conventional [41] gases. In this state the gas is enclosed between two infinite parallel planes located at y = −L/2 and y = +L/2 and in relative motion with velocities −U/2 and +U/2, respectively, along the xdirection.…”

Section: Uniform Shear Flowmentioning

confidence: 99%

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Uniform shear flow in dissipative gases: Computer simulations of inelastic hard spheres and frictional elastic hard spheres

Astillero

Santos

2005

Phys. Rev. E

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In the preceding paper (cond-mat/0405252), we have conjectured that the main transport properties of a dilute gas of inelastic hard spheres (IHS) can be satisfactorily captured by an equivalent gas of elastic hard spheres (EHS), provided that the latter are under the action of an effective drag force and their collision rate is reduced by a factor (1 + α)/2 (where α is the constant coefficient of normal restitution). In this paper we test the above expectation in a paradigmatic nonequilibrium state, namely the simple or uniform shear flow, by performing Monte Carlo computer simulations of the Boltzmann equation for both classes of dissipative gases with a dissipation range 0.5 ≤ α ≤ 0.95 and two values of the imposed shear rate a. It is observed that the evolution toward the steady state proceeds in two stages: a short kinetic stage (strongly dependent on the initial preparation of the system) followed by a slower hydrodynamic regime that becomes increasingly less dependent on the initial state. Once conveniently scaled, the intrinsic quantities in the hydrodynamic regime depend on time, at a given value of α, only through the reduced shear rate a * (t) ∝ a/ T (t), until a steady state, independent of the imposed shear rate and of the initial preparation, is reached. The distortion of the steady-state velocity distribution from the local equilibrium state is measured by the shear stress, the normal stress differences, the cooling rate, the fourth and sixth cumulants, and the shape of the distribution itself. In particular, the simulation results seem to be consistent with an exponential overpopulation of the high-velocity tail. These properties are common to both the IHS and EHS systems. In addition, the EHS results are in general hardly distinguishable from the IHS ones if α 0.7, so that the distinct signature of the IHS gas (higher anisotropy and overpopulation) only manifests itself at relatively high dissipations.

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Section: Discussionsupporting

confidence: 68%

Section: Uniform Shear Flowmentioning

confidence: 99%

Uniform shear flow in dissipative gases: Computer simulations of inelastic hard spheres and frictional elastic hard spheres

Astillero

Santos

2005

Phys. Rev. E

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“…For detailed results on the quantities pressure, shear viscosity and granular energy, and for their comparison with kinetic theory predictions, we refer to our recent study 24 . Here, we will mainly focus on the behaviour of the first normal stress difference and its kinetic and collisional components.…”

Section: Resultsmentioning

confidence: 99%

First normal stress difference and crystallization in a dense sheared granular fluid

Alam

Luding

2003

Physics of Fluids

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In the last decade, a lot of research activity took place to unveil the properties of granular materials 1,2 , primarily because of their industrial importance, but also due to their fascinating properties. This has unraveled many interesting and so far unresolved phenomena (for example, clustering, size-segregation, avalanches, the coexistence of gas, liquid and solid, etc.). Under highly excited conditions, granular materials behave as a fluid, with prominent non-Newtonian properties, like the normal stress differences 3 . While the normal stress differences are of infinitesimal magnitudes in a simple fluid (e.g. air and water), they can be of the order of its isotropic pressure in a dilute granular gas 4 . From the modelling viewpoint, the presence of such large normal-stress differences readily calls for higher-order constitutive models 5,6 even at the minimal level.Studying the non-Newtonian behaviour is itself an important issue, since the normal stresses are known to be the progenitors of many interesting and unique flow-features (e.g. rod-climbing or Weissenberg-effect, die-swelling, secondary flows, etc. 7 ) in non-Newtonian fluids. Also, normal stresses can support additional instability modes (for example, in polymeric fluids and suspensions 7−10 , which might, in turn, explain some flow-features of granular fluids. For example, particle-clustering 11−13 has recently been explained from the instability-viewpoint using the standard Newtonian model for the stress tensor 12,14,15 The kinetic theory of Jenkins & Richman 16 first showed that the anisotropy in the second moment of the fluctuation velocities, due to the inelasticity of particle collisions, is responsible for such normal stress behaviour. They predicted that the first normal stress difference (defined as N 1 = (Π xx − Π yy )/p, where Π xx and Π yy are the streamwise and the transverse components of the stress deviator, respectively, and p is the isotropic pressure, see section IIB) is maximum in the dilute limit, decreases in magnitude with density, and eventually approaches zero in the dense limit. Goldhirsch & Sela 4 later showed that the normal stress differences appear only at the Burnett-order-description of the Chapman-Enskog expansion of the Boltzmann equation. Their work has clearly established that the origin of this effect (in the dilute limit) is universal in both atomic and granular fluids, with inelasticity playing the role of a magnifier and thus making it a sizeable effect in granular fluids. While the source of the normal stress differences in the dilute limit has been elucidated both theoretically and by simulation, its dense counterpart has not received similar attention so far. This is an important limit since the onset of dilatancy (volume expansion due to shear 17,18 ), crystallization, etc. occur in the dense regime, which in turn would influence the normal stress differences.Previous hard-sphere simulations 19,3,11 did look at the normal stress differences, but they did not probe the dense limit in a systematic way. The...

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“…* The steady USF has been extensively studied. Molecular dynamics and Monte Carlo simulations [4,5,6,7,8,9,10] have been performed to measure the dependence of the stress tensor on the density and inelasticity. On the theoretical side, Lun et al [11] have obtained the rheological properties of a dense gas for small inelasticity, while Jenkins and Richman [12] have used a maximum-entropy approximation to solve the Enskog equation.…”

Section: Introductionmentioning

confidence: 99%

Inherent rheology of a granular fluid in uniform shear flow

2004

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In contrast to normal fluids, a granular fluid under shear supports a steady state with uniform temperature and density since the collisional cooling can compensate locally for viscous heating. It is shown that the hydrodynamic description of this steady state is inherently non-Newtonian. As a consequence, the Newtonian shear viscosity cannot be determined from experiments or simulation of uniform shear flow. For a given degree of inelasticity, the complete nonlinear dependence of the shear viscosity on the shear rate requires the analysis of the unsteady hydrodynamic behavior. The relationship to the Chapman-Enskog method to derive hydrodynamics is clarified using an approximate Grad's solution of the Boltzmann kinetic equation.

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Rheology of bidisperse granular mixtures via event-driven simulations

Cited by 92 publications

References 52 publications

Uniform shear flow in dissipative gases: Computer simulations of inelastic hard spheres and frictional elastic hard spheres

Uniform shear flow in dissipative gases: Computer simulations of inelastic hard spheres and frictional elastic hard spheres

First normal stress difference and crystallization in a dense sheared granular fluid

Inherent rheology of a granular fluid in uniform shear flow

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