Stress tensor and elastic properties for hard and soft spheres

Dufty, James W.

doi:10.1007/s10035-011-0290-3

Cited by 9 publications

(3 citation statements)

References 13 publications

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“…29 The bulk viscosity of hard spheres has been of particular interest. [30][31][32] Kinetic theory treatments of real molecules based on a hard sphere approximation 33 predict that the bulk viscosity should be larger than the shear viscosity at liquidlike densities. For example, the Enskog formulas for the hard sphere shear and bulk viscosities are 30…”

Section: Introductionmentioning

confidence: 99%

Transport coefficients of the Lennard-Jones fluid close to the freezing line

Heyes

Dini

Costigliola

et al. 2019

The Journal of Chemical Physics

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Molecular dynamics simulations have been carried out along four Lennard-Jones (LJ) fluid isomorphs close to the freezing line, covering a temperature, T, in the range of 0.8-350 and a number density, ρ, in the range of 1.1-3.0 in LJ units. Analysis of the transport coefficients is via the Green-Kubo time correlation function method. The radial distribution function, percolation threshold connectivity distance, self-diffusion coefficient, and shear viscosity are shown to be invariant along an isomorph to a very good approximation when scaled with Rosenfeld's macroscopic units, although there are some small departures for T ≃ 1 and lower temperatures. The thermal conductivity is shown for the first time also to be isomorph invariant. In contrast, the Einstein and moment-based frequencies, and especially the bulk viscosity, η b , show poor isomorphic collapse at low T but not surprisingly tend to an "inverse power" potential limiting value in the high T limit. In the case of the bulk viscosity, the significant departures from invariance arise from oscillations in the pressure autocorrelation function at intermediate times, which scale for inverse power potential systems but not for the LJ case, at least in part, as the pressure and bulk elastic moduli are not isomorph invariant.

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Section: Introductionmentioning

confidence: 99%

Transport coefficients of the Lennard-Jones fluid close to the freezing line

Heyes

Dini

Costigliola

et al. 2019

The Journal of Chemical Physics

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“…For different opinions see for instance Refs. [4,12,[54][55][56][57]. On the other hand, since the structural and thermodynamic properties are approaching smoothly and continuously the HS limit [53,[58][59][60], similar behavior should be expected from the elastic properties [61].…”

Section: Discussionmentioning

confidence: 70%

Elastic properties of dense hard-sphere fluids

Khrapak

2019

Phys. Rev. E

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A new analysis of elastic properties of dense hard sphere (HS) fluids is presented, based on the expressions derived by Miller [J. Chem. Phys. 50, 2733(1969]. Important consequences for HS fluids in terms of sound waves propagation, Poisson's ratio, Stokes-Einstein relation, and generalized Cauchy identity are explored. Conventional expressions for high-frequency elastic moduli for simple systems with continuous and differentiable interatomic interaction potentials are known to diverge when approaching the HS repulsive limit. The origin of this divergence is identified here. It is demonstrated that these conventional expressions are only applicable for sufficiently soft interactions and should not be applied to HS systems. The reported results can be of interest in the context of statistical physics, physics of fluids, soft condensed matter, and granular materials. arXiv:1910.00338v1 [cond-mat.mtrl-sci]

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“…as the time integral over the shear stress autocorrelation whose evolution depends on the flow [29]. Here σ xy is the Kirkwood shear stress defined in terms of the particle positions and momenta [30]; V is the volume and T the temperature of a reference state. The average h•i ref is performed with respect to the unsheared reference system.…”

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confidence: 99%

Rheology of Inelastic Hard Spheres at Finite Density and Shear Rate

et al. 2018

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Considering a granular fluid of inelastic smooth hard spheres, we discuss the conditions delineating the rheological regimes comprising Newtonian, Bagnoldian, shear thinning, and shear thickening behavior. Developing a kinetic theory, valid at finite shear rates and densities around the glass transition density, we predict the viscosity and Bagnold coefficient at practically relevant values of the control parameters. The determination of full flow curves relating the shear stress σ to the shear rate _ γ and predictions of the yield stress complete our discussion of granular rheology derived from first principles.

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Stress tensor and elastic properties for hard and soft spheres

Cited by 9 publications

References 13 publications

Transport coefficients of the Lennard-Jones fluid close to the freezing line

Transport coefficients of the Lennard-Jones fluid close to the freezing line

Elastic properties of dense hard-sphere fluids

Rheology of Inelastic Hard Spheres at Finite Density and Shear Rate

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