Generalized transport coefficients for hard spheres

Alley, William E.; Alder, B. J.

doi:10.1103/physreva.27.3158

Cited by 244 publications

(120 citation statements)

References 20 publications

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“…As is well known, there are many indications that ordinary hydrodynamics breaks down at finite wavevectors: in the present context, there have been in fact several items of MD evidence [16,17,18] that η(q) is a rapidly decreasing function, which for large q eventually approaches the free-particle result…”

Section: The Hydrodynamic Approximation C T (Q T) (βM) −1 Exp[(−η/nmmentioning

confidence: 63%

“…On a tentative basis, one may accept for the generalized viscosity the simple empirical form η(q) ∼ η[1 + A 2 q 2 ] −1 proposed by Alley and Alder [16] for dense fluids of hard spheres of diameter d at not too high wavevectors. Inserting this expression into equation (4) we obtain (6) which shows that the actual diffusion coefficient should indeed exceed D H .…”

Section: The Hydrodynamic Approximation C T (Q T) (βM) −1 Exp[(−η/nmmentioning

confidence: 99%

“…Inserting this expression into equation (4) we obtain (6) which shows that the actual diffusion coefficient should indeed exceed D H . From the estimate A 0.3d [16] and some reasonable assumptions, one can also obtain a remarkably good (even if somewhat fortuitous) agreement for D [19].…”

Section: The Hydrodynamic Approximation C T (Q T) (βM) −1 Exp[(−η/nmmentioning

confidence: 99%

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The generalized Stokes - Einstein relation for liquid sodium

Balucani¹,

Kahl

1997

J. Phys.: Condens. Matter

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Abstract. We show that a microscopic generalization of the Stokes-Einstein relation between the diffusion and shear viscosity coefficients, previously tested in simple liquids near melting, has a much wider range of application. The practical validity of the approach is accurately checked by performing extensive computer simulations in liquid sodium at temperatures ranging from 403 K to 1003 K.Transport properties such as the diffusion and shear viscosity coefficients are widely used in any macroscopic description of time-dependent phenomena in dense fluids and liquids such as, for example, ordinary Navier-Stokes hydrodynamics. These 'coarse-grained' approaches are, however, unable to predict in different thermodynamic states the actual magnitude of the transport coefficients, which depends on a variety of underlying microscopic events (comprising, e.g., collisions, vortices and particle trapping). In the last decade or so, considerable progress in the microdynamics of the liquid state has however been achieved by the development of comprehensive frameworks combining both kinetic and mode-coupling arguments [1,2]. In particular, by these approaches quite satisfactory results have been obtained for the dynamics (and consequently for the transport coefficients) of several simple liquids near freezing as well as in supercooled states [1]. In comparison, less attention has instead been devoted to realistic liquids at relatively high temperatures, where the tests of the above general framework are limited, and the results still somewhat controversial.In this work we shall explicitly consider the problem of 'predicting' the diffusion coefficient D of a simple liquid in a wide range of thermodynamic states. Specifically, we shall consider the case of molten sodium, an appropriate benchmark system because of the stability of its liquid phase over a rather large temperature interval (from the melting point at T m ∼ 371 K up to the boiling point at T b ∼ 1154 K). Although our approach is less general, it is much simpler (and equally reliable) than those referred to in the above, as will be clear in the following. We shall also compare the theoretical results for D with the experimental findings [3,4]. In order to test the validity of the predictions as accurately as possible, we have also performed a number of subsidiary molecular dynamics (MD) simulations in a model system which mimics in a rather realistic way the features of liquid Na for the properties under consideration. The effective pair potentials acting between the Na atoms are based on pseudopotential theory: we have used the Ashcroft empty-core pseudopotential [5] along with the Ichimaru-Utsumi expression for the local field correction [6]. The only parameter in the pseudopotential is the core radius, for which we have taken the usual value reported in the literature (0.9049Å) [7]. For state I (cf.

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Section: The Hydrodynamic Approximation C T (Q T) (βM) −1 Exp[(−η/nmmentioning

confidence: 63%

Section: The Hydrodynamic Approximation C T (Q T) (βM) −1 Exp[(−η/nmmentioning

confidence: 99%

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The generalized Stokes - Einstein relation for liquid sodium

Balucani¹,

Kahl

1997

J. Phys.: Condens. Matter

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“…3 to the same empirical Padé approximant used originally for MD simulations of 3D liquids of hard spheres [13] and water [16]. This approximant, η(k) ∝ (1 + αk 2 ) −1 , apparently has never been applied for 2D liquids.…”

mentioning

confidence: 99%

“…Besides η(ω), the wavenumber-dependent viscosity, η(k), has been used by theorists to quantify the viscoelastic character [13][14][15][16][17]. They have recently developed ways of computing η(k) from the trajectories of random motion of molecules [16,17].…”

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confidence: 99%

Viscoelasticity of 2D Liquids Quantified in a Dusty Plasma Experiment

2010

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The viscoelasticity of two-dimensional liquids is quantified in an experiment using a dusty plasma. An experimental method is demonstrated for measuring the wavenumber-dependent viscosity, η(k), which is a quantitative indicator of viscoelasticity. Using an expression generalized here to include friction, η(k) is computed from the transverse current autocorrelation function (TCAF), which is found by tracking random particle motion. The TCAF exhibits an oscillation that is a signature of elastic contributions to viscoelasticity. Simulations of a Yukawa liquid are consistent with the experiment.

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Simulation by Molecular Dynamics

Alder

Ladd

2003

Digital Encyclopedia of Applied Physics

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Generalized transport coefficients for hard spheres

Cited by 244 publications

References 20 publications

The generalized Stokes - Einstein relation for liquid sodium

The generalized Stokes - Einstein relation for liquid sodium

Viscoelasticity of 2D Liquids Quantified in a Dusty Plasma Experiment

Simulation by Molecular Dynamics

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