Molecular-dynamics investigation of tracer diffusion in a simple liquid: Test of the Stokes-Einstein law

Ould-Kaddour, F.; Levesque, D.

doi:10.1103/physreve.63.011205

Cited by 107 publications

(123 citation statements)

References 23 publications

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“…In the Brownian limit (tracer limit) of a binary isotopic mixture (only one particle of the heavy component), the StokesEinstein relation was also verified to hold in the form [5,7] …”

Section: E Stokes-einstein Relationmentioning

confidence: 99%

“…Several studies have been devoted to the Brownian limit [1,2,4,6,8,11], some of them especially to the question, for which range of tracer mass and size this purely hydrodynamic relation also holds on the microscopic level [5,7]. Depending on whether the mass is changed at constant size ratio or not, the SE relation was found to hold for mass ratios larger than 10 [5] and larger than 100 [7], respectively. Above these values, the tracer diffusion was considered mass-independent.…”

Section: Introductionmentioning

confidence: 99%

“…The dynamic properties of binary fluid systems where one particle species differs from the other only in size, mass or both of these parameters have been the subject of a large number of studies during the last years [1,2,3,4,5,6,7,8,9,10,11,12]. The increasing interest is, on the one hand, due to the fact that such systems serve as simple models for colloids and micellar solutions, which are of prime importance in many scientific areas such as biology or biochemistry, on the other hand it is sparked by the rapidly growing capabilities of modern computer hardware which allows us to investigate parameter ranges and system sizes that were not accessible before.…”

Section: Introductionmentioning

confidence: 99%

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Concentration and mass dependence of transport coefficients and correlation functions in binary mixtures with high mass asymmetry

et al. 2009

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Correlation functions and transport coefficients of self-diffusion and shear viscosity of a binary Lennard-Jones mixture with components differing only in their particle mass are studied up to high values of the mass ratio µ, including the limiting case µ = ∞, for different mole fractions x. Within a large range of x and µ the product of the diffusion coefficient of the heavy species D2 and the total shear viscosity of the mixture ηm is found to remain constant, obeying a generalized Stokes-Einstein relation. At high liquid density, large mass ratios lead to a pronounced cage effect that is observable in the mean square displacement, the velocity autocorrelation function and the van Hove correlation function.

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“…In the Brownian limit (tracer limit) of a binary isotopic mixture (only one particle of the heavy component), the StokesEinstein relation was also verified to hold in the form [5,7] …”

Section: E Stokes-einstein Relationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Concentration and mass dependence of transport coefficients and correlation functions in binary mixtures with high mass asymmetry

et al. 2009

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“…In fact, this approach is based on "macroscopic" liquid state assumptions and is therefore, a priori, limited to large particle immersed in a liquid. Nevertheless, it has been shown that the definition of a Stokes-Einstein like law at this scale makes sense [39][40] with an appropriate friction factor, ξ. In addition, the final relation of Eq.…”

Section: Simple Fluidsmentioning

confidence: 99%

Thermodiffusion in model nanofluids by molecular dynamics simulations

Galliéro

Volz

2008

The Journal of Chemical Physics

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In this work, a new algorithm is proposed to compute single particle (infinite dilution) thermodiffusion using Non-Equilibrium Molecular Dynamics simulations through the estimation of the thermophoretic force that applies on a solute particle. This scheme is shown to provide consistent results for simple Lennard-Jones fluids and for model nanofluids (spherical non-metallic nanoparticles + Lennard-Jones fluid) where it appears that thermodiffusion amplitude, as well as thermal conductivity, decrease with nanoparticles concentration. Then, in nanofluids in the liquid state, by changing the nature of the nanoparticle (size, mass and internal stiffness) and of the solvent (quality and viscosity) various trends are exhibited. In all cases the single particle thermodiffusion is positive, i.e. the nanoparticle tends to migrate toward the cold area. The single particle thermal diffusion 2 coefficient is shown to be independent of the size of the nanoparticle (diameter of 0.8 to 4 nm), whereas it increases with the quality of the solvent and is inversely proportional to the viscosity of the fluid. In addition, this coefficient is shown to be independent of the mass of the nanoparticle and to increase with the stiffness of the nanoparticle internal bonds. Besides, for these configurations, the mass diffusion coefficient behavior appears to be consistent with a Stokes-Einstein like law.3

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“…in colloidal suspensions. These non-Markovian effects arise because of momentum conservation, leading to slow hydrodynamic modes that manifest themselves as long-time tails in the velocity autocorrelation function (VACF) [3][4][5][6]. Recent experiments have demonstrated that the force exerted by the bath includes a deterministic component [7], well described for large colloidal spheres by the Basset-Boussinesq (BB) hydrodynamic force [8,9]:…”

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confidence: 99%

Molecular Hydrodynamics from Memory Kernels

et al. 2016

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The memory kernel for a tagged particle in a fluid, computed from molecular dynamics simulations, decays algebraically as t −3/2 . We show how the hydrodynamic Basset-Boussinesq force naturally emerges from this long-time tail and generalize the concept of hydrodynamic added mass. This mass term is negative in the present case of a molecular solute, at odds with incompressible hydrodynamics predictions. We finally discuss the various contributions to the friction, the associated time scales and the cross-over between the molecular and hydrodynamic regimes upon increasing the solute radius.The Brownian motion of a particle in a fluid finds its origin in the fluctuating force exerted by the solvent molecules on the solute. It has long been known that the canonical description of this random force by a Gaussian Markov process is only valid in limiting cases. Even in the limit where the solute is much heavier than the solvent particles, for which multiple time-scale analysis allows to recover the Smoluchowski equation for diffusion [1], nonMarkovian effects are expected when the mass density ratio is close to unity [2] -a situation which is rather the rule than the exception e.g. in colloidal suspensions. These non-Markovian effects arise because of momentum conservation, leading to slow hydrodynamic modes that manifest themselves as long-time tails in the velocity autocorrelation function (VACF) [3][4][5][6]. Recent experiments have demonstrated that the force exerted by the bath includes a deterministic component [7], well described for large colloidal spheres by the Basset-Boussinesq (BB) hydrodynamic force [8,9]:where R is the sphere radius, η the solvent viscosity and ρ 0 its mass density. The first term is the usual Stokes friction. The other two account for the inertia of the displaced fluid and involve a finite added mass m BB 0 = 2 3 πR 3 ρ 0 and a viscosity-dependent retarded component describing the transient effects of momentum diffusion in the solvent. While continuous descriptions of steady-state flows appear to hold down to the nanoscale [10][11][12], possibly at the price of adapting the hydrodynamic radius R or the boundary conditions [13], their validity for the transient regimes should be questioned. The implicit assumption of a separation of time scales between the solvent and solute dynamics, which holds a priori for colloidal particles [14], is expected to break down with smaller solutes such as nanoparticles or biomolecules.Here we address the fundamental questions that arise when approaching the regime of molecular solutes by computing directly from Molecular Dynamics (MD) simulations the memory kernel and the random noise of the Generalized Langevin Equation (GLE). A novel algorithm based on the Mori-Zwanzig formalism with high numerical stability allows us to explore long time scales for the first time. We consider the extreme case of a tagged particle (identical masses and sizes) in a pure supercritical fluid.By examining the long-time behaviour of the memory kernel, we demonstrate the gen...

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Molecular-dynamics investigation of tracer diffusion in a simple liquid: Test of the Stokes-Einstein law

Cited by 107 publications

References 23 publications

Concentration and mass dependence of transport coefficients and correlation functions in binary mixtures with high mass asymmetry

Concentration and mass dependence of transport coefficients and correlation functions in binary mixtures with high mass asymmetry

Thermodiffusion in model nanofluids by molecular dynamics simulations

Molecular Hydrodynamics from Memory Kernels

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