Diffusion and viscosity equations of state for a Lennard-Jones fluid obtained from molecular dynamics simulations

Rowley, Richard L.; Painter, M. M.

doi:10.1007/bf02575252

Cited by 134 publications

(157 citation statements)

References 10 publications

Supporting

Mentioning

143

Contrasting

Order By: Relevance

“…Time averages of the shear stress σ 12 are plotted against the strain rate s. We notice a linear relation, and define the shear viscosity η = − σ12 s . Fitting the data, we find viscosity (with standard deviation) η = 1.2175 ± 0.0085 for γ = 0.1 whose confidence interval overlaps with the value η = 1.142 ± 0.087 reported in [22], Table IV. The algorithm successfully simulates a system out of equilibrium, and the computed viscosity is consistent with previous computations for Lennard-Jones fluids.…”

Section: Rapide Notesupporting

confidence: 79%

See 1 more Smart Citation

Derivation of Langevin dynamics in a nonzero background flow field

et al. 2013

View full text Add to dashboard Cite

Abstract.We propose a derivation of a nonequilibrium Langevin dynamics for a large particle immersed in a background flow field. A single large particle is placed in an ideal gas heat bath composed of point particles that are distributed consistently with the background flow field and that interact with the large particle through elastic collisions. In the limit of small bath atom mass, the large particle dynamics converges in law to a stochastic dynamics. This derivation follows the ideas of Mathematics Subject Classification. 82C05, 82C31.

show abstract

Section: Rapide Notesupporting

confidence: 79%

“…For this choice of parameters, the Lennard-Jones particles are in a fluid regime (see e.g. [22]). We run the simulation up to time T = 500, with a stepsize of Δt = 0.005 using the following splitting algorithm.…”

Section: Rapide Notmentioning

confidence: 99%

Derivation of Langevin dynamics in a nonzero background flow field

et al. 2013

View full text Add to dashboard Cite

show abstract

“…As shown in Fig. 2, we found that our computed viscosities obtained using equilibrium approaches and those obtained using the RNEMD method are consistent with each other, and both are in good general agreement with values reported by Rowley and Painter 13 and Heyes. 14 All equilibrium simulations in Fig.…”

supporting

confidence: 88%

Are pressure fluctuation-based equilibrium methods really worse than nonequilibrium methods for calculating viscosities?

Chen

Smit

Bell

2009

The Journal of Chemical Physics

118

View full text Add to dashboard Cite

Nonequilibrium methods have become increasingly popular for calculating the viscosity of liquids. [1][2][3][4][5][6] The use of nonequilibrium methods is frequently rationalized by the notion that pressure fluctuation-based equilibrium methods, such as those using the Green-Kubo ͑GK͒ formula and the Einstein relation, do not converge well, and hence are less suitable than nonequilibrium methods. 1 In this short note, we revisit the systems on which this conclusion is based. We show that a slightly different way of analyzing the data allows us to use equilibrium molecular dynamics methods to compute viscosities with comparable accuracy and reliability as the nonequilibrium techniques considered in Ref. 1 and the reverse nonequilibrium molecular dynamics method. 7The shear viscosity can be computed using the GK formulaor, equivalently, using the Einstein relation,requires computing the mean-square displacement ͑MSD͒ of the time integral of the pressure tensor, 9where G ␣␤ ͑t͒ = ͐ 0 t P ␣␤ ͑tЈ͒dtЈ. P ␣␤ is the symmetrized traceless portion of the stress tensor, ␣␤ , defined aswhere ␦ ␣␤ is the Kronecker delta and ␦ ␣␤ = 0 when ␣ ␤. It should be noted that some researchers 10 use a weighting factor of 4/3 for the diagonal components ͑␣ = ␤͒ and 1 for the off-diagonal components ͑␣ ␤͒, but here we take the view in Refs. 8 and 9 that all weighting factors should be 1. We note further that Eqs. ͑1͒ and ͑2͒ utilize the information of the diagonal components of the pressure tensor to improve statistics. To compare our results with those in Ref. 1, we also compute the viscosity using only the off-diagonal components of the pressure tensor, i.e., when ␣ ␤, and then the normalization factors in Eqs. ͑1͒ and ͑2͒ become 6 and 12, respectively. The overhead in computing the stress tensor in the simulation is very small once the forces have been calculated. The computed pressure-pressure time correlation function was averaged over multiple time origins spaced every ten time steps and block averaging method was used to obtain viscosity estimate and corresponding standard deviation within specified correlation time period.Molecular dynamics simulations were performed for a 1000-particle Lennard-Jones ͑LJ͒ fluid using the LAMMPS ͑Ref. 11͒ package in the NVT ensemble with a Nosé-Hoover thermostat. All quantities are expressed in reduced units: 452, a time step of 0.01 and a cut-off radius of 5͒. The system was equilibrated for a period of 1 ϫ 10 3 followed by a production run of t ‫ء‬ =1ϫ 10 5 . Figure 1 shows the viscosity curves determined using the fluctuation information of all components and only the offdiagonal components of the pressure tensor ͓see SI ͑Ref. 12͔ for a typical example of a pressure-pressure time correlation function͒. The inset shows the short correlation time behavior. Since the GK formula and the Einstein relation give identical results, we do not distinguish these two approaches. We find that our viscosity calculation converges quickly and reaches a plateau within a correlation time of 2. For the inset, the...

show abstract

“…18,[21][22][23] As far as the bulk quantities for self-diffusivity and viscosity of fluids are concerned, these have been studied extensively using MD simulations. For instance, Rowley and co-workers 24 reported MD computations of the self-diffusion coefficient and the viscosity in agreement with argon experimental data. Later, Meier and co-workers 25 calculated the kinetic and potential viscosity contributions for a broad range of temperatures and densities.…”

Section: Introductionsupporting

confidence: 52%

Nonequilibrium molecular dynamics simulations of nanoconfined fluids at solid-liquid interfaces

Morciano

Fasano

Nold

et al. 2017

The Journal of Chemical Physics

View full text Add to dashboard Cite

We investigate the hydrodynamic properties of a Lennard-Jones fluid confined to a nanochannel using molecular dynamics simulations. For channels of different widths and hydrophilic-hydrophobic surface wetting properties, profiles of the fluid density, stress, and viscosity across the channel are obtained and analysed. In particular, we propose a linear relationship between the density and viscosity in confined and strongly inhomogeneous nanofluidic flows. The range of validity of this relationship is explored in the context of coarse grained models such as dynamic density functional-theory.

show abstract

Diffusion and viscosity equations of state for a Lennard-Jones fluid obtained from molecular dynamics simulations

Cited by 134 publications

References 10 publications

Derivation of Langevin dynamics in a nonzero background flow field

Derivation of Langevin dynamics in a nonzero background flow field

Are pressure fluctuation-based equilibrium methods really worse than nonequilibrium methods for calculating viscosities?

Nonequilibrium molecular dynamics simulations of nanoconfined fluids at solid-liquid interfaces

Contact Info

Product

Resources

About