Pseudo hard-sphere viscosities from equilibrium Molecular Dynamics

Abstract

Transport coefficients like shear, bulk and longitudinal viscosities are sensitive to the intermolecular interaction potential and finite size effects when are numerically determined. For the hard-sphere (HS) fluid, such transport properties are determined almost exclusively with computer simulations. However, their systematic determination and analysis throughout shear stress correlation functions and the Green-Kubo formalism can not be done due to discontinuous nature of the interaction potential. Here, we use the pseudo hard-sphere (PHS) potential to determine pressure correlation functions as a function of volume fraction in order to compute mentioned viscosities. Simulation results are compared to available event-driven molecular dynamics of the HS fluid and also used to propose empirical corrections for the Chapman-Enskog zero density limit of shear viscosity. Moreover, we show that PHS potential is a reliable representation of the HS fluid and can be used to compute transport coefficients. The molecular simulation results of the present work are valuable for further exploration of HS-type fluids or extend the approach to compute transport properties of hard-colloid suspensions.

Comment on ‘Pseudo hard-sphere viscosities from equilibrium molecular dynamics’

“…As already noted in [1], the data from [7] appears to underestimate the viscosity at lower packing fractions. Surprisingly, the results of Nicasio-Collazo et al agree more closely with true hard spheres than with PHS, in contrast to what is shown in [1]. This discrepancy likely stems from an error in unit conversion in [1]: Nicasio-Collazo et al state that they use τ ϵ = √ mσ 2 /ϵ as their unit of time, in contrast to the unit τ = √ βmσ 2 normally used for studies of true hard spheres.…”

“…In a recent article [1], Nicasio-Collazo et al explore the viscosity of the pseudo-hard-sphere (PHS) model. The authors observe shear viscosities that are significantly higher than literature data for true hard spheres.…”

“…where r is the distance between two particles, ε the interaction strength, and σ the effective diameter. As was done in [1], we set the interaction strength such that k B T/ϵ = 1.4737. After equilibration, the thermostat was switched off, velocities were reinitialized, and the simulation was continued in the microcanonical ensemble, running for 10 4 τ with an integration step size of 2 × 10 −4 τ .…”

“…This discrepancy likely stems from an error in unit conversion in [1]: Nicasio-Collazo et al state that they use τ ϵ = √ mσ 2 /ϵ as their unit of time, in contrast to the unit τ = √ βmσ 2 normally used for studies of true hard spheres. However, in the figures in [1], the literature values for hard spheres do not appear to have been converted to this new set of units, and as a result the reported hard-sphere results appear too low by a factor √ k B T/ϵ ≃ 1.21. Figure 1(b) shows the bulk viscosity η b .…”

“…This conflicts with the measurements of Nicasio-Collazo et al, which instead showed higher bulk viscosities for the PHS system at high densities. Viscosities of the hard-sphere (red) and pseudo-hard-sphere fluids (blue), as a function of the packing fraction ϕ, compared to the data in [1] (black). Shown are the shear viscosity (a), bulk viscosity (b), and longitudinal viscosity (c), each normalized by their respective Enskog prediction.…”