Bulk viscosity of the Lennard-Jones system at the triple point by dynamical nonequilibrium molecular dynamics

Abstract

Non-equilibrium Molecular Dynamics (NEMD) calculations of the bulk viscosity of the triple point Lennard-Jones fluid are performed with the aim of investigating the origin of the observed disagreement between Green-Kubo estimates and previous NEMD data. We show that a careful application of the Doll's perturbation field, the dynamical NEMD method, the instantaneous form of the perturbation and the "subtraction technique" provides a NEMD estimate of the bulk viscosity at zero field in full agreement with the value obtained by the Green-Kubo formula. As previously reported for the shear viscosity, we find that the bulk viscosity exhibits a large linear regime with the field intensity which confirms the Lennard-Jones fluid as a genuine Newtonian fluid even at triple point.

Computing bulk and shear viscosities from simulations of fluids with dissipative and stochastic interactions

“…This is the reason why it is difficult to measure the bulk viscosity in a steady-state experiment [9]. To the best knowledge of the authors, the only NEMD calculations of the bulk viscosity use either cyclic compression [9,10] or the relaxation of an instantaneous distortion [11,12]. The methods used in these studies cannot be applied to systems with stochastic dynamics -either because they are explicitly designed for Hamiltonian systems [9,10,12], or, in the case of Ref.…”

“…To the best knowledge of the authors, the only NEMD calculations of the bulk viscosity use either cyclic compression [9,10] or the relaxation of an instantaneous distortion [11,12]. The methods used in these studies cannot be applied to systems with stochastic dynamics -either because they are explicitly designed for Hamiltonian systems [9,10,12], or, in the case of Ref. [11], because they cannot be used to determine the instantaneous contribution of the random force to the viscosity (as already mentioned in [11]) due to the finite time step in MD simulations.…”

Longitudinal viscosity of two-dimensional Yukawa liquids

“…The required inputs for calculating longitudinal and bulk viscosities include time series of particles' positions, velocities, and interparticle forces. Now we review the three steps for calculating the longitudinal viscosity using the standard Green-Kubo relation [2,[15][16][17][18][19][20][22][23][24][25][26][27][28]. These Green-Kubo relations, which were originally developed for three dimensions (d = 3), are adapted here for two dimensions (d = 2) by setting the velocity and coordinate in the z direction to be zero.…”

“…GreenKubo relations are for equilibrium conditions; they use microscopic random motion of particles to determine transport coefficients without any macroscopic gradients. The longitudinal and bulk viscosities can also be calculated using the Green-Kubo relations [2,[14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] using similar equations as the shear viscosity. The required inputs for calculating longitudinal and bulk viscosities include time series of particles' positions, velocities, and interparticle forces.…”

“…This method of measuring bulk viscosity is so difficult that it has been used only for water and a handful of exotic liquids [5], and even for these substances the results for the bulk viscosity have large uncertainties. In contrast to this difficult experimental situation, however, longitudinal viscosity and bulk viscosity are mentioned more often in the theoretical literature, where it has been calculated for example using the Green-Kubo relation [2,[14][15][16][17][18][19][20][21][22][23][24][25][26][27][28], using the hydrodynamic limit [29], or derived using a Chapman-Enskog approach [30]. In this paper, we will make use of the Green-Kubo approach, which we present in Sec.…”