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

TL;DR

This paper introduces two new methods for calculating bulk viscosities in fluids using non-equilibrium molecular dynamics simulations, addressing challenges in incorporating stochastic forces.

Contribution

The paper presents novel NEMD techniques for bulk viscosity computation and analyzes the proper inclusion of dissipative and stochastic forces in simulations.

Findings

Two methods successfully compute bulk viscosities in steady-state systems.

Analysis of different Green-Kubo expressions for dissipative particle dynamics.

Validation of methods on dissipative particle dynamics fluids.

Abstract

Exact values for bulk and shear viscosity are important to characterize a fluid and they are a necessary input for a continuum description. Here we present two novel methods to compute bulk viscosities by non-equilibrium molecular dynamics (NEMD) simulations of steady-state systems with periodic boundary conditions -- one based on frequent particle displacements and one based on the application of external bulk forces with an inhomogeneous force profile. In equilibrium simulations, viscosities can be determined from the stress tensor fluctuations via Green-Kubo relations; however, the correct incorporation of random and dissipative forces is not obvious. We discuss different expressions proposed in the literature and test them at the example of a dissipative particle dynamics (DPD) fluid.