Sampling the Bulk Viscosity of Water with Molecular Dynamics Simulation in the Canonical Ensemble

The bulk viscosity, a transport coefficient in the Navier-Stokes equation, is often neglected in the continuum mechanics of Newtonian fluids. Recently, however, the role of the bulk viscosity is highlighted in the area of surface and interface related phenomena, in systematic model up-scaling and as an important quantity for the interpretation of acoustic sensor data. The prediction of the bulk viscosity usually employs molecular dynamics and the Green-Kubo linear response theory, which is used to sample transport properties in general from molecular trajectories. Since simulations are usually carried out at specified state points in concert with the evaluation of other thermodynamic properties, the role of thermostats in molecular dynamics needs to be explored systematically. In this work, we carefully investigate the role of thermostatting schemes and numerical implementations of the Green-Kubo formalism, in particular in the canonical ensemble, using two popular water force field models. It turns out that the sampling of the bulk and shear viscosities is a delicate challenge since details of thermostatting and numerical subtleties may have an influence on the results beyond statistical uncertainties. Based on the present findings, we conclude with hints on how to construct robust sampling in the canonical ensemble for the bulk viscosity.