Estimation of bulk viscosity of dilute gases using a nonequilibrium molecular dynamics approach

A method is proposed for the calculation of bulk viscosity, μ_{b}, of dilute gases using nonequilibrium molecular dynamics (NEMD) simulations. The method uses measurement of mechanical (P_{mech}) and thermodynamic pressure (P_{thermo}) in a NEMD simulation of an expanding fluid and then relates the bulk viscosity to them by the relation μ_{b}=(P_{mech}-P_{thermo})/∇·u[over ⃗], where ∇·u[over ⃗] is the controlled rate of expansion of the fluid per unit volume. A special emphasis is given to the fundamental physical understanding of bulk viscosity in this work. The proposed method is demonstrated for the estimation of bulk viscosity of dilute nitrogen gas in the temperature range of 200-800 K. Variation of bulk viscosity with temperature is reported in the above-mentioned temperature range and is found to be in a reasonably good agreement with the data available in the literature. Furthermore, variation of bulk viscosity with pressure and volumetric expansion rate is obtained. A weak linear dependency of bulk viscosity with pressure is observed, which increases with temperature. However, no significant effect of the rate of volumetric expansion is observed until 10^{8}s^{-1}. Moreover, the effect of the direction of volumetric change (expansion vs. compression) is also demonstrated in this work.