Non-local viscosity from the Green-Kubo formula

• Published in: The Journal of chemical physics Vol. 152; no. 17; p. 174108
• Main Authors: Duque-Zumajo, D, de la Torre, J A, Español, Pep
• Format: Journal Article
• Language: English
• Published: United States 07.05.2020
• ISSN: 1089-7690
• DOI: 10.1063/5.0006212

We study through MD simulations the correlation matrix of the discrete transverse momentum density field in real space for an unconfined Lennard-Jones fluid at equilibrium. Mori theory predicts this correlation under the Markovian approximation from the knowledge of the non-local shear viscosity matrix, which is given in terms of a Green-Kubo formula. However, the running Green-Kubo integral for the non-local shear viscosity does not have a plateau. By using a recently proposed correction for the Green-Kubo formula that eliminates the plateau problem [Español et al., Phys. Rev. E 99, 022126 (2019)], we unambiguously obtain the actual non-local shear viscosity. The resulting Markovian equation, being local in time, is not valid for very short times. We observe that the Markovian equation with non-local viscosity gives excellent predictions for the correlation matrix from a time at which the correlation is around 80% of its initial value. A local in space approximation for the viscosity gives accurate results only after the correlation has decayed to 40% of its initial value.