Non-local viscosity from the Green-Kubo formula

Area of Science:

• Statistical Mechanics
• Computational Physics
• Fluid Dynamics

Background:

• Mori theory, under the Markovian approximation, predicts momentum density correlations using non-local shear viscosity.
• The Green-Kubo formula is typically used to calculate non-local shear viscosity, but often suffers from a lack of plateau in the running integral.
• This plateau issue complicates the accurate determination of shear viscosity and subsequent correlation predictions.

Purpose of the Study:

• To investigate the correlation matrix of the discrete transverse momentum density field in an equilibrium Lennard-Jones fluid using molecular dynamics (MD) simulations.
• To address the plateau problem in the Green-Kubo integral for non-local shear viscosity.
• To evaluate the predictive accuracy of a corrected Green-Kubo formula and compare it with traditional approximations.

Main Methods:

• Performed MD simulations on an unconfined Lennard-Jones fluid at equilibrium.
• Employed a recently proposed correction to the Green-Kubo formula to resolve the running integral's plateau issue.
• Calculated the non-local shear viscosity using the corrected formula and applied it to Mori theory's Markovian equation.

Main Results:

• The corrected Green-Kubo formula successfully yielded an unambiguous value for the non-local shear viscosity.
• The Markovian equation, incorporating the non-local viscosity, accurately predicted momentum density correlations from approximately 80% initial correlation decay.
• A local-in-space viscosity approximation showed accuracy only after the correlation decayed to 40% of its initial value.

Conclusions:

• The corrected Green-Kubo formula effectively overcomes the plateau problem, enabling accurate calculation of non-local shear viscosity.
• The Markovian equation with non-local viscosity provides superior predictions for momentum density correlations compared to local approximations, especially at earlier times.
• This approach enhances the predictive capability of theoretical models for fluid dynamics based on equilibrium simulations.