# Viscosity, Shear Waves, and Atomic-Level Stress-Stress Correlations

## Abstract

The Green-Kubo equation relates the macroscopic stress-stress correlation function to a liquid's viscosity. The concept of the atomic-level stresses allows the macroscopic stress-stress correlation function in the equation to be expressed in terms of the space-time correlations among the atomic-level stresses. Molecular dynamics studies show surprisingly long spatial extension of stress-stress correlations and also longitudinal and transverse waves propagating in liquids over ranges which could exceed the system size. The results reveal that the range of propagation of shear waves corresponds to the range of distances relevant for viscosity. Thus our results show that viscosity is a fundamentally nonlocal quantity. We also show that the periodic boundary conditions play a nontrivial role in molecular dynamics simulations, effectively masking the long-range nature of viscosity.

- Authors:

- ORNL

- Publication Date:

- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1015744

- DOE Contract Number:
- AC05-00OR22725

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review Letters

- Additional Journal Information:
- Journal Volume: 106; Journal Issue: 11; Journal ID: ISSN 0031-9007

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOUNDARY CONDITIONS; CORRELATION FUNCTIONS; SHEAR; SPACE-TIME; STRESSES; VISCOSITY

### Citation Formats

```
Levashov, Valentin A., Morris, James R., and Egami, Takeshi.
```*Viscosity, Shear Waves, and Atomic-Level Stress-Stress Correlations*. United States: N. p., 2011.
Web. doi:10.1103/PhysRevLett.106.115703.

```
Levashov, Valentin A., Morris, James R., & Egami, Takeshi.
```*Viscosity, Shear Waves, and Atomic-Level Stress-Stress Correlations*. United States. doi:10.1103/PhysRevLett.106.115703.

```
Levashov, Valentin A., Morris, James R., and Egami, Takeshi. Tue .
"Viscosity, Shear Waves, and Atomic-Level Stress-Stress Correlations". United States. doi:10.1103/PhysRevLett.106.115703.
```

```
@article{osti_1015744,
```

title = {Viscosity, Shear Waves, and Atomic-Level Stress-Stress Correlations},

author = {Levashov, Valentin A. and Morris, James R. and Egami, Takeshi},

abstractNote = {The Green-Kubo equation relates the macroscopic stress-stress correlation function to a liquid's viscosity. The concept of the atomic-level stresses allows the macroscopic stress-stress correlation function in the equation to be expressed in terms of the space-time correlations among the atomic-level stresses. Molecular dynamics studies show surprisingly long spatial extension of stress-stress correlations and also longitudinal and transverse waves propagating in liquids over ranges which could exceed the system size. The results reveal that the range of propagation of shear waves corresponds to the range of distances relevant for viscosity. Thus our results show that viscosity is a fundamentally nonlocal quantity. We also show that the periodic boundary conditions play a nontrivial role in molecular dynamics simulations, effectively masking the long-range nature of viscosity.},

doi = {10.1103/PhysRevLett.106.115703},

journal = {Physical Review Letters},

issn = {0031-9007},

number = 11,

volume = 106,

place = {United States},

year = {2011},

month = {3}

}