# Nature of self-diffusion in two-dimensional fluids

## Abstract

Self-diffusion in a two-dimensional simple fluid is investigated by both analytical and numerical means. We investigate the anomalous aspects of self-diffusion in two-dimensional fluids with regards to the mean square displacement, the time-dependent diffusion coefficient, and the velocity autocorrelation function (VACF) using a consistency equation relating these quantities. Here, we numerically confirm the consistency equation by extensive molecular dynamics simulations for finite systems, corroborate earlier results indicating that the kinematic viscosity approaches a finite, non-vanishing value in the thermodynamic limit, and establish the finite size behavior of the diffusion coefficient. We obtain the exact solution of the consistency equation in the thermodynamic limit and use this solution to determine the large time asymptotics of the mean square displacement, the diffusion coefficient, and the VACF. An asymptotic decay law of the VACF resembles the previously known self-consistent form, 1/($$t\sqrt{In t)}$$ however with a rescaled time.

- Authors:

- Publication Date:

- Research Org.:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21); Korea Advanced Institute of Science and Technology (KAIST)

- OSTI Identifier:
- 1437764

- Alternate Identifier(s):
- OSTI ID: 1432222

- Grant/Contract Number:
- SC0008271; AC02-05CH11231; A0702001005

- Resource Type:
- Published Article

- Journal Name:
- New Journal of Physics

- Additional Journal Information:
- Journal Name: New Journal of Physics Journal Volume: 19 Journal Issue: 12; Journal ID: ISSN 1367-2630

- Publisher:
- IOP Publishing

- Country of Publication:
- United Kingdom

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICS AND COMPUTING; self-diffusion; long-time tail; anomalous diffusion; molecular dynamics simulation; consistency equation

### Citation Formats

```
Choi, Bongsik, Han, Kyeong Hwan, Kim, Changho, Talkner, Peter, Kidera, Akinori, and Lee, Eok Kyun. Nature of self-diffusion in two-dimensional fluids. United Kingdom: N. p., 2017.
Web. doi:10.1088/1367-2630/aa997d.
```

```
Choi, Bongsik, Han, Kyeong Hwan, Kim, Changho, Talkner, Peter, Kidera, Akinori, & Lee, Eok Kyun. Nature of self-diffusion in two-dimensional fluids. United Kingdom. doi:10.1088/1367-2630/aa997d.
```

```
Choi, Bongsik, Han, Kyeong Hwan, Kim, Changho, Talkner, Peter, Kidera, Akinori, and Lee, Eok Kyun. Fri .
"Nature of self-diffusion in two-dimensional fluids". United Kingdom. doi:10.1088/1367-2630/aa997d.
```

```
@article{osti_1437764,
```

title = {Nature of self-diffusion in two-dimensional fluids},

author = {Choi, Bongsik and Han, Kyeong Hwan and Kim, Changho and Talkner, Peter and Kidera, Akinori and Lee, Eok Kyun},

abstractNote = {Self-diffusion in a two-dimensional simple fluid is investigated by both analytical and numerical means. We investigate the anomalous aspects of self-diffusion in two-dimensional fluids with regards to the mean square displacement, the time-dependent diffusion coefficient, and the velocity autocorrelation function (VACF) using a consistency equation relating these quantities. Here, we numerically confirm the consistency equation by extensive molecular dynamics simulations for finite systems, corroborate earlier results indicating that the kinematic viscosity approaches a finite, non-vanishing value in the thermodynamic limit, and establish the finite size behavior of the diffusion coefficient. We obtain the exact solution of the consistency equation in the thermodynamic limit and use this solution to determine the large time asymptotics of the mean square displacement, the diffusion coefficient, and the VACF. An asymptotic decay law of the VACF resembles the previously known self-consistent form, 1/($t\sqrt{In t)}$ however with a rescaled time.},

doi = {10.1088/1367-2630/aa997d},

journal = {New Journal of Physics},

number = 12,

volume = 19,

place = {United Kingdom},

year = {2017},

month = {12}

}

DOI: 10.1088/1367-2630/aa997d

*Citation information provided by*

Web of Science

Web of Science