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 using a consistency equation relating these quantities. 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 velocity autocorrelation function. An asymptotic decay law of the velocity autocorrelation function resembles the previously known self-consistent form, $1/(t\sqrt{\ln t})$, however with a rescaled time.

10 pages, to appear in New Journal of Physics

References in corpus (4)

• Lévy walks
• Long Time Tail of the Velocity Autocorrelation Function in a Two-Dimensional Moderately Dense Hard Disk Fluid
• Normal versus anomalous self-diffusion in two-dimensional fluids: Memory function approach and generalized asymptotic Einstein relation
• Study of Transient Nuclei near Freezing

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• Density-Dependent Finite System-Size Effects in Equilibrium Molecular Dynamics Estimation of Shear Viscosity: Hydrodynamic and Configurational Study
• Molecular Hydrodynamics: Vortex Formation and Sound Wave Propagation
• Description of Brownian motion including both kinetic and hydrodynamic effects