Molecular Hydrodynamics: Vortex Formation and Sound Wave Propagation

TL;DR

This study tests the molecular-level hydrodynamic description of a 2D fluid using molecular dynamics simulations, confirming the validity of the linearized Navier-Stokes equations for certain time scales and validating key assumptions of mode-coupling theory.

Contribution

It provides quantitative validation of the hydrodynamic mode approach at molecular scales and compares molecular dynamics results with linearized Navier-Stokes predictions.

Findings

LNS equations accurately describe transverse velocity at larger times.

LNS fails to capture molecular patterns in the longitudinal velocity.

Velocity autocorrelation function aligns well with hydrodynamic assumptions.

Abstract

In the present study, quantitative feasibility tests of the hydrodynamic description of a two-dimensional fluid at the molecular level are performed, both with respect to length and time scales. Using high-resolution fluid velocity data obtained from extensive molecular dynamics simulations, we computed the transverse and longitudinal components of the velocity field by the Helmholtz decomposition and compared them with those obtained from the linearized Navier-Stokes (LNS) equations with time-dependent transport coefficients. By investigating the vortex dynamics and the sound wave propagation in terms of these field components, we confirm the validity of the LNS description for times comparable to or larger than several mean collision times. The LNS description still reproduces the transverse velocity field accurately at smaller times, but it fails to predict characteristic patterns of molecular origin visible in the longitudinal velocity field. Based on these observations, we validate the main assumptions of the mode-coupling approach. The assumption that the velocity autocorrelation function can be expressed in terms of the fluid velocity field and the tagged particle distribution is found to be remarkably accurate even for times comparable to or smaller than the mean collision time. This suggests that the hydrodynamic-mode description remains valid down to the molecular scale.