# Hydrodynamic relaxations in dissipative particle dynamics

## TL;DR

This study investigates relaxation phenomena in dissipative particle dynamics using fluctuating hydrodynamics, revealing temperature-dependent accuracy of hydrodynamic predictions and the dominance of sound wave propagation at high temperatures.

## Contribution

It provides a detailed analysis of hydrodynamic relaxations in DPD, highlighting temperature effects and the independence of transverse dynamics from shear force contributions.

## Key findings

- Hydrodynamic theory predicts transverse dynamics well at low temperatures.
- Agreement with hydrodynamics depends on viscosity definition.
- High temperatures favor sound wave propagation in longitudinal spectra.

## Abstract

This paper studies the dynamics of relaxation phenomena in the standard dissipative particle dynamics (DPD) model [Groot and Warren, JCP, 107:4423 (1997)]. Using fluctuating hydrodynamics as the framework of the investigation, we focus on the collective transverse and longitudinal dynamics. It is shown that classical hydrodynamic theory predicts the transverse dynamics at relative low temperatures very well when compared to simulation data, however, the theory predictions are, on the same length scale, less accurate for higher temperatures. The agreement with hydrodynamics depends on the definition of the viscosity, and here we find that the transverse dynamics are independent of the dissipative and random shear force contributions to the stress. For high temperatures, the spectrum for the longitudinal dynamics is dominated by the Brillouin peak for large length scales and the relaxation is therefore governed by sound wave propagation and is athermal. This contrasts the results at lower temperatures and small length scale, where the thermal process is clearly present in the spectra. The Landau-Placzek ratio is lower than the classical model Lennard-Jones liquid, especially at higher temperatures. The DPD model, at least qualitatively, re-captures the underlying hydrodynamical mechanisms, and quantitative agreement is excellent at intermediate temperatures for the transverse dynamics.