Static and Dynamic Properties of Dissipative Particle Dynamics

TL;DR

This paper analyzes the static and dynamic properties of Dissipative Particle Dynamics (DPD), deriving explicit expressions for equilibrium and transport properties, and validating them through numerical simulations, to better understand complex fluid behavior.

Contribution

It provides a comprehensive theoretical framework for DPD, including explicit calculations of viscosity and diffusion, and establishes the connection between microscopic parameters and macroscopic properties.

Findings

Temperature gradients cannot exist in the DPD fluid.

Explicit formulas for viscosity and self-diffusion are derived.

Analytic results agree with numerical simulations.

Abstract

The algorithm for the DPD fluid, the dynamics of which is conceptually a combination of molecular dynamics, Brownian dynamics and lattice gas automata, is designed for simulating rheological properties of complex fluids on hydrodynamic time scales. This paper calculates the equilibrium and transport properties (viscosity, self-diffusion) of the thermostated DPD fluid explicitly in terms of the system parameters. It is demonstrated that temperature gradients cannot exist, and that there is therefore no heat conductivity. Starting from the N-particle Fokker-Planck, or Kramers' equation, we prove an H-theorem for the free energy, obtain hydrodynamic equations, and derive a non-linear kinetic equation (the Fokker-Planck-Boltzmann equation) for the single particle distribution function. This kinetic equation is solved by the Chapman-Enskog method. The analytic results are compared with numerical simulations.