Static and dynamic properties of dissipative particle dynamics

Abstract

The algorithm for the dissipative particle dynamics ͑DPD͒ 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-diffusion͒ 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 nonlinear kinetic equation ͑the FokkerPlanck-Boltzmann equation͒ for the single-particle distribution function. This kinetic equation is solved by the Chapman-Enskog method. The analytic results are compared with numerical simulations.

Poiseuille flow to measure the viscosity of particle model fluids

“…The measured temperature was 2% lower than the input value, because the time step of ⌬t = 0.01 proved to be too large for the thermostat to work properly. This is a well known artefact of the simple DPD algorithm, 5,25 which is resolved in the Lowe-Andersen thermostat. 24 To distinguish between the effect of a large time step and viscous heating, the same simulation was performed with a smaller time step of ⌬t = 0.001.…”

“…Marsh et al derived an estimate for the dynamic viscosity based on kinetic theory. 5 There are two contributions to the viscosity. The first term is a kinetic contribution originating from the motion of the individual particles and the second term is a dissipative contribution from the energy dissipation between particles = 45 2 ͑k B T͒ 2 2 r c 3 + 1575…”

“…[2][3][4] In these simple model fluids the viscosity generally has to be measured because sufficiently accurate theoretical expressions are lacking. 5 That is, ideally the viscosity would be an input parameter but in practice the simulation must be "calibrated". There are several methods available to calculate viscosity, all with their relative advantages and disadvantages.…”

Comparison of the Accuracy and the Efficiency among Different Molecular Dynamics Methods for Calculating the Viscosity

“…The viscosity is one of the important parameters which determine the characteristics of the fluid flow and thus greatly affects the accuracy of the theoretical and engineering calculations. However, there is no exact theoretical expression for calculating the viscosity [1]. An experimental measurement or a numerical computation is always performed to get the viscosity value.…”

Exponential-time differencing schemes for low-mass DPD systems

“…The DPD method has emerged as a powerful computational tool for predicting hydrodynamic behaviour of complex-structure fluids like polymers and colloidal suspensions [1][2][3][4][5][6][7][8][9]. In the DPD method, a fluid is modelled by a set of particles that can move freely and the system conserves both mass and momentum.…”