Comparison between theoretical values and simulation results of viscosity for the dissipative particle dynamics method

In order to investigate the validity of the dissipative particle dynamics method, which is a mesoscopic simulation technique, we have derived an expression for viscosity from the equation of motion of dissipative particles. In the concrete, we have shown the Fokker-Planck equation in phase space, and macroscopic conservation equations such as the equation of continuity and the equation of momentum conservation. The basic equations of the single-particle and pair distribution functions have been derived using the Fokker-Planck equation. The solutions of these distribution functions have approximately been solved by the perturbation method under the assumption of molecular chaos. The expressions of the viscosity due to momentum and dissipative forces have been obtained using the approximate solutions of the distribution functions. Also, we have conducted nonequilibrium dynamics simulations to investigate the influence of the parameters, which have appeared in defining the equation of motion in the dissipative particle dynamics method. The theoretical values of the viscosity due to dissipative forces in the Hoogerbrugge-Koelman theory are in good agreement with the simulation results obtained by the nonequilibrium dynamics method, except in the range of small number densities. There are restriction conditions for taking appropriate values of the number density, number of particles, time interval, shear rate, etc., to obtain physically reasonable results by means of dissipative particle dynamics simulations.