Stochastic simulation of transport processes in liquids

Abstract

The subject of this paper is molecular stochastic modeling the transport processes in liquids. The proposed method and the corresponding algorithm are an alternative to the molecular dynamics method. However, unlike the latter the system of Newtonian equations is not solved for modeling the phase trajectories of the system studied. The phase trajectories of the molecular system are simulated stochastically. For this purpose, the database of the intermolecular forces acting on each molecule of the system during the considered time interval has been created. The distribution function of these forces has been built. It was shown that this distribution function can be approximated by certain analytic function. The dependency of the parameters of this function on the liquid temperature and parameters of the intermolecular interaction potential (the Lennard-Jones interaction potential is used) is determined. Using this distribution function the force acting on each molecule at given time is determined. After that the coordinates and velocity of all molecules of the system are calculated. As a result, the full information about the phase variables of the molecular system is obtained. All macroscopic characteristics of the system (temperature, pressure, transport coefficients etc.) are calculated by means of the methods of nonequilibrium statistical mechanics. The transport coefficients are calculated using fluctuation-dissipation theorems that relate transport coefficients to the evolution of the corresponding correlation functions. The algorithm was tested on the calculation of the viscosity of several simple liquids.