Local stress tensor calculation by the Method-of-Plane in microscopic systems with macroscopic flow: a formulation based on the velocity distribution function

Abstract

In this work, we showed a calculation method of local stress tensor applicable to non-equilibrium MD systems based on the Method of Plane (MoP). From the relation between the macroscopic velocity distribution function and the microscopic molecular passage across a fixed control plane, we derived a method to calculate the basic properties of the macroscopic momentum conservation law including the density, the velocity, the momentum flux, the interaction and kinetic terms of the stress tensor defined on a surface with a finite area. Any component of the streaming velocity can be obtained on a control surface, which enables the separation of the kinetic momentum flux into the advection and stress terms in the framework of MoP. We verified the present method through the extraction of the density, velocity and stress distributions in a quasi-1D steady-state Couette flow system and in a quasi-2D steady-state system with a moving contact line. In our method, as opposed to volume average method, the density, mass and momentum fluxes are defined on a surface, which is essential to be consistent with the mass and momentum conservation laws in dynamic systems.