Microscopic determination of macroscopic boundary conditions in Newtonian liquids

TL;DR

This paper investigates how microscopic boundary conditions in Newtonian liquids influence macroscopic boundary conditions, using molecular dynamics simulations to connect microscopic details with phenomenological slip parameters in fluid mechanics.

Contribution

It introduces two frameworks for deriving macroscopic boundary conditions from microscopic particle system descriptions in Newtonian liquids.

Findings

Microscopic boundary conditions can be linked to slip parameters in macroscopic models.

Two different limits lead to distinct frameworks for boundary condition determination.

Simulation results support the proposed connection between microscopic and macroscopic boundary conditions.

Abstract

We study boundary conditions applied to the macroscopic dynamics of Newtonian liquids from the view of microscopic particle systems. We assume the existence of microscopic boundary conditions that are uniquely determined from a microscopic description of the fluid and the wall. By using molecular dynamical simulations, we examine a possible form of the microscopic boundary conditions. In the macroscopic limit, we may introduce a scaled velocity field by ignoring the higher order terms in the velocity field that is calculated from the microscopic boundary condition and standard fluid mechanics. We define macroscopic boundary conditions as the boundary conditions that are imposed on the scaled velocity field. The macroscopic boundary conditions contain a few phenomenological parameters for an amount of slip, which are related to a functional form of the given microscopic boundary condition. By considering two macroscopic limits of the non-equilibrium steady state, we propose two different frameworks for determining macroscopic boundary conditions.