Microscopic determination of macroscopic boundary conditions in Newtonian liquids

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.

arXiv comment21 pages, 9 figures

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Cited by in corpus (5)

• Statistical mechanical expressions of slip length
• Equilibrium measurement method of slip length based on fluctuating hydrodynamics
• Equilibrium molecular dynamics evaluation of the solid-liquid friction coefficient: role of timescales
• Theoretical framework for the atomistic modeling of frequency-dependent liquid-solid friction
• Extraction of slip velocity in NEMD Couette flow systems using frictional dissipation