Abstract
To characterize liquid-solid friction using molecular dynamics simulations, Bocquet and Barrat (BB) [Phys. Rev. E 49, 3079–3092 (1994)] proposed to use the plateau value of a Green-Kubo (GK) integral of the friction force. The BB method is delicate to apply in finite-size simulations, where the GK integral vanishes at long times. Here, we derive an expression for the GK integral in finite-size systems, based on a Langevin description of a coarse-grained system effectively involving a certain thickness of liquid close to the wall. Fitting this expression to GK integrals obtained from simulations of a liquid slab provides the friction coefficient and the effective thickness of the coarse-grained system. We show that the coarse-grained system for a Lennard-Jones fluid between flat and smooth solid surfaces is 2–3 molecules thick, which provides a criterion for measuring the friction coefficient independently of confinement. As compared to nonequilibrium simulations, the new approach is more accurate and removes some ambiguities of nonequilibrium measurements. Overall, we hope that this new method can be used to characterize efficiently liquid-solid friction in a variety of systems of interest, e.g., for nanofluidic applications.
Highlights
To describe flows in macroscopic channels, one can combine a continuum description of mass transport in the bulk with a no-slip boundary condition (BC) for the fluid velocity at the wall
The Bocquet and Barrat (BB) formula, identifying the liquid-solid friction coefficient with the plateau value of a GK integral, poses some problems in finite-size simulations, where the GK integral vanishes at long times. This formula can be obtained from a Langevin description of a diffusing wall in contact with a semi-infinite liquid
We derived the analytical expression of the GK integral for a finite-size liquid slab confined between immobile walls by applying the Langevin description to a coarse-grained system involving effectively a fraction of the confined liquid, assuming a simple Maxwell-type memory kernel relating the slip velocity and velocity of the coarse-grained system
Summary
To describe flows in macroscopic channels, one can combine a continuum description of mass transport in the bulk (e.g., the Navier-Stokes equation) with a no-slip boundary condition (BC) for the fluid velocity at the wall. Camargo et al. considered the mechanical balance and local constitutive equation of a thin slab of layered fluid formed near the wall covering the liquid-solid interface (mentioned as a “pillbox” for a spherical interface) and derived the boundary condition In contrast with these recent articles, here we propose a pragmatic approach to extend the BB formula to finite-size systems by introducing a simple expression for the memory kernel and fitting the full GK curve based on a coarse-grained description without dealing with the details of local mechanics. The two features could correspond to the time- and length-scale separation mentioned in Nakano and Sasa, and the effective coarse-grained system could be related to the thin slab in Camargo et al.
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