Revisiting the Green-Kubo relation for friction in nanofluidics

TL;DR

This paper derives a new Green-Kubo relation for liquid-solid friction that overcomes previous challenges, enabling accurate measurement of effective interfacial friction and linking it to slip length, thus improving understanding of nanoscale hydrodynamics.

Contribution

The authors introduce a modified Green-Kubo relation that reliably measures effective interfacial friction without the plateau problem, connecting microscopic fluctuations to macroscopic slip behavior.

Findings

The new relation avoids the plateau issue in force autocorrelation functions.

Continuum hydrodynamics accurately describes nanoscale confinement down to 1 nm.

The method allows comparison of different surface slippage properties.

Abstract

A central aim of statistical mechanics is to establish connections between a system's microscopic fluctuations and its macroscopic response to a perturbation. For non-equilibrium transport properties, this amounts to establishing Green-Kubo (GK) relationships. In hydrodynamics, relating such GK expressions for liquid-solid friction to macroscopic slip boundary conditions has remained a long-standing problem due to two challenges: (i) The GK running integral of the force autocorrelation function decays to zero rather than reaching a well-defined plateau value; and (ii) debates persist on whether such a transport coefficient measures an intrinsic interfacial friction or an effective friction in the system. Inspired by ideas from the coarse-graining community, we derive a GK relation for liquid-solid friction where the force autocorrelation is sampled with a constraint of momentum conservation in the liquid. Our expression does not suffer from the "plateau problem" and unambiguously measures an effective friction coefficient, in an analogous manner to Stokes' law. We further establish a link between the derived friction coefficient and the hydrodynamic slip length, enabling a straightforward assessment of continuum hydrodynamics across length scales. We find that continuum hydrodynamics describes the simulation results quantitatively for confinement length scales all the way down to 1 nm. Our approach amounts to a straightforward modification to the present standard method of quantifying interfacial friction from molecular simulations, making possible a sensible comparison between surfaces of vastly different slippage.