Revisiting the Green–Kubo relation for friction in nanofluidics

Bui, Anna; Cox, Stephen

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.

Citation

Bui, A., & Cox, S. (2024). Revisiting the Green–Kubo relation for friction in nanofluidics. The Journal of Chemical Physics, 161, Article 201102. https://doi.org/10.1063/5.0238363

• Journal Article Type: Article
• Acceptance Date: Nov 12, 2024
• Online Publication Date: Nov 27, 2024
• Publication Date: Nov 27, 2024
• Deposit Date: Nov 27, 2024
• Publicly Available Date: Nov 27, 2024
• Print ISSN: 0021-9606
• Electronic ISSN: 1089-7690
• Publisher: American Institute of Physics
• Peer Reviewed: Peer Reviewed
• Volume: 161
• Article Number: 201102
• DOI: https://doi.org/10.1063/5.0238363
• Public URL: https://durham-repository.worktribe.com/output/3107539