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Revisiting the Green-Kubo relation for friction in nanofluidics
Anna T Bui1, Stephen J Cox1,2
1Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom.
The Journal of Chemical Physics
|November 27, 2024
Summary
This study introduces a new Green-Kubo relation for liquid-solid friction, solving the "plateau problem" and measuring effective friction. It links this to hydrodynamic slip length, validating continuum hydrodynamics down to 1 nm confinement.
Area of Science:
- Statistical Mechanics
- Non-equilibrium Thermodynamics
- Fluid Dynamics
Background:
- Establishing connections between microscopic fluctuations and macroscopic properties is key in statistical mechanics.
- Green-Kubo (GK) relations are used for non-equilibrium transport properties.
- Relating GK expressions for liquid-solid friction to macroscopic slip boundary conditions is challenging due to the "plateau problem" and debates on friction measurement.
Purpose of the Study:
- Derive a Green-Kubo relation for liquid-solid friction that overcomes existing challenges.
- Unambiguously measure an effective friction coefficient.
- Link the derived friction coefficient to hydrodynamic slip length for assessing continuum hydrodynamics.
Main Methods:
- Developed a modified Green-Kubo relation for liquid-solid friction.
- Incorporated a constraint of momentum conservation in the liquid for sampling force autocorrelation.
- Linked the effective friction coefficient to hydrodynamic slip length.
Main Results:
- The derived Green-Kubo relation resolves the "plateau problem" associated with force autocorrelation functions.
- The method unambiguously quantifies an effective friction coefficient, analogous to Stokes' law.
- Continuum hydrodynamics accurately describes simulation results down to 1 nm confinement scales.
Conclusions:
- The new approach provides a robust method for quantifying interfacial friction in molecular simulations.
- Enables direct comparison of friction between surfaces with varying slippage characteristics.
- Validates the applicability of continuum hydrodynamics at nanoscale confinement.
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