Green-Kubo measurement of liquid-solid friction in finite-size systems

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.