On the Green-Kubo relationship of the liquid-solid friction coefficient

TL;DR

This paper introduces a novel derivation of the Green-Kubo relation for liquid-solid friction, emphasizing the role of non-Markovian dynamics and superdiffusive behavior in wall-liquid interactions.

Contribution

It presents a new theoretical derivation using a Langevin approach that accounts for memory effects in wall-liquid dynamics.

Findings

Derivation based on a non-Markovian Langevin equation

Identification of superdiffusive motion in wall fluctuations

Highlights subtleties in wall-liquid dynamic interactions

Abstract

In this paper, we propose a new derivation for the Green-Kubo relationship for the liquid-solid friction coefficient, characterizing hydrodynamic slippage at a wall. It is based on a general Langevin approach for the fluctuating wall velocity, involving a non-markovian memory kernel with vanishing time integral. The calculation highlights some subtleties of the wall-liquid dynamics, leading to superdiffusive motion of the fluctuating wall position.