Theoretical framework for the atomistic modeling of frequency-dependent liquid-solid friction

Haruki Oga,Cecilia Herrero,Yasutaka Yamaguchi,Laurent Joly,Takeshi Omori,Samy Merabia

doi:10.1103/physrevresearch.3.l032019

Abstract

Nanofluidics shows great promise for energy conversion and desalination applications. The performance of nanofluidic devices is controlled by liquid-solid friction, quantified by the Navier friction coefficient (FC). Despite decades of research, there is no well-established generic framework to determine the frequency dependent Navier FC from atomistic simulations. Here, we have derived analytical expressions to connect the Navier FC to the random force autocorrelation on the confining wall, from the observation that the random force autocorrelation can be related to the hydrodynamic boundary condition, where the Navier FC appears. The analytical framework is generic in the sense that it explicitly includes the system size dependence and also the frequency dependence of the FC, which enabled us to address (i) the long-standing plateau issue in the evaluation of the FC and (ii) the non-Markovian behavior of liquid-solid friction of a Lennard-Jones liquid and of water on various walls and at various temperatures, including the supercooled regime. This new framework opens the way to explore the frequency dependent FC for a wide range of complex liquids.

Highlights

Nanofluidics is the discipline that describes fluid motion in nanoconfinement, whose unique behavior in the mass and ionic transport should be a key ingredient in future technologies for fluid filtration and energy harvesting [1,2,3,4,5]
We have derived analytical expressions to connect the Navier friction coefficient (FC) to the random force autocorrelation on the confining wall, from the observation that the random force autocorrelation can be related to the hydrodynamic boundary condition, where the Navier FC appears
The expressions are generic in the sense that they explicitly include the system size dependence and the FC can be frequency dependent, which enabled us to address (i) the plateau issue on the evaluation of the FC and (ii) the non-Markovian behavior of the liquid-solid friction

Summary

Introduction

Nanofluidics is the discipline that describes fluid motion in nanoconfinement, whose unique behavior in the mass and ionic transport should be a key ingredient in future technologies for fluid filtration and energy harvesting [1,2,3,4,5]. Nakano and Sasa [24,25] introduced explicit assumptions on the scale separation between the microscopic motion of molecules and the macroscopic motion of fluid and proposed a new way to estimate λ based on linearized fluctuating hydrodynamics. These works from the two groups involved elaborate mathematical manipulations and only reported the pure viscous (Markovian) behavior of the Navier FC, for a Lennard-Jones (LJ) liquid on a simple model wall. Non-Markovian behavior of the FC was recently reported for a LJ liquid on a fcc lattice [26], and it is plausible that more complex liquids such as water show such behavior, in analogy with their bulk transport properties [27,28,29,30,31,32]

Published by the American Physical Society

Results

Conclusions