Challenges in Nanofluidics—Beyond Navier–Stokes at the Molecular Scale

Peter Daivis,Billy Todd

doi:10.3390/pr6090144

Abstract

The fluid dynamics of macroscopic and microscopic systems is well developed and has been extensively validated. Its extraordinary success makes it tempting to apply Navier–Stokes fluid dynamics without modification to systems of ever decreasing dimensions as studies of nanofluidics become more prevalent. However, this can result in serious error. In this paper, we discuss several ways in which nanoconfined fluid flow differs from macroscopic flow. We give particular attention to several topics that have recently received attention in the literature: slip, spin angular momentum coupling, nonlocal stress response and density inhomogeneity. In principle, all of these effects can now be accurately modelled using validated theories. Although the basic principles are now fairly well understood, much work remains to be done in their application.

Highlights

The classical Navier–Stokes theory describing flow of Newtonian fluids has been remarkably successful, but it is inadequate under certain conditions
We review some recent advances in the fluid dynamics of nanoconfined liquids, placing them in context and discussing the conditions under which they become important
We have provided a brief review of three fundamental phenomena that should be included in an accurate continuum treatment of nanofluidics: slip, spin angular momentum coupling, and non-local response

Summary

Introduction

The classical Navier–Stokes theory describing flow of Newtonian fluids has been remarkably successful, but it is inadequate under certain conditions. One of the difficulties with computation of the slip length and slip friction coefficient by direct evaluation in non-equilibrium molecular dynamics that simulate flow through a channel is thatk for high slip systems, the velocity profile is almost flat. Extrapolation of such a velocity profile to the position where the velocity is zero is extremely error prone [12]. Another way is to evaluate the instantaneous velocity of the fluid averaged over a region within a distance ∆ of the wall This has the disadvantage that averaging over a finite region could result in error, but the calculation of the slip friction coefficient for a given wall–fluid combination can be repeated for different values of. It has been adapted to a cylindrical geometry [22] for studies of the slip friction coefficient of water in carbon nanotubes [10,23]

Spin Angular Momentum Coupling

Nonlocal Response

Density Inhomogeneity

Findings

Conclusions