Darcy-Weisbach friction factor at the nanoscale: From atomistic calculations to continuum models

Abstract

A modification of the Darcy-Weisbach friction factor applicable to nanoscale liquid transport processes is proposed. Non-equilibrium molecular dynamics simulations allow us to access the atomic behaviour of liquids moving in nanochannels, and by comparing atomistic simulation results with continuum Navier-Stokes solutions, we extend the applicability of continuum theory to nanoscale liquid flows. We find that classical continuum theory predictions of power dissipation do not apply in the case of nanochannels and have to be modified accordingly with input from atomistic simulations such as slip velocity and profiles of variable viscosity. The mathematical form of the friction factor expression persists for quite small nanochannel widths, i.e., the form of the relation for the friction factor f Re = const. is practically maintained even at the nanoscale, but the value of the constant significantly increases with increasing hydrophilicity.