Slip boundary conditions in nanofluidics from the molecular theory of solvation

Abstract

We propose the derivation and calculation of the hydrodynamic slip length from the first principles of statistical mechanics, based on a combination of linear response theory and equilibrium molecular theory of solvation. The slip length obtained is independent of the type of flow and is related to the fluid organisation near the solid surface, as governed by the solid–liquid and liquid–liquid interactions. In a wide range of shear rates and surface–liquid interactions, the slip length is expressed in terms of the Green–Kubo–Nakano relations as a function of the anisotropic inhomogeneous time correlation function of density fluctuations of the liquid in contact with the surface. The presented treatment generalises the phenomenological definition of the friction coefficient and the slip length to a tensor quantity, which reflects an anisotropic nature of an ordered crystalline surface. We derive generic analytical expressions for the liquid–surface friction coefficient and slip length for an arbitrary surface–liquid interaction potential. We further illustrate it by numerical calculations for the case of a laminar flow of several molecular liquids and water, at ambient conditions in contact with the (100) FCC surface of gold, copper and nickel modelled using all-atom or united-atom models for liquids and the Steele potential for crystalline surfaces. The values obtained for slip length range from few to hundreds of nanometres and are consistent with experimental measurements. We also calculate pressure and temperature dependence on the slip length for water in a wide range of these thermodynamic parameters. The information obtained is intended to be used, in particular, to control or manipulate the flow in electrokinetic processes.