Theory of Viscosity of Confined Fluids in Small / Nano Systems (Theory of Interfacial Viscosity)

TL;DR

This paper develops a molecular theory for the viscosity of confined and interfacial fluids in nano systems, based on Enskog kinetic theory and Boussinesq equations, providing explicit expressions and dimensionless forms.

Contribution

It introduces a novel molecular framework for calculating interfacial and confined fluid viscosities using kinetic theory and surface pressure tensor analysis.

Findings

Derived microscopic expressions for surface pressure tensor components.

Obtained interfacial shear and dilatational viscosities.

Presented dimensionless viscosity equations versus reduced density.

Abstract

In this paper we present the molecular theory of viscosity of confined fluids in small or nano systems. This theory is also applicable to the interfacial viscosity. The basis of this research work is the Enskog kinetic theory and the Boussinesq constitutive equation. The Enskog kinetic theory is first transformed into a two-dimensional form. Then the potential energy collisional transfer part of the flux vector and the contribution to the surface pressure tensor due to collisional transfer are derived. Then the kinetic energy part of the flux vector and consequently the contribution to the surface pressure tensor due to flow of molecules is obtained. The microscopic expression of total surface pressure tensor is obtained by adding of the potential energy collisional transfer part and the kinetic energy contribution. Then the expression of interfacial shear and dilatational viscosities are concluded by the comparison of corresponding terms of the two microscopic and macroscopic surface pressure tensor equations. Finally the dimensionless forms of interfacial shear viscosity, interfacial dilatational viscosity and the surface tension equations are derived and they are plotted versus the reduced superficial number density.