Utilization of the second gradient theory in continuum mechanics to study motions and thermodynamics of liquid-vapor interfaces

TL;DR

This paper applies second gradient theory to continuum mechanics to analyze liquid-vapor interfaces, deriving equations for motion, thermodynamics, and surface tension, including explanations for the Marangoni effect.

Contribution

It introduces a thermomechanical model based on second gradient theory that links continuum mechanics with molecular theories of capillarity and explains surface tension phenomena.

Findings

Equivalence to mean-field molecular theories at equilibrium

Derivation of Kelvin circulation theorems for such fluids

Deduces dynamical surface tension and explains Marangoni effect

Abstract

A thermomechanical model of continuous fluid media based on second gradient theory is used to study motions in liquid-vapor interfaces. At equilibrium, the model is shown to be equivalent to mean-field molecular theories of capillarity. In such fluids, conservative motions verify first integrals that lead to Kelvin circulation theorems and potential equations. The dynamical surface tension of liquid-vapor interfaces is deduced from viscous fluid equations. The result provides and explains the Marangoni effect.