Boundary conditions for a capillary fluid in contact with a wall

TL;DR

This paper derives boundary conditions for a capillary fluid in contact with a wall, accounting for molecular forces, surface energy, and curvature, using a second gradient fluid model and virtual work principle.

Contribution

It introduces a novel approach to boundary conditions for capillary fluids considering second gradient effects and surface energy dependence on fluid density.

Findings

Derived limit conditions involving fluid density, its normal derivative, and surface curvature.

Established a framework for analyzing fluid-solid contact with molecular force considerations.

Provided mathematical expressions for boundary conditions in capillary fluid models.

Abstract

Contact of a fluid with a solid or an elastic wall is investigated. The wall exerts molecular forces on the fluid which is locally strongly nonhomogeneous. The problem is approached with a fluid energy of the second gradient form and a wall surface energy depending on the value of the fluid density at the contact. >From the virtual work principle are obtained limit conditions taking into account the fluid density, its normal derivative to the wall and the curvature of the surface