On the moving contact line singularity: Asymptotics of a diffuse-interface model

TL;DR

This paper investigates the moving contact line problem using a diffuse-interface model, demonstrating how it resolves classical singularities and exploring various model extensions for more realistic scenarios.

Contribution

It introduces a diffuse-interface approach to address the contact line singularity and analyzes its asymptotic behaviour, including extensions like slip and precursor films.

Findings

Resolves stress and pressure singularities at the contact line

Provides asymptotic analysis of the diffuse-interface model

Explores model extensions for realistic boundary conditions

Abstract

The behaviour of a solid-liquid-gas system near the three-phase contact line is considered using a diffuse-interface model with no-slip at the solid and where the fluid phase is specified by a continuous density field. Relaxation of the classical approach of a sharp liquid-gas interface and careful examination of the asymptotic behaviour as the contact line is approached is shown to resolve the stress and pressure singularities associated with the moving contact line problem. Various features of the model are scrutinised, alongside extensions to incorporate slip, finite-time relaxation of the chemical potential, or a precursor film at the wall.