Modelling of the moving deformed triple contact line: influence of the fluid inertia

TL;DR

This paper develops a model for the movement of the triple contact line considering both surface heterogeneities and fluid inertia, highlighting how inertia influences pinning and intermittent motion.

Contribution

It introduces a novel model that incorporates fluid inertia and surface defects to analyze contact line dynamics, derived from Hamilton's principle.

Findings

Inertia can cause pinning and intermittent motion of the contact line.

The model predicts rapid capillary rise behavior on inhomogeneous surfaces.

Viscous dissipation in the bulk is negligible compared to near the contact line.

Abstract

For partial wetting, motion of the triple liquid-gas-solid contact line is influenced by heterogeneities of the solid surface. This influence can be strong in the case of inertial (e.g. oscillation) flows where the line can be pinned or move intermittently. A model that takes into account both surface defects and fluid inertia is proposed. The viscous dissipation in the bulk of the fluid is assumed to be negligible as compared to the dissipation in the vicinity of the contact line. The equations of motion and the boundary condition at the contact line are derived from Hamilton's principle. The rapid capillary rise along a vertical inhomogeneous wall is treated as an example.