Relaxation of a dewetting contact line Part 1: A full-scale hydrodynamic calculation

TL;DR

This paper provides a comprehensive hydrodynamic analysis of dewetting contact line relaxation in a specific geometry, revealing complex bifurcation behavior and the importance of viscous effects near critical conditions.

Contribution

It offers a full-scale lubrication theory calculation of contact line relaxation, challenging simplified models and highlighting the transition in dispersion relations near the critical capillary number.

Findings

Contact line stability is maintained below the critical capillary number.

Dispersion relation transitions from |q| to q^2 near the critical point.

Viscous effects are essential and cannot be encapsulated by a simple macroscopic contact angle law.

Abstract

The relaxation of a dewetting contact line is investigated theoretically in the so-called "Landau-Levich" geometry in which a vertical solid plate is withdrawn from a bath of partially wetting liquid. The study is performed in the framework of lubrication theory, in which the hydrodynamics is resolved at all length scales (from molecular to macroscopic). We investigate the bifurcation diagram for unperturbed contact lines, which turns out to be more complex than expected from simplified 'quasi-static' theories based upon an apparent contact angle. Linear stability analysis reveals that below the critical capillary number of entrainment, Ca_c, the contact line is linearly stable at all wavenumbers. Away from the critical point the dispersion relation has an asymptotic behaviour sigma~|q| and compares well to a quasi-static approach. Approaching Ca_c, however, a different mechanism takes over and the dispersion evolves from |q| to the more common q^2. These findings imply that contact lines can not be treated as universal objects governed by some effective law for the macroscopic contact angle, but viscous effects have to be treated explicitly.