Dewetting of a corner film wrapping a wall-mounted cylinder

TL;DR

This paper combines theoretical and numerical methods to analyze the stability and breakup of a liquid film wrapping a wall-mounted cylinder, highlighting the influence of film size and wettability on film stability and droplet formation.

Contribution

It introduces a combined linear stability analysis and numerical simulations to better understand film dewetting and breakup mechanisms around cylindrical structures.

Findings

Film size is the dominant factor in stability.

Thinner films are more sensitive to perturbations.

Numerical simulations reveal secondary droplet formation and crest coalescence.

Abstract

In this study, we investigate the stability of a liquid film that partially wets a corner between a cylinder and a substrate, using a combination of theoretical and numerical approaches. The film stability, which depends on the film size and the wall wettability, is firstly predicted by a standard linear stability analysis (LSA) within the long-wave theoretical framework. We find that the film size plays the most important role in controlling the film stability. Specifically, the thinner the film is, the more sensitive it becomes to the large-wavenumber perturbation. The wall wettability mainly impacts the growth rates of perturbations and slightly influences the marginal stability and post-instability patterns of wrapping films. We compare the LSA predictions with numerical results obtained from a disjoining pressure model (DPM) and Volume-of-Fluid (VOF) simulations, which provide more insights into the film breakup process. At the early stage there is a strong agreement between the LSA predictions and the DPM results. Notably, as the perturbation grows, thin film regions connecting two neighboring satellite droplets form which may eventually lead to a stable or temporary secondary droplet, an aspect which the LSA is incapable of capturing. In addition, the VOF simulations suggest that beyond a critical film size the crest coalescence mechanism becomes involved during the breakup stage. Therefore, the LSA predictions are able to provide only an upper limit on the final number of satellite droplets.