Dynamics of gravity driven three-dimensional thin films on hydrophilic-hydrophobic patterned substrates

TL;DR

This study numerically explores how gravity-driven thin liquid films behave on patterned substrates with hydrophilic and hydrophobic regions, revealing mechanisms to control film spreading and fingering patterns.

Contribution

It introduces a numerical analysis of thin film dynamics on patterned substrates, predicting contact line growth rates and offering insights for experimental control of film behavior.

Findings

Hydrophilic stripes guide the film, while fingers develop on hydrophobic stripes.

Fingering occurs on hydrophobic domains, spreading on hydrophilic domains.

Quantitative prediction of contact line growth rate on checkerboard patterns.

Abstract

We investigate numerically the dynamics of unstable gravity driven three-dimensional thin liquid films on hydrophilic-hydrophobic patterned substrates of longitudinal stripes and checkerboard arrangements. The thin film can be guided preferentially on hydrophilic longitudinal stripes, while fingers develop on adjacent hydrophobic stripes if their width is large enough. On checkerboard patterns, the film fingering occurs on hydrophobic domains, while lateral spreading is favoured on hydrophilic domains, providing a mechanism to tune the growth rate of the film. By means of kinematical arguments, we quantitatively predict the growth rate of the contact line on checkerboard arrangements, providing a first step towards potential techniques that control thin film growth in experimental setups.