Rayleigh and depinning instabilities of forced liquid ridges on heterogeneous substrates

TL;DR

This paper investigates how liquid ridges on inclined, heterogeneous surfaces depin and break up, revealing complex transition behaviors influenced by surface heterogeneities and inclination.

Contribution

It provides a detailed analysis of depinning and breakup mechanisms of liquid ridges on heterogeneous substrates using numerical simulations and bifurcation techniques.

Findings

Ridges can depin and slide downslope under certain conditions.

Transverse instabilities can cause ridges to break into drops before depinning.

Different transition scenarios depend on substrate heterogeneity and slope.

Abstract

Depinning of two-dimensional liquid ridges and three-dimensional drops on an inclined substrate is studied within the lubrication approximation. The structures are pinned to wetting heterogeneities arising from variations of the strength of the short-range polar contribution to the disjoining pressure. The case of a periodic array of hydrophobic stripes transverse to the slope is studied in detail using a combination of direct numerical simulation and branch-following techniques. Under appropriate conditions the ridges may either depin and slide downslope as the slope is increased, or first breakup into drops via a transverse instability, prior to depinning. The different transition scenarios are examined together with the stability properties of the different possible states of the system.