Contact angle hysteresis effects on a drop sitting on an incline plane

TL;DR

This paper investigates how contact angle hysteresis affects the shape and contact angles of a liquid drop on an inclined plane, providing an analytical model validated by experiments that describes the drop's morphology during hysteresis cycles.

Contribution

It introduces a truncated analytical solution within the lubrication approximation to accurately describe static drop shapes and contact angle distributions during hysteresis cycles.

Findings

Analytical solution matches experimental data for static drop shapes.

Complete description of drop footprint and contact angles achieved.

Model applicable for small measured drop parameters.

Abstract

We study the contact angle hysteresis and morphology changes of a liquid drop sitting on a solid substrate inclined with respect to the horizontal at an angle $\alpha$. This one is always smaller than the critical one, $\alpha_{crit}$, above which the drop would start to slide down. The hysteresis cycle is performed for positive and negative $\alpha$'s ($|\alpha|<\alpha_{crit}$), and a complete study of the changes in contact angles, free surface and footprint shape is carried out. The drop shape is analyzed in terms of a solution of the equilibrium pressure equation within and out of the long--wave model (lubrication approximation). Within this approximation, we obtain a truncated analytical solution that describes the static drop shapes, that is successfully compared with experimental data. This solution is of practical interest since it allows for a complete description of all the drop features, such as its footprint shape or contact angle distribution around the drop periphery, starting from a very small set of relatively easy to measure drop parameters.