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

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 $α$. This one is always smaller than the critical one, $α_{crit}$, above which the drop would start to slide down. The hysteresis cycle is performed for positive and negative $α$'s ($|α|<α_{crit}$), 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.