Contact angles of a drop pinned on an incline

TL;DR

This paper derives an exact first-order expression for the retentive force factor of a drop pinned on an inclined surface with small tilt or Bond number, validated by numerical simulations.

Contribution

It provides a novel analytical expression for the retentive force factor of a drop on an incline, extending understanding of contact line physics under small perturbations.

Findings

Retentive force factor is pi/2 at first order in tilt or Bond number.

Exact computation of the drop profile in the same approximation.

First order approximations agree well with Surface Evolver simulations.

Abstract

For a drop on an incline with small tilt angle or small Bond number, when the contact line is a circle, we show that the retentive force factor is exactly pi/2 at first order in the tilt angle or the Bond number. The retentive force factor is the ratio between the weight component along the slope and a capillary force defined as surface tension times radius of contact line times difference of cosines of contact angles at the back and at the front of the drop. The drop profile is computed exactly in the same approximation. These results are compared with Surface Evolver results, showing a surprisingly large range of applicability of first order approximations.