Contact angle hysteresis and static friction for two-dimensional droplets

TL;DR

This paper investigates contact angle hysteresis and static friction in two-dimensional droplets, analyzing droplet behavior on inclined planes and ceilings, revealing stable configurations, bifurcations, and relations between volume and Bond number.

Contribution

It introduces a unified framework for analyzing static friction and contact angle hysteresis in 2D droplets, including stable states and bifurcation phenomena.

Findings

Identification of two stable configurations of pendent droplets.

Relation between pinch-off volume and Bond number.

Visualization of droplet shape changes with inclination angle.

Abstract

Contact angle hysteresis of droplets will be examined in light of static friction between liquid drop and solid surface. Unlike frictions in solid-solid interfaces, pinning forces at contact points or contact lines would be the cause of friction. We will define coefficients of static friction and relate them with advancing and receding contact angles for the case of two-dimensional droplets. In our work sessile drops in an inclined plane, and pendent drops in a slanted ceiling will all be analyzed within a single framework with the inclination angle as a free parameter. We can then visualize the gradual change of shapes of a droplet put on a plane as the inclination angle changes adiabatically to make a complete turn. We point out that there could be two distinct stable configurations of pendent droplets for the same physical conditions, hence dubbed the bifurcation. And in the case of pendent droplets we investigate at what ranges of parameters pinch-offs occur, and find an interesting relation between the fallen-out volume and the Bond number.