Gravitational dependence of contact angle hysteresis for a solid defect pinning a liquid-vapor interface

TL;DR

This paper analyzes how gravity influences contact angle hysteresis caused by a solid defect pinning a liquid-vapor interface, revealing that defect size, not capillary length, governs the behavior when the defect is small.

Contribution

It provides an analytical solution for contact angle hysteresis considering gravity effects, highlighting the importance of defect extension over capillary length.

Findings

Defect extension is the key length scale in contact angle hysteresis under gravity.

Analytical solutions are derived for both parabolic and Gaussian pinning forces.

Gravity's influence depends on the relative size of the defect to the capillary length.

Abstract

We study the case of contact angle hysteresis, when a solid defect is quasi-statically pulled out and pushed into a liquid, in the presence of gravity. We solve the problem analytically in an approximation which, in the case of a truncated parabolic pinning force becomes exact in the the limit of slow variations in the height of the liquid vapour interface. The case of a Gaussian pinning force is solved by a geometrical construction. We show that the extension of the defect, and not the capillary length, is the determining length scale, when the extension of the defect is much smaller than the capillary length.