Droplets on Inclined Plates: Local and Global Hysteresis of Pinned Capillary Surfaces

TL;DR

This paper develops a theory that accounts for contact line pinning and hysteresis to accurately predict droplet shapes on inclined plates, revealing the influence of hysteresis, Bond number, and deposition history.

Contribution

It introduces a new model incorporating contact line pinning and hysteresis effects, improving predictions of droplet shapes on inclined surfaces.

Findings

Critical tilt depends on hysteresis range and Bond number in 2D.

In 3D, initial width and deposition history affect droplet stability.

The theory aligns well with experimental observations.

Abstract

Local contact line pinning prevents droplets from rearranging to minimal global energy, and models for droplets without pinning cannot predict their shape. We show that experiments are much better described by a theory, developed herein, that does account for the constrained contact line motion, using as example droplets on tilted plates. We map out their shapes in suitable phase spaces. For 2D droplets, the critical point of maximum tilt depends on the hysteresis range and Bond number. In 3D, it also depends on the initial width, highlighting the importance of the deposition history.