Too fast to grow: Dynamics of pendant drops sliding on a thin film

TL;DR

This study investigates how slight tilting of a substrate causes pendant drops to transition from growing by fluid accumulation to shrinking while sliding, revealing a novel decay regime in drop dynamics.

Contribution

The paper introduces the discovery of a decay regime for pendant drops on slightly tilted substrates, supported by experiments, simulations, and analytical modeling.

Findings

Drops shrink rather than grow when the substrate is tilted around 2 degrees.

A critical inclination angle marks the transition between growth and decay regimes.

Analytical predictions match experimental and simulation results.

Abstract

Pendant drops suspended on the underside of a wet substrate are known to accumulate fluid from the surrounding thin liquid film, a process that often results in dripping. The growth of such drops is hastened by their ability to translate over an otherwise uniform horizontal film. Here we show that this scenario is surprisingly reversed when the substrate is slightly tilted ($\approx 2$ deg) ; drops become too fast to grow and shrink over the course of their motion. Combining experiments and numerical simulations, we rationalize the transition between the conventional growth regime and the previously unknown decay regime we report. Using an analytical treatment of the Landau-Levich meniscus that connects the drop to the film, we quantitatively predict the drop dynamics in the two flow regimes and the value of the critical inclination angle where the transition between them occurs.