Dynamics of Perfectly Wetting Drops under Gravity

TL;DR

This study investigates the long-term dynamics of small, perfectly wetting silicone oil droplets on a vertical surface, revealing deviations from classical theory due to van der Waals forces.

Contribution

It provides the first experimental observation of a two-dimensional similarity solution for droplet shape and identifies van der Waals forces as a key factor in long-time deviations.

Findings

Intermediate-time $t^{1/3}$ scaling observed

Two-dimensional similarity solution characterized

Long-time deviations explained by van der Waals forces

Abstract

We study the dynamics of small droplets of polydimethylsiloxane (PDMS) silicone oil on a vertical, perfectly-wetting, silicon wafer. Interference videomicroscopy allows us to capture the dynamics of these droplets. We use droplets with a volumes typically ranging from 100 to 500 nanolitres (viscosities from 10 to 1000 centistokes) to understand long time derivations from classical solutions. Past researchers used one dimensional theory to understand the typical $t^{1/3}$ scaling for the position of the tip of the droplet in time $t$. We observe this regime in experiment for intermediate times and discover a two-dimensional, similarity solution of the shape of the droplet. However, at long times our droplets start to move more slowly down the plane than the $t^{1/3}$ scaling suggests and we observe deviations in droplet shape from the similarity solution. We match experimental data with simulations to show these deviations are consistent with retarded van der Waals forcing which should become significant at the small heights observed.