Spatters and Spills: Spreading Dynamics for Partially Wetting Droplets

TL;DR

This paper introduces a solvable model for the spreading dynamics of partially wetting droplets, accounting for both capillary and gravitational regimes, and validates it with experimental data on household fluids.

Contribution

The paper develops a unified, explicit model for droplet spreading that accurately describes both small and large droplet behaviors, validated by experimental measurements.

Findings

Model accurately predicts spreading dynamics in both regimes.

Good agreement between predictions and experimental data.

Equilibrium contact angles are consistent across regimes.

Abstract

We present a solvable model inspired by dimensional analysis for the time-dependent spreading of droplets that partially wet a substrate, where the spreading eventually stops and the contact angle reaches a nonzero equilibrium value. We separately consider small droplets driven by capillarity and large droplets driven by gravity. To explore both regimes, we first measure the equilibrium radius versus a comprehensive range of droplet volumes for four household fluids, and we compare the results with predictions based on minimizing the sum of gravitational and interfacial energies. The agreement is good, and gives a reliable measurement of an equilibrium contact angle that is consistent in both small and large droplet regimes. Next we use energy considerations to develop equations of motion for the time dependence of the spreading, in both regimes, where the driving forces are balanced against viscous drag in the bulk of the droplet and by friction at the moving contact line. Our approach leads to explicit prediction of the functional form of the spreading dynamics. It successfully describes prior data for a small capillary-driven droplet, and it fits well to new data we obtain for large gravity-driven droplets with a wide range of volumes.