Analysis of the Spreading Radius in Droplet Impact: The Two-Dimensional Case

TL;DR

This paper investigates the maximum spreading radius of droplets impacting surfaces in two-dimensional geometries, providing a correlation based on energy analysis validated by simulations and experiments.

Contribution

It introduces a new correlation predicting droplet spreading radius incorporating dissipation effects, validated through simulations and existing experimental data.

Findings

Dissipation by head loss is crucial for accurate predictions.

The correlation effectively predicts maximum spreading radius across different conditions.

Simulation results agree well with the theoretical model.

Abstract

We study droplet-impact problems in a three-dimensional cylindrical or equivalent two-dimensional Cartesian geometry. Such structures do have an approximate experimental realization, and they are often simulated a test-bed for computational methods. We focus on droplet impact on a smooth homogeneous surface as well as head-on collision of two droplets. We perform an energy-budget analysis and introduce a correlation which predicts the maximum spreading radius as a function of Reynolds number and Weber number. We show how the dissipation term in this analysis can be decomposed into boundary-layer dissipation in the droplet lamella (where applicable), and head loss. We use existing results in the literature (simulations and experiments), as well as our own simulation results to validate the correlation. Dissipation by head loss is a key term in the analysis: only by modeling it accurately can one obtain good agreement between the simulations and the theory.