Maximum droplet volume on cylindrical surfaces

TL;DR

This paper develops a new semi-empirical model to accurately predict the maximum droplet volume on horizontal fibers, considering fiber size and wettability, validated through experiments and simulations.

Contribution

It introduces a universal scaling law for maximum droplet volume on fibers, improving predictive accuracy over existing models.

Findings

The model accurately predicts maximum droplet volume across various fiber sizes.

Normalized volume depends only on contact angle, independent of fiber dimensions.

Validation confirms the model's applicability from thin fibers to flat surfaces.

Abstract

The maximum volume ($\Omega$) of a droplet that can remain attached to a horizontal fiber defines the stability limit of droplet-fiber interactions, phenomena common in nature and critical to diverse engineering applications. Existing predictive models for $\Omega$ show limitations in accurately capturing the dependence of $\Omega$ on fiber size and wettability. To address this gap, we systematically investigate $\Omega$ on a horizontal fiber through numerical simulations and experiments. A comprehensive semi-empirical model for $\Omega$ is developed and validated against both experimental measurements and reference simulations. This model establishes a new scaling under which the normalized maximum droplet volume depends solely on the contact angle and remains valid across a wide spectrum from a sub-millimeter thin fiber to the flat-surface limit, regardless of the diverse morphologies that droplets exhibit.