Maximum droplet volume on cylindrical surfaces

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.