On the (In)Equality of Droplet Rebound Dynamics at Fixed Weber Number.

The similarity of droplet impacts on nature-mimicking superhydrophobic surfaces is traditionally compared using the dimensionless Weber number. Yet, maintaining a constant We by decoupling droplet diameter and impact velocity influences secondary forces, challenging this assumption of similarity. In this work, we investigate water droplet impacts on a lotus-leaf-mimicking laser-textured superhydrophobic aluminum surface at two constant Weber number levels (25 and 50), varying droplet diameter from 2.1 to 4.15 mm. Our results confirm that maximum spreading depends on the Reynolds number at a fixed We, as smaller, faster droplets spread less due to increased relative viscous dissipation. We propose a modified empirical scaling model that describes our data with high accuracy and generalizes successfully to external datasets. Crucially, we demonstrate that the contact time of a droplet of a given size is not strictly velocity-independent, unveiling a Weber number-dependent inertia-capillary scaling. We show that this is driven by a shift in rebound dynamics, where the relative timescale of spreading increases over retraction for larger droplets. These findings demonstrate that We is insufficient to characterize droplet rebound across varying scales and that accounting for size-dependent deviations is critical for the precise design of technologies that leverage droplet-surface interactions.