Droplet impact dynamics on superhydrophobic surfaces with convex hemispherical shapes

Functional solid surfaces that can realise rapid shedding of liquid droplets have received significant research interest due to their close relevance to many industrial applications. Droplet impact on superhydrophobic surfaces with point-like protrusions has been demonstrated to take off as rings, which alters droplet impact dynamics and thus reduces contact time compared to flat surfaces. However, the essential role of the size ratio of protrusion-to-droplet (λ) for droplets impinging on such surface is rarely considered. Here, we numerically investigate droplet impact on superhydrophobic surfaces with convex hemispherical shapes using a phase-field model coupled with dynamic contact angles. The postimpact outcome regimes occurring for varied λ and Weber number (We) values, spanning 0 ≤ λ ≤ 1.44 and 0.69 ≤ We ≤ 33.68, are mapped on a We−λ diagram. Three distinct dynamic behaviours of droplet impact are identified: contactless bouncing, conventional bouncing, and ring bouncing. Detailed comparative analyses of these impact outcomes are also presented, including the evolution of droplet morphology, impact force, maximum impact pressure, pressure distribution, and velocity vector distribution. The results reveal a previously unknown phenomenon in contactless bouncing, where the impact force exhibits an initial increase followed by a subsequent decrease, while the maximum impact pressure remains approximately constant. Annular rotating retraction results in a longer contact time. Breakup occurs near the necked area, inducing a part of the droplet to depart from the surface as a jet. In addition, it is observed that the dimensionless maximum wetting area becomes independent of the λ and follows a scaling law of 0.67We3/5 if the We exceeds 2.75. Ring bouncing exclusively occurs within the range of 0.24 ≤ λ ≤ 0.96 and We ≥ 24.74, resulting in an approximate 50% reduction in non-dimensional contact time compared to conventional bouncing. These findings favour the understanding of the underlying mechanisms governing droplet impact and thereby provide available guidance to the design of superhydrophobic surfaces.