Dynamics of Solid-Liquid Compound Droplets on Cylindrically Concave Superhydrophobic Surfaces

The generation of compound droplets through droplet-particle interactions has garnered significant attention due to its relevance in diagnostics, biomolecule encapsulation, functional coating, and targeted drug delivery. This study explores the dynamics of a deionized water droplet of 3 mm diameter impacting a freely placed glass bead of 1 mm diameter on superhydrophobic concave surfaces exhibiting a static contact angle of 153°. Single-droplet impact experiments are performed across a Weber number range of 8.20-57.10, and high-speed visualization reveals the formation of stable compound droplets with single or binary particles, followed by lift-off. Results indicate that the maximum spreading diameter (β_max) and the residence time of the composite droplet decrease with the increasing concavity ratio (δ) due to differences in axial and azimuthal spreading and gravity. Additionally, higher surface concavity ratios suppress spreading and reduce residence time for a given We. For instance, the compound droplet on a concave surface exhibited a 30% reduction in contact time compared to its flat counterpart. A theoretical scaling based on a modified capillary length accounts for curvature effects in azimuthal spreading, while a simplified lift-off model captures the vertical displacement of compound droplets. The droplet extension on a concave surface follows the relation D_z^max/D₀ ≈ f(We, δ, Bo), and for a flat plate, when δ → 0, the correlation reduces to the established scaling law D_z^max/D₀ ≈ We^1/4. The proposed models show strong agreement with experimental observations, offering insights into compound droplet manipulation on curved superhydrophobic substrates.