Deposition and rebound of impacting droplets on spherical surfaces

Deposition and rebound after droplet impacting curved surfaces have wide applications in chemical engineering while the critical conditions between them remain unclear. Here, a numerical model based on the Volume of Fluid method and coupled with the dynamic contact angle model is validated and then adopted to simulate the impacting processes of droplets on the convex and concave spherical surfaces. The effects of the Weber number, surface contact angle, and sphere-to-droplet curvature ratio on the temporal morphology, spreading characteristics, and final states of impacting droplets on the spherical surfaces are obtained. As the Weber number increases or the static contact angle and curvature ratio decrease, the impacting droplet spreads faster and yields a larger maximum spreading factor. Decreasing the contact angle and curvature ratio promotes the droplet deposition. With the increase of the Weber number, the final state of an impacting droplet tends to change from full deposition to partial rebound at a smaller contact angle or curvature ratio but from full deposition to full rebound at a larger contact angle or curvature ratio. Furthermore, a theoretical model based on energy conservation is proposed to predict the critical Weber number between the droplet deposition and rebound. Apart from reducing the impacting Weber number and surface contact angle, decreasing the surface curvature ratio enlarges the viscous dissipation during impact and thus enhances the droplet deposition. The results can provide guidance for controlling the droplet deposition and rebound in the applications of chemical spraying, inkjet printing, and pesticide spraying.