Scaling analysis for azimuthal spreading and contact time of droplet impacting on superhydrophobic cylindrical surfaces

Abstract

Drop impact on superhydrophobic surfaces has gained great attention because of its physics and application in water repellency, drag reduction, and anti-icing. Spreading lengths and the contact time are the crucial parameters determining the extend of drop–surface interaction and effective heat transfer between the two and are, hence, trivial to many engineering applications. Post-collisional dynamics over cylindrical geometries are quite different from that of the flat surfaces due to the asymmetry in spreading and retraction dynamics. The dynamics are mainly governed by the impact Weber number and curvature ratio of impacting surface to drop. The spreading dynamics in axial direction is found to be fairly predicted by the governing laws coined for flat surfaces. However, the spreading dynamics in the azimuthal direction is quite complex. Herein, we propose a simple scaling analysis for the spreading dynamics in the azimuthal direction as well as for the contact time of the impacting drop with the surface. A modified capillary length is proposed accounting the curvature effect of the substrate by incorporating a centrifugal component of acceleration for the expanding lamella over the curved surface. With the proposed modified capillary length, a universal scaling relationship for azimuthal spreading length and contact time is developed. The proposed scaling laws are found to be in good agreement with the experimental results from the present study as well as with the existing literature for a wide range of Weber numbers and surface curvature.