Analytical Model of Post-Impact Droplet Spreading on a Micro-Patterned Superhydrophobic Surface With Surface Slip

Abstract

Several analytical models exist to predict droplet impact behavior on superhydrophobic surfaces. However, no previous model has rigorously considered the effect of surface slip on droplet spreading and recoiling that is inherent in many superhydrophobic surfaces. This paper presents an analytical model that takes into account surface slip at the solid-fluid interface during droplet deformation. The effects of slip are captured in terms that model the kinetic energy and viscous dissipation and are compared to a classical energy conservation model given by Attane et al. and experimental data from Pearson et al. A range of slip lengths, Weber numbers, Ohnesorge numbers, and contact angles are investigated to characterize the effects of slip over the entire range of realizable conditions. We find that surface slip does not influence normalized maximum spread diameter for low We but can cause a significant increase for We > 100. Surface slip affects dynamical parameters more profoundly for low Oh numbers (0.002–0.01). Normalized residence time and rebound velocity increase as slip increases for the same range of We and Oh. The influence of slip is more significantly manifested on normalized rebound velocity than normalized maximum spread diameter. Contact angles in the range of 150°–180° do not affect impact dynamics significantly.