Droplet entrapment on inclined substrates by enforcement of pearl formation

Abstract

Sliding droplets on an inclined substrate may deposit a residual liquid termed as pearling. This three-dimensional mechanism can be observed even on near-perfect surfaces, and it is mainly affected by the Bond number, inclination angle, and capillary number. However, specifically designed surfaces can alter the dynamic contact line and enforce droplets to deposit a pearl. We model three-dimensional droplet motion under long-wave assumption with a precursor film model for such substrates where the surface is designed as a continuous function and integrate governing equations using quadratic finite element method with adaptive mesh refinement. For various surface structures, energies, and inclination angles, we show the expedition/promotion of pearl formation alongside its mechanism, and how to periodically trap droplets inside the grooves. Finally, we discuss the volume control of entrapped droplets.