Upward Splashing of a Droplet Impacting an Inclined Superhydrophobic Surface

Abstract

It has long been held that when a droplet impacts obliquely onto a smooth dry surface at normal ambient temperature and pressure, upward splashing can be more easily suppressed than downward splashing. However, in this research, we experimentally find that for a superhydrophobic surface, increasing the wall inclination beforehand suppresses downward splashing and subsequently suppresses upward splashing. The spreading theory for an inclined surface is modified to predict the spreading process on an inclined superhydrophobic wall. Due to the existence of an asymmetric boundary layer between the upward and downward sheet on an inclined wall, the thickness and growth rate of the upward rim are smaller than those of the downward rim; for this reason, the upward side of the spreading sheet splashes more easily on a superhydrophobic wall, considering the theory of a droplet splashing on a flat surface. However, because the upward rim velocity is smaller than the downward rim velocity, the downward lamella splashes more easily than the upward lamella on a smooth surface. We attempt to theoretically describe the interval of the stochastic flow mode (spreading/splashing) that exists in practice for the first time. We also give the phase diagram containing three flow patterns, namely, two-side spreading, upward-only splashing, and two-side splashing, in the parameter space of the Weber number We and the wall inclination angle χ. The theory agrees well with the experimental results.