Splashing of droplets impacting superhydrophobic substrates

Abstract

A drop of radius $R$ of a liquid of density $\unicode[STIX]{x1D70C}$, viscosity $\unicode[STIX]{x1D707}$ and interfacial tension coefficient $\unicode[STIX]{x1D70E}$ impacting a superhydrophobic substrate at a velocity $V$ keeps its integrity and spreads over the solid for $V<V_{c}$ or splashes, disintegrating into tiny droplets violently ejected radially outwards for $V\geqslant V_{c}$, with $V_{c}$ the critical velocity for splashing. In contrast with the case of drop impact onto a partially wetting substrate, Riboux & Gordillo (Phys. Rev. Lett., vol. 113, 2014, 024507), our experiments reveal that the critical condition for the splashing of water droplets impacting a superhydrophobic substrate at normal atmospheric conditions is characterized by a value of the critical Weber number, $We_{c}=\unicode[STIX]{x1D70C}\,V_{c}^{2}\,R/\unicode[STIX]{x1D70E}\sim O(100)$, which hardly depends on the Ohnesorge number $Oh=\unicode[STIX]{x1D707}/\sqrt{\unicode[STIX]{x1D70C}\,R\,\unicode[STIX]{x1D70E}}$ and is noticeably smaller than the corresponding value for the case of partially wetting substrates. Here we present a self-consistent model, in very good agreement with experiments, capable of predicting $We_{c}$ as well as the full dynamics of the drop expansion and disintegration for $We\geqslant We_{c}$. In particular, our model is able to accurately predict the time evolution of the position of the rim bordering the expanding lamella for $We\gtrsim 20$ as well as the diameters and velocities of the small and fast droplets ejected when $We\geqslant We_{c}$.

On the splashing of high-speed drops impacting a dry surface

“…The splashing criterion within this theory is defined as β = √ F L /(2σ ). The agreement of this latter theory with multiple experiments has influenced recent modifications that consider the drop impact on heated (Staat et al 2015), moving (Hao & Green 2017), inclined or hydrophobic (Quintero, Riboux & Gordillo 2019) surfaces.…”

Spreading and splashing of drops impacting rough substrates

“…Moreover, figures 6 and 7 also show that the droplet disintegrates more irregularly when increases. The first row, highlighted in black, corresponds to the case of a smooth glass substrate, the second row, highlighted in blue, corresponds to experiments done with a SH coating (Quintero et al 2019) whereas the rest of the cases correspond to SC sandpapers. The splash cases are highlighted in pink.…”

“…Motivated by the observations above, in the remainder of this contribution, three different theoretical frameworks will be used to predict, in an approximate way, the splash transition on rough substrates: the one for smooth partially wetting substrates deduced in Riboux & Gordillo (2014) and will be employed here to describe the splash transition in the case We ε 1 and the rim wets the rough substrate. Moreover, a new result will be derived to describe the splash of drops impacting on wetting substrates when We ε 1 whereas the results in Quintero et al (2019) will be used to predict the value of the critical Weber number when the rim does not wet the solid. The similitudes between the present experimental results and those previously reported for smooth or SH coatings are further supported by the experimental evidence depicted for the case of water drops in figure 10, where it is shown that, in analogy with SH substrates, air pockets are entrapped between the expanding liquid film and the solid.…”

How a raindrop gets shattered on biological surfaces

“…Recently, drop impact on engineered microscale structures has been known to exhibit asymmetric spreading (11) and retraction (4) and a pancake-shaped rebouncing (12), finally leading to the rapid drop detachment with a significant decrease in the contact time (4,12). However, the role of microscale structures during drop impact was underestimated since most studies have focused on drop impacts at low speeds (4,5,13,14), much lower than real raindrop impact speeds in natural events.…”