On the Oblique Impact Dynamics of Drops on Superhydrophobic Surfaces. Part II: Restitution Coefficient and Contact Time.

Abstract

We tested oblique drop impacts on a superhydrophobic surface at normal Weber numbers ( Wen) in the range of 3-45, and at varying angles of incidence (AOIs), ranging from 0° (normal impact) to 60° (highly oblique). Our objective is to define the influence of the AOI on the restitution coefficient and on the contact time of rebounding droplets. To interpret the overall restitution coefficient of oblique drop rebounds (ε), we decoupled it into two separate components: a normal (εn) and a tangential restitution coefficient (εt). We discovered that, regardless of the impact angle, εn can be accurately predicted as a function of the normal Weber number (εn = 0.94 Wen-1/4). We support this finding with a mathematical derivation from theory, indicating a general scaling relationship of εn ∼ Wen-1/4 for the normal restitution coefficient. Likewise, the tangential restitution coefficient (εt) can also be predicted as a function of Wen (εt = 1.20 Wen-0.12) but is much larger than εn. As a result, the overall restitution coefficient (ε) increases for more oblique impacts because most of the tangential velocity is preserved. Furthermore, using the observed correlations for εn and εt, we derived a model to predict the overall restitution coefficient of rebounding drops at any Wen and AOI. The model's predictions are highly accurate, lying close to our experimental observations in all cases. Regarding the contact time ( tc), we found that for normal impacts, tc increased slightly as Wen was raised. We associate this behavior with partial penetration of the liquid into the surface's pores, which results in greater solid-liquid adhesion, prolonging detachment. For highly oblique impacts (AOI = 60°), we observed the reverse trend: the drop's contact time decreases for higher- Wen impacts. We attribute this correlation to stretched rebounding behavior, which accelerates the rebounding of highly oblique impacts.