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 ( We) 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 (ε) and a tangential restitution coefficient (ε). We discovered that, regardless of the impact angle, ε can be accurately predicted as a function of the normal Weber number (ε = 0.94 We). We support this finding with a mathematical derivation from theory, indicating a general scaling relationship of ε ∼ We for the normal restitution coefficient. Likewise, the tangential restitution coefficient (ε) can also be predicted as a function of We (ε = 1.20 We) but is much larger than ε. 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 ε and ε, we derived a model to predict the overall restitution coefficient of rebounding drops at any We and AOI. The model's predictions are highly accurate, lying close to our experimental observations in all cases. Regarding the contact time ( t), we found that for normal impacts, t increased slightly as We 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- We impacts. We attribute this correlation to stretched rebounding behavior, which accelerates the rebounding of highly oblique impacts.

Droplet dynamics on slippery surfaces: small droplet, big impact

“…Compared to normal impact, more attention has been given to oblique impact for practical application [107][108][109][110][111]. A droplet in oblique impact is subject to a combination of downward motion along the surface with a tangential impinging velocity of v 0 sinf and motion normal to the surface with an impinging velocity of v 0 cosf, where v 0 is the impact velocity and f is the tilt angle of the surface.…”

“…7c. This is explained by the asymmetric drop deformation during a collision and asymmetric bouncing mechanism to reduce the contact time [70,110]. On another note, oblique bouncing or migration can occur on the horizontally placed surface but with wetting or thermal gradient due to the unbalanced interfacial forces created by such heterogeneous architectures [113][114][115][116].…”

Rebound Dynamics of Two Droplets Successively Impacting an Inclined Surface

“…In nature and industrial fields, the droplet encounters various solid surface, such as curve, textured, and inclined surface [24][25][26][27][28][29][30][31][32][33][34]. Compared with the flat horizontal surface, the outcomes are more complex, and the results may be different.…”

“…It is demonstrated that the droplet impacting an inclined surface behaves asymmetry between the tangential and lateral direction along the surface, which can promote the droplet to rebound from the surface. Meanwhile, due to the tangential velocity, the droplet slides along the inclined surface, away from the impact position [31][32][33]. If two droplets impact an inclined surface successively, the off-center impact should be observed, which is different from horizontal surface and still poorly understood, especially on superhydrophobic surfaces.…”

Models of processes accompanying crystallization of supercooled droplets

“…Кристаллизация растворенных в переохлажденной воде кристаллов описывается уравнением Кана-Хиллиарда [3] = ∇ • ( )∇ ( ) − ∆ ⁄ (здесь концентрация кристаллов, -коэффициент градиента энергии, = ( ) -коэффициент подвижности, ( ) -гомогенная свободная энергия) и уравнением Гинсбурга-Ландау; при исследовании процессов кристаллизации используется теория неустойчивости Муллинс-Cикерки [4]. Данные об особенностях кристаллизации переохлажденной воды получены в предшествующих исследованиях [5][6][7][8]. Стремление понять внутреннюю структуру воды возрастает тем более, чем больше накапливается фактов о ее разнообразных проявлениях [9][10][11][12].…”