Submillimeter-Sized Bubble Entrapment and a High-Speed Jet Emission during Droplet Impact on Solid Surfaces

Droplet impacting on pillared hydrophobic surfaces with different solid fractions

HYPOTHESIS

The solid fraction of the substrate is expected to influence the bouncing behavior of an impinging droplet, thereby affecting spreading and contact time. Hence, it should be possible to alter the velocity and pressure distribution of impacting droplet, and also affect the impact velocity for droplet penetration right upon impact.

SIMULATIONS

We systematically investigate the impact dynamics of water droplets on pillared hydrophobic surfaces with different solid fractions using phase-field simulations. The velocity and pressure distributions of impacting droplets on pillared hydrophobic surfaces with varied Weber numbers and solid fractions are studied. In addition, the influences of the solid fraction on the bouncing behaviors of the impinging droplet, such as the maximum wetting spreading, the maximum impacting depth, and the contact time, are also investigated to further understand the impact event.

FINDINGS

We show that a three-peak pressure profile appears on the top of the pillared hydrophobic surface during droplet impact by varying the solid fraction of the surface. The first peak is generated by the impact of the droplet itself, while the second peak arises from the droplet recoil impact associated with the dynamic properties of the jet. Moreover, we identify a hitherto unknown third pressure peak related to the hydrodynamic singularity that emerges due to the convergence of the fluid during the droplet rebound. This solid fraction-dependent impacting behavior reveals the intricate interplay between droplet dynamics and the underlying surface characteristics, providing valuable insights into the design and optimization of micro/nano structured hydrophobic surfaces for various applications.

Singular jets during droplet impact on superhydrophobic surfaces

HYPOTHESIS

The impact of droplets is prevalent in numerous applications, and jetting during droplet impact is a critical process controlling the dispersal and transport of liquid. New jetting dynamics are expected in different conditions of droplet impact on super-hydrophobic surfaces, such as new jetting phenomena, mechanisms, and regimes.

EXPERIMENTS

In this experimental study of droplet impact on super-hydrophobic surfaces, the Weber number and the Ohnesorge number are varied in a wide range, and the impact process is analyzed theoretically.

FINDINGS

We identify a new type of singular jets, i.e., singular jets induced by horizontal inertia (HI singular jets), besides the previously studied singular jets induced by capillary deformation (CD singular jets). For CD singular jets, the formation of the cavity is due to the propagation of capillary waves on the droplet surface; while for HI singular jets, the cavity formation is due to the large horizontal inertia of the toroidal edge during the retraction of the droplet after the maximum spreading. Key steps of the impact process are analyzed quantitatively, including the spreading of the droplet, the formation and the collapse of the spire, the formation and retraction of the cavity, and finally the formation of singular jets. A regime map for the formation of singular jets is obtained, and scaling relationships for the transition conditions between different regimes are analyzed.

Jetting Dynamics of Viscous Droplets on Superhydrophobic Surfaces

We investigated the dynamics of liquid jets engendered by the impact of droplets on a fractal superhydrophobic surface. Depending on the impact conditions, jets emanate from the free liquid surface with several different shapes and velocities, sometimes accompanied by droplet ejection. Experimental outcomes exhibit two different regimes: the singular jet and columnar jet. We found that droplet impacts at a lower impact velocity and low viscosity result in singular jets, attaining a maximum velocity nearly 20-fold higher than the impact velocity. The high-speed video frames reveal that the formation and subsequent collapse of the cylindrical air cavities within the droplet favor the formation of these high-speed singular jets. In contrast, the capillary wave focusing engenders columnar jets at a moderate to high impact velocity. With an increase in viscosity, singular jets are suppressed at lower impact velocities, whereas columnar jets are seen regularly. The columnar jets ascend and grow over time, feeding a bulbous mass, and subsequently the bulb separates itself from the parent jet due to capillary pinch-off phenomena. The quantitative analysis shows that columnar jets' top jet drop size varies nonmonotonically and is influenced by preceding jetting dynamics. At moderate viscosity, the drop size varies with jet velocity, following a power-law scaling. At very high viscosities, both singular and columnar jetting events are inhibited. The results are relevant to several recent technologies, including microdispensing, thermal management, and disease transmission.

Penetration and ligament formation of viscoelastic droplets impacting on the superhydrophobic mesh

Spraying occurs by the impact of water droplets on the superhydrophobic wire meshes by liquid penetration during the spreading and recoiling. We have shown that adding a small amount of high molecular weight polymer (PEO) alters the ligaments formation and stabilizes them due to its high elasticity. Consequently, it suppresses droplet spray during droplet spreading and recoiling (recoil penetration). In the wide range of the impact velocities, the penetrated ligaments retracted back to the mesh after reaching the maximum length and eventually merged with the droplet on the mesh. The empirical fitting shows that the ligament evolution follows the parallel spring-dashpot model of Kelvin–Voigt. The additive polymer also changes the recoil penetration mechanisms from cavity collapse to cavity detachment due to the higher retraction velocity of the cavity near the mesh that is induced by the upward flow formed by the retraction of the ligaments to the mother droplet. A model based on mass conservation is proposed to calculate the variation of the maximum ligament size.

Successive Rebounds of Impinging Water Droplets on Superhydrophobic Surfaces

When a water droplet strikes a superhydrophobic surface, there may be several to a few tens of rebounds before it comes to rest. Although this intriguing multiphase flow phenomenon has received a great deal of attention from interfacial scientists and engineers, the underlying dynamics have not yet been completely resolved. In this paper, we report on an experimental investigation into the bouncing behavior of water droplets impinging on macroscopically flat superhydrophobic surfaces. We show that the restitution coefficient, which quantifies the energy consumed during impact and rebound, exhibits a nonmonotonic dependence on the Weber number. It is the droplet-surface friction that restricts the rebound height of the impinging droplet, so its restitution coefficient increases with the Weber number when the impact velocity is below a critical value. Above this value, the viscous friction within a thin liquid layer close to the superhydrophobic surface becomes dominant, and thus, the restitution coefficient decreases sharply. On the basis of energy analyses, semiempirical formulas are proposed to describe the restitution coefficient, and these can be employed to predict the number of successive rebounds of impinging droplets on superhydrophobic surfaces.

A new scaling number reveals droplet dynamics on vibratory surfaces

HYPOTHESIS

Droplet spreading on surfaces is a ubiquitous phenomenon in nature and is relevant with a wide range of applications. In practical scenarios, surfaces are usually associated with certain levels of vibration. Although vertical or horizontal modes of vibration have been used to promote droplet dewetting, bouncing from immiscible medium, directional transport, etc., a quantitative understanding of how external vibration mediates the droplet behaviors remains to be revealed.

METHODS

We studied droplets impacting on stationary and vibratory surfaces, respectively. In analogy to the Weber number We=ρU_i²D₀/γWe = ρUi2D0/γ, we define the vibration Weber number We^*=ρU_v²D₀/γ to quantitively analyze the vibration-induced dynamic pressure on droplet behaviors on vibratory surfaces, where ρ,γ,D₀,U_iandU_v are liquid density, surface tension, initial droplet diameter, impact velocity of the droplet, and velocity amplitude of vibration, respectively.

FINDINGS

We demonstrate that the effect of vibration on promoting droplet spreading can be captured by a new scaling number expressed as We^*/[We^1\2sin(θ/2)], leading to (D_m - D_m0)/D_m0 ∝ We^*/[We^1\2sin(θ/2)], where θ is the contact angle, and D_m0 and D_m are the maximum diameter of the droplet on stationary and vibratory surfaces, respectively. The scaling number illustrates the relative importance of vibration-induced dynamic pressure compared to inertial force and surface tension. Together with other well-established non-dimensional numbers, this scaling number provides a new dimension and framework for understanding and controlling droplet dynamics. Our findings can also find applications such as improving the power generation efficiency, intensifying the deposition of paint, and enhancing the heat transfer of droplets.

Bouncing-to-wetting transition of water droplets impacting soft solids

Soft surfaces impacted by liquid droplets trap more air underneath than their rigid counterparts. The extended lifetime of the air film not only facilitates bouncing behaviours of the impacting droplets but also increases the possibility of interactions between the air film itself and the air cavity formed inside the droplets by capillary waves. Such interactions may cause rupture of the trapped air film by a so-called dimple inversion phenomenon and suppress bouncing. In this work, we systematically investigate the relationship between air cavity collapse and air film rupture for water droplets impacting soft, hydrophobic surfaces. By constructing a bouncing-to-wetting phase diagram based on the rupturing dynamics of the trapped air film, we observe that the regime in which air film rupture is induced by dimple inversion consistently separates the bouncing regime and the one in which wetting is caused by random rupture. We also found that air film rupture by dimple inversion in-turn affects both the collapsing dynamics of the air cavity and the resulting high-speed jet. We then provide a detailed characterisation of the collapsing dynamics of the air cavity and subsequent jetting.

Drop Impact on Heated Nanostructures

Drop impact on a heated surface not only displays intriguing flow motion but also plays a crucial role in various applications and processes. We examine the impact dynamics of a water drop on both heated flat and nanostructured surfaces, with a wide range of impact velocity (V) and surface temperature (T_s) values. Via high-speed imaging and temperature measurements, we construct phase diagrams of different impact outcomes on these heated surfaces. Like those on the heated flat surface, water drops can deposit, spread, rebound, or break-up with atomizing on the heated nanostructures as V and T_s are increased. We find a significant influence of nanostructures on the impact dynamics by generating particular events in specific parameter ranges. For example, events of splashing, gentle central jetting, and violent central jetting are observed on and thus triggered by the heated nanostructures. The heated nanotextures with high roughness can easily trigger the splashing and the central jetting. Our data of the normalized maximum spreading diameter for the heated surfaces display distinct trends at low and high Weber number (We) ranges, where We compares the kinetic to surface energy of the impacting droplet. Finally, compared with the flat surface, the dynamic Leidenfrost temperature (T_L^D) for We ≈ 10 is decreased (by ≈60 °C) by the high-roughness nanotextures. In addition, our experimental data of T_L^D is consistent with a model prediction proposed by balancing the droplet dynamic and vapor pressure.

Bubble entrapment during the recoil of an impacting droplet

When a droplet impacts a (super-)hydrophobic surface, there is a range of Weber numbers within which bubble entrapment will occur during droplet recoil due to closure of the air cavity developed when the droplet spreads out during the impact. In this study, we studied bubble entrapment using a microelectromechanical system (MEMS)-based acoustic sensor fabricated on a substrate. We found that bubble entrapment is followed by an acoustic vibration that can be detected by the sensor. Moreover, the frequency of the vibration is inversely proportional to the radius of the droplet, which indicates that this vibration is the resonant oscillation of the bubble. Therefore, the MEMS-based acoustic sensor can be used not only to detect but also to measure the size of the entrapped bubble. Finally, we demonstrated that it is possible to prevent bubble formation by allowing the air to escape to the underside of the droplet contact area. This can be done by creating through-holes on the substrate or decorating the substrate with sufficiently large textures.