Impact of viscous droplets on different wettable surfaces: Impact phenomena, the maximum spreading factor, spreading time and post-impact oscillation

Splashing on Soft Elastic Substrates

Drop impact onto soft substrates is important in applications such as bioprinting, spray coating, and aerosol drug delivery. Experiments are conducted to determine the effect of elasticity on the splash morphology, as defined by the splashing threshold, spine number, spreading factor, and retraction factor. PDMS silicone gel and gelatin hydrogel are used as the substrates because they have different wetting properties and a large range of elasticities. The splash threshold, as defined by the Weber number We, increases as the substrate elasticity decreases indicating that it is harder to splash on soft substrates. After impact, the drop spreads to a maximum diameter that decreases for soft substrates, irrespective of wetting properties, illustrating the role of substrate deformation in the energy balance during splashing. The number of spines that form at the leading edge of the drop depends upon the elasticity and the wetting properties of the liquid/substrate system. Following spreading, the drop retracts to an equilibrium diameter which does not show a strong correlation with any material properties. The reported results agree well with the existing literature for most cases and also provide new insights into gels with small elasticity.

Impact Behaviors on Superhydrophobic Surfaces for Water Droplets of Asymmetric Double-Chain Quaternary Ammonium Surfactants

Improving water droplet deposition on superhydrophobic surfaces is essential in many agricultural and industrial spraying processes. Adding surfactants is generally considered a simple way to enhance the wetting ability of droplets on surfaces. However, finding effective surfactants for the deposition and spread of high-speed impacting droplets on superhydrophobic surfaces remains a challenge. Here, we propose a model to predict the deposition results of impacting droplets on superhydrophobic surfaces by studying the droplets containing a series of asymmetric double-chain quaternary ammonium ionic surfactants with different chain lengths. By introducing the molecular diffusion rate, the ability of molecules to reduce surface tension, as well as the stability of aggregates into the model, the impact outcomes of surfactant droplets on the superhydrophobic surface are described and predicted. This study provides a beneficial blueprint for the selection of surfactants and the control of droplet impact behavior on superhydrophobic surfaces.

Directional Transportation of Impacting Droplets on Wettability-Controlled Surfaces

Although a superhydrophobic surface could realize rapid rebounding (i.e., short contact time) of an orthogonal impacting droplet, the rebounding along the original impacting route may limit its engineering application; in contrast, the directional transportation seems to be more promising. Here, we achieve directional transportation of a droplet impacting a wettability-controlled surface. When the droplet eccentrically impacts on the boundary between the superhydrophobic part and the hydrophilic part, it undergoes spreading, retracting, departure, throwing, and breaking up stages, and finally bounces off directionally. The directional transportation distance could even reach more than ten times the droplet size, considered the adhesion length (i.e., covering length on the hydrophilic part by the droplet at the maximum spreading) is optimized. However, there is a critical adhesion length, above which the directional transportation does not occur. To be more generalized, the adhesion length is de-dimensionalized by the maximum spreading radius, and the results show that as the dimensionless adhesion length increases, the transportation distance first increases and then decreases to zero. Under the present impacting conditions, the optimal dimensionless adhesion length corresponding to the maximum transportation distance is near 0.4, and the critical dimensionless adhesion length is about 0.7. These results provide a fundamental understanding of droplet directional transportation and could be useful for related engineering applications.

Anisotropic behaviours of droplets impacting on dielectrowetting substrates

The spreading of a sessile droplet on a solid substrate is enhanced if a non-uniform electric field is applied at the contact-line region. This so-called dielectrowetting effect holds great potential in controlling the spreading of droplets by varying the strength of the electric field. In this paper, we experimentally and theoretically study the effect of the dielectrowetting on the dynamics of droplets impacting on a solid surface having electrodes to impose the non-uniform electric field to the liquid. We experimentally study the anisotropic behaviours in both the spreading and retracting stages: the droplets spread more but retract with significantly smaller rates in the direction parallel to the electrodes. We provide a theoretical explanation for the spreading enhancement caused by dielectrowetting by decoupling it from inertia-induced spreading. We also theoretically account for the reduction in retraction rate using force balance at the contact line. The theoretical analysis in both the spreading and retracting stages is verified experimentally.

The Impact of Single- and Multicomponent Liquid Drops on a Heated Wall: Child Droplets

This paper presents the experimental research into the impingement of single- and multicomponent liquid drops on a solid wall. We focus on studying the conditions and characteristics of two impact scenarios: rebound and breakup. We performed a comprehensive analysis of the effect of a group of factors on the drop transformation and fragmentation characteristics. These factors include the drop velocity and size, Weber number, impinging angle, wall temperature, thermophysical properties of the wall material, surface roughness, hydrophilic and hydrophobic behavior of the surface, homogeneity and inhomogeneity of the drop composition, as well as viscosity and surface tension of the liquid. We compared the outcomes of one, two, and three drops with the same total volume on a wall. Histograms were plotted of the number and size distribution of the emerging secondary droplets. The results include the critical conditions for the intense breakup of drops. Such factors as wall heating, its roughness, impinging angle, drop size and velocity affected the breakup conditions most notably. The variation of a group of these factors could provide a 2–25-fold increase in the liquid surface area as a result of the impact.

Coalescence, Spreading, and Rebound of Two Water Droplets with Different Temperatures on a Superhydrophobic Surface

This paper studied the coalescence, spreading, and rebound of two droplets with different temperatures on a superhydrophobic surface. When the temperature of the impacting droplet was the same as that of the stationary droplet, there was a large deformation of both droplets before the coalescence and the energy dissipation was also large. The coalescence happened at the time close to the maximum spreading. When the temperature of the impacting droplet increased, the deformation of both droplets became smaller before the coalescence and the coalescence happened at or even before the droplets started to spread. The energy dissipation and loss in the later situation is less than those in the previous case. The rebounding characteristics of the merged droplets were also found to be dependent on the temperature. There is an optimum temperature at which the merged droplets can rebound for more times due to the balance of energy loss and also the interaction of the merged droplets with the underlying superhydrophobic substrate. These findings may help further the fundamental understanding of droplet collision on a superhydrophobic surfaces and also offer an alternative strategy to remove droplets from the underlying surfaces for different industrial applications, including condensation heat transfer in steam power plants and phase-change-based thermal management systems.

Sessile Microdrop Coalescence on Partial Wetting Surfaces: Effects of Surface Wettability and Stiffness

We experimentally investigated the coalescence of two sessile microdrops on rigid surfaces with diverse wettability (macroscopic apparent water contact angles of θ_app ≈ 13-110°) and on hydrophobic surfaces (θ_app ≈ 110-124°) with very different stiffness properties (Young's moduli of E ≈ 1.1 MPa to 130 GPa). We show that the coalescence contains two fast regimes, in which a liquid meniscus bridging the parent droplets rapidly grows, forming a hemi-ellipsoidal droplet, and a slow regime, in which the merged hemi-ellipsoidal droplet relaxes to the equilibrium hemispherical cap. Whereas the fast bridging regimes last less than 2 ms and are almost independent of surface wettability and stiffness, the relaxation regime, which was only observed on sufficiently hydrophobic and rigid surfaces with low wetting hysteresis, continues for a few tens to several hundreds of milliseconds depending on surface properties. We further demonstrate that the slow droplet relaxation can be described neither by the bulk hydrodynamics nor by a microscopic model concerning liquid evaporation near the droplet edge, but by the molecular kinetic theory for the motion of the three-phase contact line.

Robust adhesion of droplets via heterogeneous dynamic petal effects

HYPOTHESIS

Bionics and dynamic interface wetting intensely appeal to many research communities due to their unique practical implications. The rose petals had a highly robust dynamic water-retaining capacity under heavy precipitation. We predicted that the roses became more "hydrophilic" at higher Weber numbers.

EXPERIMENTS

Fresh rose petals were directly impacted by droplets, and facile artificial petal-like substrates and superhydrophobic substrates were used in the comparative analysis. The wetting dynamics of the droplet (e.g., topography, bounce dynamics, contact time, three-phase contact lines, and oscillations) were investigated when interacting with four selected target substrates.

FINDINGS

The present work first time investigated the dynamic wetting rule of the sticky superhydrophobic substrates (SSHS). Simulated and experimental investigations confirmed that the unique coupling synergy between the pinning effect and the inhomogeneous micropapillaes resulted in lopsided contact line velocities, which remarkably suppressed the lateral oscillation and rebounding. This may be a new strategy when designing dynamic water-repellent surfaces and open a promising avenue for emerging areas such as super-efficiency energy conversion and harvesting.

Experiments and modeling of nonlinear frequency response of oscillations of a sessile droplet subjected to horizontal vibrations

In this paper, we experimentally studied the response frequency of oscillations of a sessile water droplet, subjected to horizontal vibrations at varying excitation frequency (5-250 Hz and 40 kHz) and amplitude (0.015 mm to 0.5 mm for low frequencies and 600nm for ultrasonic frequency), as well as static contact angle of the glass substrate ([Formula: see text], [Formula: see text] , [Formula: see text], [Formula: see text]). The droplets were pinned during the experiments and non-axisymmetric oscillation modes were excited due to the horizontal vibrations. For the first time, we observed that at a sufficiently high vibration amplitude, when the excitation frequency is lower than the smallest natural frequency of the sessile droplet, the droplet oscillates at a response frequency multiple of the excitation frequency. At higher excitation frequencies up to several hundreds of Hz, the droplet oscillates nearly at the excitation frequency. At ultrasonic excitation frequency, however, the droplet cannot follow the excitations, since there is a physical limitation for forming infinite modes (infinite wavenumber) on the surface of a small droplet. We have modeled these behaviors with a nonlinear mass-spring-damper system by combining two established models: the Duffing and Van der Pol equations, in order to simulate both nonlinear damping and stiffness.

Viscous Droplet Impact on Nonwettable Textured Surfaces

Viscous droplet impact on nonwettable surfaces with complex geometry is of technological importance, but the fundamental understanding of the dynamics is not entirely understood yet. In this work, liquid drops with various viscosities and impact velocities were investigated, and their behavior was correlated with contact time upon impinging nonwettable flat and textured surfaces. It was shown that in the inertial-capillary regime, the contact time between the droplet and a flat surface is independent of impact velocity, whereas for the viscous-capillary regime, it increases with impact velocity. Drops impacting on nonwettable surfaces with single and multiple macroscopic ridges generally leave the surface at a reduced contact time, compared to flat surfaces. The incorporation of a single macrotexture results in a steplike reduction in the contact time because the impacting drop reaches the maximum spreading diameter, a condition that must happen when the capillary number is below unity.

Spreading Dynamics of Droplet Impact on a Wedge-Patterned Biphilic Surface

The influence of apex angle and tilting angle on droplet spreading dynamics after impinging on wedge-patterned biphilic surface has been experimentally investigated. Once the droplet contacts the wedge-patterned biphilic surface, it spreads radially on the surface, with a tendency toward a more hydrophilic area. After reaching the maximum spreading diameter, the droplet contracts back. From the experimental results, the normalized diameter β ( β = D / D 0 ) was found to be related with the Weber number ( W e = ρ D V 2 / γ ) as β max ∼ W e 1 / 5 . during the first spreading process. Below 67.4°, a larger apex angle can help a droplet to spread on the surface more quickly. The maximum spreading diameter has a tendency to increase with the Weber number, and then decrease after the Weber number, beyond 2.7. Approximately, the critical Weber number is about 5, when the droplet lifts off the surface. Considering the effect of apex angle, the maximum normalized spreading diameter has a rough expression as β ∼ α τ

An electric-field-dependent drop selector

Drop manipulation on hydrophobic surfaces is of importance in lab-on-a-chip applications. Recently, superhydrophobic surface-assisted lab-on-a-chips have attracted significant attention from researchers due to their advantages of contamination resistance and low adhesion between the drop and the surface during manipulation. However, control over both static and dynamic interactions between a drop and a superhydrophobic surface has been rarely achieved. In this study, we designed an electric-field-dependent liquid-dielectrophoresis force to manipulate a drop on a superhydrophobic surface. This type of control has been found to be fast in response, bio-friendly, convenient, repeatable, and energy efficient. Moreover, the adhesion force and rebounding for both the static and the dynamic interactions between the drop and the surface under an electric field have been explored. It was found that the adhesion force could be reversibly tuned three-fold without breaking the Cassie-Baxter state. Rebounding experiments showed a close to linear relation between energy dissipation and the applied voltage. This relation was used to tune the on-demand behaviors of a drop on a surface in a proof-of-concept experiment for drop sorting. This electric-field-dependent drop manipulation may have potential applications in digital microfluidics, micro-reactors and advanced lab-on-a-drop platforms.

Droplet Jumping: Effects of Droplet Size, Surface Structure, Pinning, and Liquid Properties

Coalescence-induced droplet jumping has the potential to enhance the efficiency of a plethora of applications. Although binary droplet jumping is quantitatively understood from energy and hydrodynamic perspectives, multiple aspects that affect jumping behavior, including droplet size mismatch, droplet-surface interaction, and condensate thermophysical properties, remain poorly understood. Here, we develop a visualization technique utilizing microdroplet dispensing to study droplet jumping dynamics on nanostructured superhydrophobic, hierarchical superhydrophobic, and hierarchical biphilic surfaces. We show that on the nanostructured superhydrophobic surface the jumping velocity follows inertial-capillary scaling with a dimensionless velocity of 0.26 and a jumping direction perpendicular to the substrate. A droplet mismatch phase diagram was developed showing that jumping is possible for droplet size mismatch up to 70%. On the hierarchical superhydrophobic surface, jumping behavior was dependent on the ratio between the droplet radius R_i and surface structure length scale L. For small droplets ( R_i ≤ 5 L), the jumping velocity was highly scattered, with a deviation of the jumping direction from the substrate normal as high as 80°. Surface structure length scale effects were shown to vanish for large droplets ( R_i > 5 L). On the hierarchical biphilic surface, similar but more significant scattering of the jumping velocity and direction was observed. Droplet-size-dependent surface adhesion and pinning-mediated droplet rotation were responsible for the reduced jumping velocity and scattered jumping direction. Furthermore, droplet jumping studies of liquids with surface tensions as low as 38 mN/m were performed, further confirming the validity of inertial-capillary scaling for varying condensate fluids. Our work not only demonstrates a powerful platform to study droplet-droplet and droplet-surface interactions but provides insights into the role of fluid-substrate coupling as well as condensate properties during droplet jumping.

Non-wet kingfisher flying in the rain: The water-repellent mechanism of elastic feathers

HYPOTHESIS

Flying in the rain presents a greater challenge for smaller animals such as kingfishers, compared with aircraft in the same situation. Regardless, kingfishers have developed advanced water repellency as reflected in the hydrophobicity and elasticity of their feathers. Therefore, it is possible to confirm that the elastic superhydrophobic surface can enhance the water repellency of the surface by experimental and theoretical analysis.

EXPERIMENTS

A simplified device simulating droplet impact on a kingfisher feather was configured for comparison. Moreover, the dynamic behavior of droplets (with varying Weber numbers-2 ≤ W_e ≤ 42) impinging on the elastic and rigid substrate was analyzed, such as spreading, retraction, lift-off, the secondary droplet, and contact time with a high-speed camera.

FINDINGS

The elastic substrate significantly affected the retraction and lift-off of the droplet-that is, an earlier and more efficient morphological rearrangement of the droplet-reducing the contact time by up to 8.3% (17 < W_e ≤ 32). The combination of elasticity and hydrophobicity is a new bioinspired strategy that provides an insight into one of the mechanisms by which birds flying in the rain cannot be bedewed while guiding the design of water-repellent surfaces.