We have investigated the influence of impact velocity and intrinsic surface wettability of nanostructures on the impact dynamic behaviors of water droplets on nanostructure surfaces. Nanowires array surfaces with tunable wettabilities ranging from superhydrophilic to superhydrophobic were fabricated by the deposition of surface modifiers differing in alkyl chain length. The transition criteria of rebound/wetting state and rebound/splashing state based on the relationship between the Webber (We) number and the surface free energy were determined. We have confirmed that the critical We number that determines the transition of the rebound/wetting increased as surface energy decreased. Additionally, the We number at which fragmentation occurred on our superhydrophobic surface was relatively low compared to previously reported values.
Recently, drop impact of water on nanostructured surfaces have been investigated, aiming at elucidation of the interactions between various dynamic motions of water droplets and physicochemical control parameters of the surface and water liquid. These control parameters include wettability of the surface, surface tension, impact velocity of the droplet, liquid density, liquid viscosity, and surface roughness.1–10 Understanding the behaviors of droplets impacting a nanostructured solid surface plays an important role in industrial and environmental processes, such as spray cooling, ink-jet printing, and deposition of rain on solid surfaces.11 Droplets that impact a textured solid surface immediately spread at the moment of impact. When a droplet has enough kinetic energy, it is able to penetrate into a nanostructured surface and soak into the material (Wenzel regime).12 Kinetic energy of droplets can be increased by the augmenting the height of the droplet above the surface, which increases the droplet's potential energy that is then converted to kinetic energy during movement. In contrast, if a water droplet has low inertia (a drop gently deposited on a surface) or if the surface has an intrinsic wettability of hydrophobic or superhydrophobic materials, the drop would not exhibit any wetting behavior or completely rebound during surface impact (Cassie regime).13 Drop fragmentation due to the rupture of the expanding lamella during the impact of droplets with relatively large kinetic energy has also been observed on superhydrophobic surfaces.
For a given surface, the transition between the Wenzel and Cassie regimes depends on kinetic parameters of the liquids used and the inherent surface properties of the material, such as intrinsic wettability and surface geometrics. The kinetic parameters are described in terms of a dimensionless number called the Weber number, We, the ratio of kinetic energy to surface energy, which is represented by We= ρRV2/σ, where R is the drop radius, ρ is the fluid density, V is the impact velocity and σ is the surface tension. Several groups have investigated the effects of droplet impact on surface systems in various ways. Rioboo et al.7 studied the influence of drop size and We number on the impact or deposition processes. Their studies demonstrated that the minimum velocity to achieve rebounding of impacting droplets depends on the inverse square root of the drop diameter. Other authors, including Jung et al.,1 Reyssat et al.,5 and He et al.,8 have investigated the effects of geometric parameters, such as micro−patterning on the surface, and other impact parameters, such as height, diameter, pitch, and impact velocity, on impact dynamics. These researchers thoroughly investigated the criteria for impact velocity and geometric parameters that achieved transitions from anti-wetting states to wetting states in their systems. Various topographic requirements were established, such as micropost spacing, diameter, and height to demonstrate wetting behavior on well-defined structured surfaces. Beside topographic parameters, it is known that the intrinsic surface energy and kinetic energy of the droplets are other important factors influencing impact dynamics of water droplets. Though these factors have been important to our study, there still does not exist a known relationship of wetting behavior of water droplets, including sticking, rebounding, and fragmentation on nanostructured surfaces, with the intrinsic wettability of the chosen material surface and the impact velocity of droplet.
Here, a study was conducted on the dynamic impact behaviors of water droplets with a quasi-aligned tungsten oxide nanowire-array surface. Parameters such as the impact velocity of droplets and surface energy were tested. In general, it is more effective to control the dynamic behaviors of water droplets impacting on the surface by changing the intrinsic wettabilities of the surface. This is better accomplished by chemical modification of the surface than by altering the geometric parameters of the surface, which usually requires stringent and sophisticated processes. In a previous study,14 the effects of chemical surface modifications on the wetting transition for impinging water droplets were investigated, but this investigation was performed under limited dynamic conditions of fixed impact velocity. The focus of this paper is to quantitatively determine the requirements for wetting transitions, in terms of the We number, on surfaces that have different surface energies due to different surface modifiers present on the surface. Such a series of experimental approaches on given surfaces with static geometric parameters provides information on the design of solid surfaces with desired wettability and water-repellent properties. Numerical simulations were performed to guide proper modeling of impingement moments on the surface. These simulations were also used to describe the spreading state of freely falling water droplets through the evaluation of the dynamic behaviors of the water droplets and the dynamic pressure occurring during impact.
The tungsten oxide nanostructures used as the solid surface were prepared using a simple thermal evaporation method. The detailed synthesis of tungsten oxide nanowire arrays was described previously.15 As shown in Fig. 1(a), the quasi−aligned nanowires were prepared at a high density and were straight and smooth with a typical length of approximately 100 μm, diameters ranging from 50 to 300 nm, and internanowire spacings around 500 nm. The tungsten oxide nanowires surface was initially superhydrophilic due to the presence of the OH group that was inherently present on the tungsten oxide surface. To obtain substrates with various surface energies, alkyltrichlorosilane (R−SiCl3) was deposited on sample surfaces by immersing the substrates in 3 mmol R−SiCl3 dissolved in toluene, where R= C6, C9, C12, C15, C18 in alkyl chain. The static water contact angles (CAs) were measured on the modified surfaces and increased with increasing alkyl chain length in R−SiCl3 as discussed in a previous study.14 Total surface free energies (|$\gamma^{tot}_s$|) calculated from the dispersive (|$\gamma^{d}_s$|), and polar (|$\gamma^{p}_s$|) components, however, generally decreased as a function deposition of a surface modifier with longer alkyl chains (Fig. 1(b)).
(a) SEM image of tungsten oxide nanowire arrays, (b) Contact angles (CAs) and surface free energies of the nanostructures modified by R−SiCl3 as a function of the alkyl chain length.
(a) SEM image of tungsten oxide nanowire arrays, (b) Contact angles (CAs) and surface free energies of the nanostructures modified by R−SiCl3 as a function of the alkyl chain length.
In our studies, we first performed numerical simulations of initial droplet impingement on the surface to understand dynamic behavior and pressure changes of the water droplet. Individual snapshots from numerical simulations were recorded for later analysis. Next, experimental videos of droplet impact events were created from the summation of sequential images recorded by a high-speed camera with a frame rate of 1 picture/0.5 ms. Snapshots and videos were compared to analyze droplet impact dynamics on superhydrophobic nanowire surfaces coated with C18−SiCl3 as is shown in Fig. 2(b). In numerical simulations, level set methods were used to track moving interfaces of liquid. At the bottom of domain, a hydrophobic boundary condition of CA equal to 180° was imposed. Additionally, drop diameter and impact velocity were 1 mm and 0.35 m·s-1, respectively. The governing equation is
where the level set function, ϕ, represents interface shape; u is the velocity of fluid; and δ and κ are the thickness of interface and re−initialization factor, respectively. To simulate fluid flow, the incompressible Navier−Stokes equation was applied. Numerical domain and boundary conditions are described in Fig. 2(a). This computation was performed with the commercial software COMSOL MULTIPHYSICS™ version 3.4. The sequential images for video analysis were obtained by a high-speed camera (Fastcam 1024 PCI, Photron) operating at 2000 frames·s-1. A droplet of approximately 5 μL with a radius of approximately 1 mm was freely dropped normal to the superhydrophobic nanostructured surface with the static CA of 163.5°.
(a) Numerical domain and boundary conditions used in the numerical simulation (R, a radius of droplet; n, outward normal vector; T, shear stress tensor), (b) Sequential images of a simulated water droplet with a We number of 1.63 impinging on the nanostructured surface (left, color images) and the same experiment except using real water are compared (right, gray scale images).
(a) Numerical domain and boundary conditions used in the numerical simulation (R, a radius of droplet; n, outward normal vector; T, shear stress tensor), (b) Sequential images of a simulated water droplet with a We number of 1.63 impinging on the nanostructured surface (left, color images) and the same experiment except using real water are compared (right, gray scale images).
Firstly, the drop with the We number of 1.63 was deformed near the bottom, followed by initial flatness and then by deformation into a rim. A two-stage approach, including contact stage and spreading stage, has been generally used in the investigations of droplet impact on solid surfaces.16–18 In the contact stage, the initial impact generates a dynamic pressure along the normal direction to the surface. At spreading, the dynamic pressure from the impact is moved from normal to lateral directions on the surface. This occurs from kinetic energy conversion into surface energy of the water droplet. Although we demonstrated typical dynamic behaviors during impact with superhydrophobic surfaces at given We values, the outcomes of a drop impacting on a surface are also applicable to general hydrophobic surfaces up to spreading stage. This can be found even though impact velocity or surface free energy changes during testing. On a hydrophilic surface, a water droplet starts to penetrate into the textured surface as early as the contact stage, as observed in a previous study.14 If the surface has a relatively high surface energy through the chemical modification of R−SiCl3 to contain short alkyl chains, the liquid is forced to touch the bottom between nanoposts after the spreading and then soak into the surface (wetting state). If the surface is superhydrophobic enough to endure the kinetic energy of the freely dropped droplet, both ends of the spreading droplet retract, and the droplet bounds off the substrate (rebound state). In cases where the droplet has sufficiently high impact velocity, receding breakup is observed, and tiny droplets from both ends of the spreading droplet are observed (fragmentation).
Wetting/antiwetting behaviors of the water droplets with various We numbers impacting the nanostructure surfaces having various surface energies were investigated. Outcomes of the water droplet impinging on the chemically modified nanostructures are shown in Fig. 3, where the We number is a function of the surface free energy of the substrate. To calculate the total surface free energy of chemically modified nanostructures, we used the geometric−mean method from known CAs of diiodomethane and water.19 The We numbers were determined by varying the impact speed, which was adjusted by the drop height of the droplet (diameter of ∼ 1 mm). Both unmodified and C6-modified SiCl3 surfaces showed wetting behaviors irrelevant to the impact velocity, corresponding to soaking of the droplets into the nanostructures (wetting region in Fig. 3). In general, nanostructured surfaces with an intrinsic water CA of the flat one of below ∼ 90° become more hydrophilic than flat one. The measured advancing CAs of the droplets when placed on unmodified and C6−SiCl3 modified flat surfaces were 6.6° and 56.6°, respectively. In the transition region (Fig. 3), two kinds of transitions, rebound/wetting and rebound/fragmentation, were observed. When alkyl chain length increased from C9−SiCl3 to C15−SiCl3, the wetting transition from the rebound region to the wetting region occurred along with increases in the We number. Although the transition was not linear, we conclude that changing surface energy through surface modification induced a limit between rebound and wetting states. The critical impact velocity (Vc) where a transition from rebound to wetting state was initially observed increased with increasing alkyl tail length in the surface modifier. We also observed a partial wetting state in the transition region where a water droplet was partially pinned only at the contact area during a short period after impact.
Wetting behaviors of the impacting water droplets with various We numbers on the nanostructures composed with various surface energies (wetting, filled circles; rebound, open circles; fragmentation, filled rectangles). The critical We numbers at the rebound/wetting transition were calculated from the CA hysteresis energy for a given surface that are marked by open red circles.
Wetting behaviors of the impacting water droplets with various We numbers on the nanostructures composed with various surface energies (wetting, filled circles; rebound, open circles; fragmentation, filled rectangles). The critical We numbers at the rebound/wetting transition were calculated from the CA hysteresis energy for a given surface that are marked by open red circles.
According to the studies of Reyssat et al.5 and Rioboo et al.,7 rebound of the impacting droplet requires an excess kinetic energy to overcome the surface energy stored in expansion and retraction processes during impacting. The minimum We number to observe rebound, called critical We number (Wec), can be induced by equating the kinetic energy to the hysteresis energy of the impacting droplet as a function of advancing and receding CAs values. This relationship is defined by the following:
where θa and θr are advancing and receding CAs, respectively. To test the requirements for transition, the calculated Wec [Eq. (2)] values, shown as red open circles, were added to Fig. 3. Comparison of the data in Fig. 3 confirmed that the calculated values agreed reasonably well with the experimentally observed transition criterion.
For the superhydrophobic surface coated with C18−SiCl3, results from the impacting droplet as impact velocity increased were different than with other modified substrates. Here, the impacting droplet completely rebounded off the surface in relatively low We number regions (between 0 and 45). The transition to wetting state also did not occur even at higher impact velocity. In the higher values of We (above 52), splashing impacts occurred, and the surface maintained its superhydrophobicity. This was due to the formation of many satellite droplets during retraction and spreading of the water film. These results indicated that superhydrophobic surface with lower CA hysteresis prevents the impacting droplet from penetrating between the nanoposts and prevent the transition from liquid−air−solid interface to the liquid−solid interface. In the spreading stage, the destabilized rim of the water film was easily deformed as the moving contact line decreased. It was also noted that fragmentation occurred at lower overall We numbers on our nanostructured surfaces than has been reported with other systems.5,20 According to known references 5 and 7, the existence of an air fraction in the surface results in minimization of the viscous dissipation in the water lamella film and makes the liquid smoothly spread over the surface when there is relatively low impact velocity.
In conclusion, we have investigated the outcomes of impacting water droplets as a function of the kinetic parameter, the We number, and surface free energy parameters. We have also quantitatively determined requirements for rebound to the wetting state and for rebound to fragmentation. Our experimental results confirmed that calculated critical values matched rebound/wetting transition results. This dynamic analysis for the impacting droplet on nanostructured surfaces as a function of varied surface energies provides a simple strategy for the design of nanostructure surfaces with desired dynamic wettabilities. Additionally, these can be utilized in the construction of databases for impact dynamics studies.
This work was supported by grants from the National Research Foundation (NRF2010-0009545, NRF2010-0015975), and by the Korean Research Foundation Grants funded by the Korean Government (MOEHRD) (KRF-2008-005-J00501).