Chapter 1 Introduction
5.1 Introduction
The liquid droplet impact behavior on a dry surface has been studied intensively in the last few decades, due to its numerous practical applications such as ink jet printing, direct injection for internal combustion engines, microelectronic fabrication, and rain drops (Yarin, 2006; Vadillo et al., 2009). It has been known that such behavior is dictated by several parameters including the physical properties of the liquid, e.g., viscosity and surface tension, the kinematic properties of the droplet, e.g., volume and impact velocity, and the wettability of the surface itself, e.g., contact angle and roll-off angle (Rioboo et al., 2001; Lee and Lee, 2011). Depending on the value of these parameters, there are at least six possible outcomes when a liquid droplet impinges on a dry but wettable surface: deposition, prompt splash, corona splash, receding break-up, partial rebound, and complete rebound (Rioboo et al., 2001). In contrast to the liquid droplet impact behavior on a wettable surface, the impact behavior on a non-wettable surface is still not completely understood.
Many published studies have shown that in the case of a water droplet impinging on a non-wettable surface (e.g., a superhydrophobic surface), it deforms and flat- tens into a pancake shape, then spreads on the surface, subsequently recedes after it
reaches its maximum spreading diameter, and finally rebounds off the surface com- pletely. Although those studies do agree on the overall impact behavior, there remain some significant discrepancies that still need to be resolved. The biggest obstacle that hinders investigators from drawing a unified conclusion is the use of a non-ideal super- hydrophobic surface where the impinging water droplet is pinned onto the surface at a certain condition (Rioboo et al., 2002; Biance et al., 2006; Jung and Bhushan, 2009;
Lee and Lee, 2011). Such surface properties transition from Cassie state to Wenzel state in a higher Weber number regime and has continued to prevent investigators from obtaining valid experimental data, which in turn complicates the process of in- terpreting and modeling the impact behavior correctly. Further, the use of thermody- namically modified surfaces (e.g., superheated plates), as superhydrophobic surfaces add to the confusion, mainly because of the underestimated effects of water evapora- tion and convection (Chandra and Avedisian, 1991). Therefore, the objective of this work is to fully characterize the water droplet impact behavior on an ideal Cassie state superhydrophobic surface via carefully controlled experimental procedures at standard room temperature and pressure. This ideal superhydrophobic surface has the capability to remain in a Cassie state in any experimental conditions, such that water droplets will never get pinned onto this surface even in a very high Weber number regime and at a non-elevated temperature. Comparison between commonly used superhydrophobic surfaces is summarized in Table 5.1.
One widely known example of the above mentioned discrepancies is whether or not the impact behavior on a non-wettable surface satisfies the energy conservation principle. It was long thought that the impact behavior at a low viscosity regime on a non-wettable surface would satisfy the conservation of energy. Based on this energy conservation approach, Chandra and Avedisian (1991) suggested a model where the maximum spreading factor would scale as the square root of the Weber number of the droplet. However, there was a considerable difference between this proposed model and the experimental data observed by Biance et al. (2006), which might have been caused by the underestimated effect of water evaporation and upward flow of air, due to convection from the superheated Leidenfrost surface. Works done by Pasandideh-
Fard et al. (1996), Kim and Chun (2001), Ukiwe and Kwok (2004), Vadillo et al.
(2009), and Li et al. (2010) on various surfaces show that the conservation of energy indeed holds, as long as the effect of viscous dissipation and wettability are taken into account.
On the contrary, works by Clanet et al. (2004), Bartolo et al. (2005), and Biance et al. (2006) show that a straightforward energy conservation approach cannot be used due to the existence of internal flows induced by an “effective gravity” during the impingement. According to this effective gravity theory, the maximum spreading factor does not scale as the square root of the Weber number, but instead scales as the Weber number to the one-fourth power. However, the conclusion of these studies has been refuted by Eggers et al. (2010), mainly because they only investigated a small regime where both energy conservation and effective gravity approaches could not be reliably discriminated. Work by Eggers et al. (2010) suggests that in the low viscosity regime, the maximum spreading radius is, indeed, dictated by a balance between kinetic energy and capillary forces, not by the effective gravity. More recently, Lee and Lee (2011) suggest that a more accurate model for the maximum spreading factor could indeed be made by incorporating a geometrical modification induced by surface textures into the energy conservation principle. Note that different materials, ranging from superheated Leidenfrost surfaces (Chandra and Avedisian, 1991; Biance et al., 2006), to hydrophobic metal and polymeric surfaces (Pasandideh-Fard et al., 1996; Ukiwe and Kwok, 2004; Bartolo et al., 2005; Vadillo et al., 2009), as well as micro-textured hydrophobic surfaces (Clanet et al., 2004; Biance et al., 2006; Tsai et al., 2009; Lee and Lee, 2011), were used in these published works.
The complication introduced by surface properties’ transition to the otherwise simple problem has led many studies to revolve around it, leaving several other im- portant impact behavior characteristics unexplored. Despite their importance, these impact behavior characteristics, which include critical Weber number, volume ratio, and restitution coefficient, have received the least amount of attention due to the excessive amount of effort spent drawing a unified conclusion about the maximum spreading factor. Until now, only Range and Feuillebois (1998) and Rioboo et al.
Table 5.1. Comparison between superhydrophobic surfaces.
Surface Static
contact angle
Roll-off angle
Contact angle hysteresis
Droplet pinning condition
Liquid- vapor- solid interface Micropatterned Si
pillars (Jung and Bhushan, 2008)
173 3 1 W e >78 no
Microtextured
wax (Biance
et al., 2006)
160 N/A N/A W e < 1
and W e >85
no
Superheated plate (Chandra and Avedisian, 1991)
180 N/A 0 no pin-
ning
yes
Lotus leaf (Koch and Barthlott, 2009)
162 4 4 N/A yes
CNT arrays (this study)
173 3 3 no pin-
ning
yes
(2001) have mentioned the existence of critical Weber numbers. A critical Weber number is basically a threshold that separates two different outcomes when a drop impinges the surface and is a unique property of a surface that depends heavily on its wettability. Hence, a critical Weber number of an ideal superhydrophobic surface should be different than that of any other wettable surfaces. Although they discussed the role of critical Weber numbers on the morphology of an impinging droplet, their discussions were based on phenomena observed on conventional materials, not on non-wettable surfaces.
Another example of an important characteristic that has also been neglected is the restitution coefficient, which is defined as a ratio between the droplet’s velocity before and after the impact. So far, the restitution coefficient has only been briefly mentioned by Richard and Quere (2000) and Biance et al. (2006). Although both of them claimed that superhydrophobic surfaces were used in their experiment, their experimental data did not agree with each other. Richard and Quere (2000) show that the restitution coefficient is approximately constant over a large range of Weber numbers, while Biance et al. (2006) suggest restitution coefficient scales as the inverse of a square root of the Weber number. Such a discrepancy might have been caused by the use of different types of non-wettable surface, where Richard and Quere (2000) used a proprietary micro-textured hydrophobic surface, while Biance et al. (2006) used a superheated Leidenfrost surface. This clearly shows that the droplet impact behavior is heavily influenced by the types of surface used in the experiment, and highlights the importance of using an ideal Cassie state superhydrophobic surface to provide valid experimental data.
This work presents for the first time a complete characterization of water droplet impact behavior on a Cassie state nanostructured superhydrophobic surface. Ex- perimental data are gathered comprehensively via carefully controlled experimental procedures at standard room temperature and pressure over a wide range of Weber number. These experimental data are presented in the form of several important impact behavior characteristics, which include critical Weber number, volume ratio, restitution coefficient, as well as maximum spreading diameter. Empirical approxima-
tions and interpretations of the data, as well as brief comparisons to the previously proposed scaling laws, are also shown here. This work will ultimately provide the basis for future study to develop a logical mathematical model that describes the droplet impact behavior on a non-wettable surface by eliminating any complications induced by surface properties transition.