Effect of the surface wettability on condensation mode and performance

The surface wettability plays a significant role in understanding condensation phenomena and droplets dynamic. Depending on the wettability of the condensing surface, water vapor will condense in the form of a continuous liquid film (FWC) or individual droplets (DWC). The surface wettability is characterized in terms of the equilibrium contact angle (CA), which is described as the angle that liquid/vapor interface makes with the solid surface, and it is controlled by changing the surface free

energy and the surface roughness. For the droplet deposited on an ideal smooth surface, Young [148] first proposed the equilibrium contact angle (𝜃_𝑦) relation, which demonstrates the force balance at the three-phase contact line of the liquid, solid and vapor phases, as follow;

cos 𝜃𝑦 =𝛾𝑠𝑣_𝛾−𝛾𝑠𝑙

𝑙𝑣

(5.3)

Where 𝛾_𝑠𝑣

,

𝛾𝑠𝑙

and

𝛾𝑙𝑣 are the solid-vapor, solid-liquid, and liquid-vapor interfacial

surface energies, respectively. Based on Young's relation [148], if the equilibrium contact angle is higher than 90°, the surface is called hydrophobic and it has low surface energy; whereas if the contact angle is less than 90° the surface is called hydrophilic and it has high surface energy as shown in Figure 5.3. Moreover, it should be noted that the Young equation is applied only to calculate the contact angle for the ideal smooth and homogenous surfaces. However, for the non- ideal rough surfaces, Young's relation cannot be used to calculate the contact angle. Continuing the work of Young, Wenzel [80] and Cassie-Baxter [81] proposed two models to define the contact angle on rough and porous surfaces as shown in Figure 5.4. In Wenzel model, the liquid fills up the grooves of the rough surface, there are no air bubbles underneath the droplet, and the contact angle (𝜃_𝑤 ) is defined by the following relation ;

cos 𝜃_𝑤 = 𝑟 cos 𝜃_𝑦

(5.4) Where 𝑟 is the surface roughness, which represents the ratio of the total surface area to the projected area, and 𝜃𝑤 is the Wenzel contact angle. It can be noticed by equation (5.4)

that 𝑟 = 1 for a smooth surface and 𝑟 > 1 for a rough surface. In contrast, considering the case where the liquid droplet does not penetrate the roughness, which means it rests

on the tips of the roughness, the contact angle ( 𝜃_𝐶𝐵) is defined by Cassie and Baxter model as follow;

cos 𝜃_𝐶𝐵 = 𝑓 cos 𝜃_𝑦 + (𝑓 − 1)

(5.5) Where, 𝜃_𝐶𝐵 is the contact angle in Cassie mode, and 𝑓 is the ratio of the solid area contacting the droplet to the projected area.

Figure 5.4: The modes of interactions between the solid surface and droplets (a) Young state [148] (b) Wenzel state [80] (c) Cassie-Baxter state [81].

According to Wenzel and Cassie–Baxte models, the wettability of a surface can be controlled by changing its surface roughness. Increasing the surface roughness makes a hydrophilic surface even more hydrophilic by decreasing the contact angle, and when it becomes less than 5°, the surface is called superhydrophilic. However, increasing the roughness of a hydrophobic surface will make it even more hydrophobic. When the contact angle is higher than 150°, the surface is called superhydrophobic. When a water droplet contacts a superhydrophobic surface, it will ball up, while it will spread out completely when it touches a superhydrophilic surface.

It is clear that Wenzel and Cassie wetting modes can both exist on the rough surfaces. However, owing to the lower contact angle hysterias in Cassie-Baxter mode, the

droplets on the substrate have lower adhesion resulting in higher mobility compared to Wenzel mode. As a result, Cassie-Baxter mode is desired to promote efficient dropwise condensation. Accordingly, techniques and focus of research are in progress to improve dropwise condensation (DWC) performance by enhancing droplets mobility.

Figure 5.5: Condensing droplet morphologies. Time-lapse schematics of (a) Wenzel (W), (b) partially wetting (PW) , and (c) suspended (S) droplet morphologies. Environmental scanning electron microscopy (ESEM) images of droplets with (d) W, (e) PW, and (f) S morphologies on a nanostructured surface [149].

Over the past decade, Researchers have focused on increasing water repellency and limiting droplet adhesion on condensing surfaces by developing structured superhydrophobic surfaces [150-153]. On these structured superhydrophobic surface, droplets can depart either by gravity if they have small adhesion to the surface, or by coalescence-induced droplet jumping if they have large adhesion to the surface [154]. During dropwise condensation, it was observed three distinct droplet morphologies depending upon the structure geometry and nucleation density [149] for the condensing

liquid droplets: Wenzel wetting mode (W) where condensed droplets wet the cavities of the structured surface (Figure 5.5a, d), partially wetting mode (PW) where the droplets form a liquid bridge connecting the base of the droplet (Figure 5.5b, e) or suspended Cassie wetting mode (S) where condensed droplets sit on top of the structured surface (Figure 5.5c, f). For condensation heat transfer enhancement, both the partially droplets (PW) and the suspended droplets (S) are desirable due to their higher mobility compared to that for Wenzel (W) droplets. However, It was demonstrated by Miljkovic et al. [155] that the condensing surface with the partially wetting droplets (PW) has higher growth rates compared to the surface with suspended droplets (S) formation. In their study, they have used a specific geometry and investigated the effect of the droplet morphology on the droplets growth rate and the individual droplet heat transfer. They found an enhancement by 6x and 4-6x in the growth rate and individual droplet heat transfer of PW droplets, respectively compared to that of S droplets. The difference was because that the air in the composite air-solid interface, where the S droplets are suspended on, add more thermal resistance to the droplet growth. It was also demonstrated that for a condensing surface favoring only S droplet formation, the heat transfer performance was degraded by 71% in comparison with a flat hydrophobic surface. Consequently, in order to enhance the dropwise condensation on superhydrophobic surfaces, special designs are required by controlling the surface structure length scale and geometry, droplet morphology, nucleation density, and departure dynamics. In general, in order to maximize the condensation heat transfer performance, the condensing surface should have three characteristics: high nucleation density, low contact angle hysteresis to reduce

the droplet departure diameter, and a low apparent contact angle to minimize the conduction thermal resistance of the condensate droplet [108].

CHAPTER 6

In document Non-Destructive Determination of Magnetic Audio Tape Degradation for Various Tape Chemistries Using Spectroscopy and Chemometrics (Page 89-95)