Range of Applicability of the Wenzel and Cassie−Baxter Equations for Superhydrophobic Surfaces

Abstract

The Wenzel and Cassie-Baxter equations depending on the extent of liquid/solid interfacial contact area were generally used to estimate water contact angles on superhydrophobic surfaces. In this study, a simple method is proposed on the criterion to use the Wenzel and Cassie-Baxter equations to evaluate the contact angle results on superhydrophobic surfaces. In this method, the difference between the theoretical (geometric) and experimental contact angle-dependent Wenzel roughness parameter, Delta r(w), and Cassie-Baxter solid/liquid contact area fraction, Delta f(s)(CB) were determined, and the validity of these equations was evaluated. We used the data of eight recent publications where the water drop sits on square and cylindrical pillar structured superhydrophobic model surfaces. We evaluated the contact angle results of 166 patterned samples with our method. We also found that the effect of contact angle error margins was low to vary these parameters. In general, the use of the Wenzel equation was found to be wrong for most of the samples (74% of the samples for cylindrical and 58% for square pillar patterned surfaces), and the deviations from the theory were also high for the remaining (26% for cylindrical and 42% for square) samples, and it is concluded that the Wenzel equation cannot be used for superhydrophobic surfaces other than a few exceptions, especially for cylindrical patterns. For the Cassie-Baxter equation, two situations are possible: for positive Delta f(s)(CB), there is only a partial contact of the drop with the top solid surface, and, for negative Delta f(s)(CB), the penetration of the drop in between the pillars is possible, and thus the liquid drop is in contact with the lateral sides of the pillars. We found that 65% of the samples containing cylindrical pillars (52-77% with error margins) and 44% of the samples containing square pillars (38-50% with error margins) resulted in negative Delta f(s)(CB)(red) values. In addition, large deviations of experimental water contact angle results, theta r(e) from the theoretical theta r(CB) were also determined for most of the samples, indicating that the Cassie-Baxter equation should be applied to superhydrophobic surfaces with caution.

Complete Synthesis of Germanium Nanocrystal Encrusted Carbon Colloids in Supercritical CO2 and their Superhydrophobic Properties

“…However, the double rough effect of nanocrystal texturing of microspheres is more similar to the natural surface structuring of a lotus leaf which may be more accurately explained by the Cassie-Baxter model. 39 According to this model, the contact of a droplet with a hydrophobic architecture is the combination of its contact with the actual material and the air pockets surrounding this material, increasing the apparent contact angle. The effect of this superhydrophobic coating is shown in Figure 7c, where surface tension in the liquid forms near perfect spherical droplets of water which exhibited roll-off angles of just 2-3°.…”

Wetting Transition Characteristics on Microstructured Hydrophobic Surfaces

“…13,14) Recently, some researchers have studied on the transition state where Cassie and Wenzel states are present simutaneously. 1,9,15) Studies of transition from Cassie state to Wenzel state have been carried out and some important factors, affecting the occurrence of transition, such as contact line density, energy barrier, and spacing factors have been discussed. [16][17][18][19] Moulinet and Bartolo studied the droplet equilibrium state deposited on hydrophobic rough surfaces by using the real-time 3D imaging technique for different droplet sizes.…”

“…20) Erbil and Cansoy estimated the droplet penetration between the pillars by suggesting the modified Cassie-Baxter equation based on the geometry of square and cylindrical pillar patterns. 9) Although a number of studies have reported some important physics behind droplet wetting behavior on hydrophobic surfaces on the basis of experiments and modeling, clear understanding of transition wetting phenomena showing penetration of liquid between pillars is required for designing and controlling hydrophobic surfaces effectively. This article reports the experimental study on transition wetting behavior of water droplet on microstructured hydrophobic surfaces manufactured by CNC machining process and self-replication way with hydrophobic polydimethylsiloxane(PDMS).…”

Design of a robust superhydrophobic surface: thermodynamic and kinetic analysis

“…The existence of a depinned state with static CAM can be determined by noticing the departure of an experimentally recorded APCA from the Cassie contact angle. In the process of investigating reported CAMs in literature, for surfaces with θY > 90°, Erbil et al conducted a detailed mathematical analysis of the deviation of APCA from that predicted by Wenzel and Cassie equations 5,43,44 . APCAs for 28 different surfaces (with known θY and square pillar geometry) were listed and, using the Cassie equation, converted to a solid fraction term.…”