Wenzel State rough surfaces

As stated, the Young equation is only valid for solid, ideal, and smooth surfaces thus the wetting behavior of a rough surface is described by the Wenzel equation (Equation 10.18) ... 

Before proceeding further we note that the problem of drops on top of rough surfaces with pillars or protrusions is different from the one in which rough surfaces have cavities. In case of rough substrates (made of hydrophilic materials) with pillars, a Cassie-Baxter state will typically transition to a Wenzel state by simply displacing the air which is part of the ambient, thus trapping of air is not possible. 

As expected, it has been measured that the large soUd-liquid friction achieved in the impregnated Wenzel state, results in a no-slip BC at the surface as illustrated by the values of fceff — 0 reported in Fig. 3 ( ). In the Fakir (Cassie) state, however, the trapped air is responsible for a finite slip length, the evolution of which is shown in Fig. 3 (o) as a function of the roughness lateral scale L. The measured values... 

Figure 1. Behavior of a droplet on a perfectly flat surface (a), on a rough surface according to the Wenzel state (h) and on a rough surface according to the Cassie-Baxter state (c).

In the Wenzel (W) state the topographic properties of the surface are descrihed hy a roughness factor r [4], which gives the ratio of the effective area of actual, rough surface to the ideal flat surface, i.e. r 1. The apparent contact angle is given by... 

Many experimental results have been reported (Patankar 2004 Ran et al. 2008 Shirtcliffe et al. 2005) on the transition of the Wenzel state to the Cassie state. For example, Shirtcliffe et al. (2005) observed the transition of water from the Wenzel state to the Cassie state on patterned copper surfaces with different roughness. Similarly, Ran et al. (2008) studied the surface wettability of nano-porous alumina substrates and were able to transform from the Wenzel state to the Cassie state by systematically changing the hole diameter and hole depth. 

Figure 9.1 (a) Cassie-Baxter state that promotes liquid repellenqr. (b) Wenzel state where the liquid penetrates in the rough asperities of the surface, increasing the surface-liquid adhesion, (c) SLIPS type of surface where the lubricant covers the surface features, (d)... 

The Wenzel state explains why hydrophobic surfaces tend to be even more hydrophobic (when 6 > 90 , O is always greater than 0) when surface roughness increases and why hydrophilic surfaces tend to be even more hydrophilic (when 9 < 90 , 9 is always less than 9) when surface roughness increases [24-25]. 

Behavior of a liquid drop on a rough surface. Left, liquid penetrates into the spikes (Wenzel state) right liquid suspends on the spikes (Cassie-Baxter state) [72],... 

Optical lithography can be used to transfer the patterns from the mold onto the substrate. In one example, a sequential application of polymer molds engraved with microscale and nanoscale features with a UV-curable resin of polyurethane acrylate resulted in a surface with two-tier roughness morphology. A subsequent treatment with trichloro(lH,lH,2H,2H-perfluorooctyl) silane rendered the surface superhydrophobic and displayed both the Cassie—Baxter and the Wenzel state 0eong et al., 2009). 

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