page_title: Wetting
section_title: Cassie–Baxter model
hierarchical_section_title: Wetting / Non-ideal rough solid surfaces / Cassie–Baxter model
caption_attribution_description: English: liquid drop in Cassie-Baxter state
context_page_description: Wetting is the ability of a liquid to maintain contact with a solid surface, resulting from intermolecular interactions when the two are brought together. The degree of wetting is determined by a force balance between adhesive and cohesive forces. Wetting deals with three phases of matter: gas, liquid, and solid. It is now a center of attention in nanotechnology and nanoscience studies due to the advent of many nanomaterials in the past two decades.
  Wetting is important in the bonding or adherence of two materials. Wetting and the surface forces that control wetting are also responsible for other related effects, including capillary effects.
  There are two types of wetting: non-reactive wetting and active wetting.
context_section_description: When dealing with a heterogeneous surface, the Wenzel model is not sufficient. A more complex model is needed to measure how the apparent contact angle changes when various materials are involved. This heterogeneous surface, like that seen in Figure 8, is explained using the Cassie–Baxter equation (Cassie's law):
  Here the rf is the roughness ratio of the wet surface area and f is the fraction of solid surface area wet by the liquid. It is important to realize that when f = 1 and rf = r, the Cassie–Baxter equations becomes the Wenzel equation. On the other hand, when there are many different fractions of surface roughness, each fraction of the total surface area is denoted by .
  A summation of all  equals 1 or the total surface. Cassie–Baxter can also be recast in the following equation:
  Here γ is the Cassie–Baxter surface tension between liquid and vapor, γi,sv is the solid vapor surface tension of every component, and γi,sl is the solid liquid surface tension of every component. A case that is worth mentioning is when the liquid drop is placed on the substrate and creates small air pockets underneath it. This case for a two-component system is denoted by:
  Here the key difference to notice is that there is no surface tension between the solid and the vapor for the second surface tension component. This is because of the assumption that the surface of air that is exposed is under the droplet and is the only other substrate in the system. Subsequently, the equation is then expressed as (1 – f). Therefore, the Cassie equation can be easily derived from the Cassie–Baxter equation. Experimental results regarding the surface properties of Wenzel versus Cassie–Baxter systems showed the effect of pinning for a Young angle of 180 to 90°, a region classified under the Cassie–Baxter model. This liquid/air composite system is largely hydrophobic. After that point, a sharp transition to the Wenzel regime was found where the drop wets the surface, but no further than the edges of the drop. Actually, the Young, Wenzel and Cassie-Baxter equations represent the transversality conditions of the variational problem of wetting.
caption: Figure 8: Cassie–Baxter model
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