Wenzel wetting model

As described by the Wenzel wetting model, the increase of surface roughness should lead to a certain increase of contact angle (CA) values. To verify this statement, we investigated three different kinds of commonly used thin films known to be very different in grain size and, therefore, in surface roughness. Figure 3 shows the comparison of a 50 nm Au film, an 800 nm native oxidized titanium film (TiO") and an 800 nm wet chemically oxidized titanium film (TiO ) on a polished silicon substrate. 

Surface Tension, Capillarity and Contact Angle, Rgute 8 Effect of surface stnictures on wetting behavior, (a) Wenzel s model where the liquid penetrates between the structures, (b) Cassie-Baxter modet where water does not wet the surface between the structures... 

The Young equation cannot be used directly to explain the effect of surface roughness on the wettability of a material because it is valid only for ideal smooth solid surfaces. There are two wetting models that are proposed when a water droplet sits on rough surfaces, these are the Wenzel model and the Cassie-Baxter model. 

Wettability of a rough surface can be described by the Wenzel [7] model if the surfaces are completely wetted by the liquid into the protrusions on the surface. The Cassie-Baxter [8,9] model gives an idea about wettability of rough hydrophobic surfaces. In the case of such surfaces, the air trapped into hierarchical roughness prevents water penetration into the surface protrusions. 

In this work, ordered arrays of core-shell particles were used as model surfaces to study the water wetting behaviour of these surfaces. Two factors were varied in the wetting experiments (i) the shell chemistry and hence the solid surface tension of the organic shell, and (ii) the height roughness from sub- xm up to xm roughness values whereas the Wenzel roughness factor was kept constant. 

The Cassie-Baxter-Wenzel theory [44, 47,48] defines the critical contact angle value on the smooth surface above this value, the Cassie-Baxter model is more stable wetting state and below this value the Wenzel model is the most stable wetting state. If the measured contact angle on a smooth surface is lower than this critical value and if the superhydrophobic behaviour is observed, the transition between the two models should be possible like, for example, with the LDPE surface treated in both plasmas. In this case, the roughness factor is 1.043, the contact angle on the dried surface reaches a value of 171° and the contact angle on the same surface partially wetted with water vapour or dipped in water is only 140°. 

Wenzel s equation applies to what is called homogeneous wetting, and it can only be applied to homogeneous, rough surfaces. Surfaces having heterogeneous character can be modeled with the Cassie-Baxter model [43] ... 

The Young s equation is the well-known relationship used to describe a sessile drop at equilibrium on top of a solid surface. This relationship has been discussed thermodynamically and microscopically for purely flat surfaces in the literature. To characterize the non-flatness of a surface, one may introduce the Wenzel s roughness r defined as the area of the wall surface devided by the area of its projection onto the horizontal plane. Obviously, r is equal to 1 once the surface is flat. For r>l, it is known that Young s equation has to be modified to take into account the increase of surface. The generalization of Young s relation is the so-called Wenzel s law. In this presentation, we will study this relation within microscopic models. We will in particular show that the roughness may enhance the wetting of the substrate even at the microscopic scale. 

In the context of the fimdamental relation between surface topography and wetting behavior as modeled by Wenzel or Cassie and Baxter one has to consider the relevance of geometrical parameters for the complex porous and textured textile substrate. It is of interest in this context that a paper by Hsieh et al. [26], who studied the wetting of water and ethylene... 

It is not within the scope of the present chapter to derive appropriate -and maybe even analytical - models to describe the influence of geometrical parameters on the wetting behavior of textile fabrics. However, it is of interest at this point to mention two attempts to derive geometric parameters of the rough surfaces, which are more sensitive than the rather crude Wenzel factor to describe topographic peculiarities such as the two-scale roughness pattern of the Lotus leaf. 

Figure 4.8 Schematics of a motion of the contact hne of a hquid droplet sitting on a solid surface, leading to a corresponding free energy variation for a smooth surface (Young model, a), complete penetration of the liquid into the recessed features of a pattern (Wenzel model, b), and for heterogeneous wetting regimes with absence of penetration (Cassie-Baxter model, c) and for partial penetration (d). In the Wenzel model, rfp = AB + BC + CD + DE)I AB + CD) according to the letters in (b). In the Cassie-Baxter model, (j) = (AB)I(AB + BE) according to the letters in (c).

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