Cassie-Baxter equation

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When air pockets are present on a rough surface, the Cassie-Baxter equation can also be applied to the contact angle estimate of a water drop on such a surface. Since the contact angle of water in air is equal to 180°, by taking 02 = 180°, which corresponds to (cos ft = -1), Equation (676) then becomes... 

The modified Cassie-Baxter equation was successfully used to interpret some of the contact angle data reported for heterogeneous surfaces. 

A treatment similar to Wenzel s has been given by Cassie and Baxter [69] for chemically heterogeneous surfaces. For the case of a surface consisting of two types of patches, for which the intrinsic contact angles are 0] and 02, respectively, minimization of the system free energy leads to the Cassie-Baxter equation ... 

Wetting, Lotus effect, super-hydrophobicity, water repellence, contact angle, Wenzel equation, Cassie-Baxter equation, roU-off angle... 

Cassie-Baxter equations for the surface topographies shown in Fig. 1 are developed and listed. 

In the present work, we aimed to examine how the structure of a nanosphere array affected the contact angle between a liquid droplet and fluorinated surfaces. Four types of silica nanospheres with various diameters were stacked to form different organized arrays using a self-assembly technique. To clarify the superhydrophobicity, we proposed a modified parameter into the conventional Cassie-Baxter equation. This mathematical model presented in this study can probably shed some light on how the variation of particle size would induce the superhydrophobicity of nanosphere surfaces. 

According to equation (5), the contact area is a decreasing function of the included angle i.e., for a smaller contact area (or a smaller included angle), a greater contact angle of water droplet can be achieved, obeying the Cassie-Baxter equation. Two boundary conditions can be used to examine the hydrophobic behavior of sphere arrays (i) when 26 = 0° = 0), Os is thus equal to zero, i.e., a perfect superhy-... 

State, which is described by the Cassie-Baxter equation and is based on air trapping between the liquid and the roughness (see Figure 10.5) [51,52,55],... 

E. Bormashenko, Young, Boruvka-Neumann, Wenzel and Cassie-Baxter equations as the transversality conditions for the variational problem of wetting. Colloids Surfaces 345,163-165, (2009). 

Figure 10.1 Schematic of a drop partially wetting (a] a smooth, defect-free solid (Young s equation], (b] a homogenous, rough surface (Wenzel s equation], and (c] a heterogeneous, rough surface (the Cassie-Baxter equation],...

For the case of a composite interface (Fig. 6b), consisting of the solid-liquid fraction f = fsLyO = o) and liquid-vapor fraction = 1— l>cos 2 = —1), combining the Eqs. (2) and (3) yields the Cassie-Baxter equation ... 

Cassie-Baxter-equation is suitable for apphcations where heterogeneous wetting is taking place (composite sohd/hquid-air interface) cos 6strm fsl cos 6jyt+ 1) — 1. 

Due to this effect, the interface and therefore adhesion between the solid and liquid are increased compared with that observed on the flat surface of the same material. (2) If the liquid wets the structured surface incompletely, a composite solid/liquid-air interface is formed. In this case the relation between the contact angle of liquid on the flat surface fh,t, the contact angle of liquid on the structured surface 0, and the ratio of the solid surface in contact with liquid is given by Cassie-Baxter equation (Cassie and Baxter, 1944) ... 

Keywords Wetting Rough surfaces Wenzel equation Cassie-Baxter equation... 

Since one of the components (f- is air, cosl80°=-l, Eq. (4.3) becomes the famous Cassie-Baxter equation ... 

Fig. 4.1 Schematic of the heterogeneous surfaces fabricated on Si-wafer to test the Cassie-Baxter equation (d diameter of the texture, D diameter of the contact area during water contact angle measurement) (Reproduced with permission from [3], Copyright 2007 American Chemical Society)...

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