Cassie and Baxter

The second set of equations come from Cassie and Baxter - l. Cassle eonsidered a smooth, but chemically patchwlse heterogeneous solid surface, composed of fractions and with ideeil contact angles and a, respectively. For the average he wrote the Cassie equatiorfi ... 

The significance of the latter parameters can be realised if one considers the initial drop impact. In a fibrous structure such as paper a liquid is unable to discern differences in pore depth until entering the bulk structure. Prior to penetration, following dissipation of mechanical forces, drop wetting and spreading of an aqueous ink jet drop will be primarily determined by the combined effects of chemical heterogenity and physical roughness. The combination of these effects can be approximated (24) in terms of Cassie and Baxter (25) and Shuttleworth and Bailey s (26) equations ... 

In 1944, Cassie and Baxter derived an equation describing contact angle hysteresis for composite smooth solid surfaces with varying degrees of heterogeneity ... 

The effect of roughness on the wettability of an idealized sinusoidal surface has been studied with a digital computer. The equations of Wenzel and of Cassie and Baxter are discussed in relation to the model. The heights of the energy barriers between metastable states of a drop are seen to be of utmost importance in determining the magnitude of contact angle hysteresis. 

Equation of Cassie and Baxter. Cassie and Baxter [2] extended Wenzel s treatment to composite surfaces. The same assumptions necessary for the derivation of Wenzel s equation are necessary, except that Equation 66 is replaced by 70, and Equation 68 is replaced by 71. These two changes are direct consequences of the difference between the geometry of composite and noncomposite surfaces. 

These assumptions lead directly to Cassie and Baxter s equation,... 

Maximum and minimum possible angles Most probable contact angles, 0 Lower. Calculated from Wenzel s equation Upper. Calculated from Cassie and Baxter s equation Possible curve of receding angles Possible curve of advancing angles... 

Cassie and Baxter analyzed the effect of chemical heterogeneity on wettability and developed the equation. 

Fig. 6. Effect of roughness on contact angle A, maximum and minimum angle B, Wenzel equation (lower) and Cassie and Baxter equation (upper) 6, and 6 possible receding and advancing angles (Ref. )...

Fig. 9. Effect of surface chemical heterogeneity (0, = 120°, 0j = 0°) on contact angle hysteresis A, Cassie and Baxter angle, curves 1-4 represent effect of assumed energy barriers (Ref.

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 ... 

The earliest theoretical work to model the apparent contact angle of drops on rough surfaces can be attributed to Wenzel [13] and Cassie and Baxter [14]. Wenzel... 

For this reason, Cassie and Baxter described in 1944 a second model in which they predicted that a liquid contacts a solid only on top of the structures and does not sink into the space between them [10]. That is why this state is usually called the fakir state . In this case, the increase of the contact angle is caused by the decreased contact area fraction of the solid (/i) and the increased area of air underneath the drop(/2) ... 

For the second case, Cassie and Baxter modified Wenzel s equation by introducing the fractions f and /2, where f ccxresponds to the area in contact with the liquid divided by the projected area, and, to the area in contact with the air trapped... 

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... 

The influence of surface heterogeneity was analyzed by Cassie and Baxter [127] (as described in Chapter 11). Deryaguin has suggested the possibility of adoption of metastable configurations as a result of surface roughness [120]. He considered the wetting line to move in a series of thermodynamically irreversible jumps from one metastable configuration to the next. 

Equation (7.35) is known as the equation of Cassie and Baxter. It could be shown theoretically that the free energy barrier between metastable states is greatly reduced on composite surfaces. This may explain the large reduction in hysteresis which has been observed experimentally. 

On the other hand, Cassie and Baxter" considered a heterogeneous surface made up of two species with area fractions and ( 2 = 1 — i and contact angles 9 and 02- When the individual areas are much smaller than the droplet size, they found that the apparent contact angle (9c-b) is given by... 

---