Equation of Cassie and

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. 

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. 

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 ... 

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. 

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 ... 

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

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. )...

This reasoning was followed by Flory and Rehner in their analysis of swelling networks. We may also calculate the equilibrium from a free energy which does not contain 0, provided the result is corrected afterwards by means of equation (78). Clearly, this method is equivalent, since /c>/7z == ( 0/dV)Vo = —upo, where a represents the hydrostatic pressure due to network interlinking. Barkas and Cassie have used this method to correct the sorption isotherm of wood and of wool. In Fig. 21 the drawn curve represents the sorption of water by wool measured directly. The swelling involved in this sorption, however, is opposed by forces whose Sorption magnitude may be estimated from stress-strain data in the stretch of wool. If the vapour pressure is corrected according to equation (78), one finds the much lower vapour pressures of the dotted curve. This curve extends no further than to 50% relative vapour pressure. 

For the system wool-water a theory of this kind has been developed by Cassie and in a particularly interesting paper by Hailwood and Horrobin The latter postulated formation of a monohydrate, i. e., binding of one water molecule by each monomeric residue of the fibre portion taking part in absorption. For the isotherm they gave the equation ... 

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 ... 

According to Wenzel s equation, obviously, high roughness can enhance the hydrophilicity of a native hydrophilic surface. In our study, such porous film is much rougher than relatively flat surface obtained without using template, so this model can explain why our as-synthesized films show superhydrophilicity with a CA about 5°. After modification with a lower surface free energy material, the air can be trapped in such ordered pore array, and hence a composite surface composed of air and pore array is formed. The measurements show that the surface is superhydrophobic with water CA of 154°. In this case, the Cassie equation is applicable. Based on a simplified model, as schematically illustrated in Fig. 6, the relationship... 

Both theoretical equations have been used to estimate the deviations of the surface composition from that of the solution, by plotting the mole fraction h-ddpo, at the surface, as calculated by the Cassie and Israelachvili ... 

In the simplest case, the wettability of a solid surface is commonly evaluated by the contact angle given by Young s equation. Then Wenzel proposed a model describing the contact angle on a rough surface, and Cassie proposed an equation for the surface composed of solid and air. The concepts of these equations are outlined in fig. 7.18 [106]. 

Wetting on rough or chemically patterned surfaces has also been studied for a long time. Two well-known equations, the Wenzel s equation [11] and the Cassie s equation [12] are introduced to characterize the macroscopic apparent contact angle in terms of surface roughness and inhomogeneity (see Equations (4.6) and (4.7) in Section 4.3). There have been many works on the derivation and validity of these two equations [10,13-17], despite some controversies on their correctness [18-22]. In particular, they cannot describe the contact angle hysteresis and cannot explain some of the experimental observations [18,23]. Various modifications or variations of these two equations are proposed and studied [10,20,24-26]. 

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