Contact angle, definition theory

Roll-up. The principal means by which oily soil is removed is probably roU-up. The appHcable theory is simply the theory of wetting. In briefest outline, a droplet of oily soil attached to the substrate forms at equiUbrium a definite contact angle at the oil-sohd-air boundary line. This contact angle (Fig. 4) is the result of the interaction of interfacial forces in the three phase boundaries of the system. These interfacial forces, expressed in mN/m(= dyn/cm), or interfacial free energy values expressed in mj/m (erg/cm s) are conveniently designated 1SA iSlj subscripts relate to the Hquid-air,... 

Interfadal tension between two fluid phases is a definite and accurately measurable property depending on the properties of both phases. Also, the contact angle, depending now on the properties of the three phases, is an accurately measurable property. Experimental approaches are described, e.g., in Refs. 8,60, and 63 and in Ref. 62, where especially detailed discussion of the Wilhehny technique is presented. Theories such as harmonic mean theory, geometric mean theory, and acid base theory (reviewed, e.g., in Refs. 8, 20, and 64) allow calculation of the soHd surface energy (because it is difficult to directly measure) from the contact angle measurements with selected test liquids with known surface tension values. These theories require introduction of polar and dispersive components of the surface free energy. 

The real three-phase region (tube) is replaced by a triple line (TL) as the new model element for thermodynamic considerations. In theory, its position results from the extrapolation of the three undisturbed D-faces to their common intersection. Accordingly, the tangent lines on these extrapolated D-faces Dsl and Dlv to the point of intersection lead by definition to the thermodynamic contact angle For reasons of exactness, 0 is introduced for the thermodynamic equilibrium of the three-phase system. The static contact angle 0o in Sect. 4.1 refers to the triple line at rest, i.e., to mechanical equilibrium which is a necessary but insufficient condition for thermodynamic equilibrium. 6 is the first excess quantity for the TL. As the position of any of the three D-faces can be chosen arbitrarily, the position of the TL and the value for 8 are arbitrary too. Fortunately, this vagueness is of no serious consequence as long as the two-phase and three-phase boundaries possess microscopic thicknesses. Note that 0 is... 

It is useful to first review some classical concepts of inert systems. The limitations of the inert theory with respect to reactive systems as well as potential modifications are discussed. As noted in Sec. 2.1, the definitions of both the contact line and the contact angle are predicated on the intersections of interfaces between dissimilar phases. Physically speaking, the term interface refers to a thin stratum—in some cases only several molecules thick—in which the density p varies rapidly from its bulk value in phase 1 to its bulk value in the adjoining phase 2 (Fig. 2), in the direction Z of its gradient. 

There is no doubt that heterogeneity affects the wetting properties of any solid substrate. However, heterogeneity of the surface is apparently not the sole reason for static hysteresis of the contact angle. This follows from the fact that not all the predictions made on the basis of this theory have turned out to be true [39,40]. Besides that, static hysteresis of the contact angle has been observed in cases of quite smooth and uniform surfaces [41 5]. Further, it is present even on surfaces that are definitely molecularly smooth free liquid films [60,61]. 

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