Thermodynamic contact angle

At present, when working with high-purity materials, smooth solid surfaces and low P02 atmospheres, the thermodynamic contact angle in a particular system can be determined at best within about five degrees. Roughness must be very low, particularly in non-wetting systems in order to obtain such an accuracy. The control of P02 is critical for oxidisable liquids and solids, specially at relatively low temperatures, and dynamic vacuum is often preferable to a static neutral gas atmosphere. 

In the further elaboration a general phenomenological framework for wetting can be developed. Because of its thermodynamic nature, this framework is macroscopic and static it refers to equilibrium or to reversible processes. So, the kinetics of wetting cannot be analyzed in this way and only one contact angle, the equilibrium angle, can be considered. It remains an issue how this thermodynamic contact angle relates to the one that is physically measurable. Another typical feature is that interfaces are always taken to be at equilibrium with the adjacent... 

T wo important conclusions of the weak fluctuation approach are that, a) the energy barriers between stable configurations are much lower than those predicted by Johnson and Dettre, and that contact angle hysteresis disappears below some threshold level of surface heterogeneity. An important consequence of the latter conclusion is that determination of the thermodynamic contact angle does not require an ideal solid surface. ... 

In the Wenzel approach the space between the protrusions on the surface is assumed filled by the liquid and the apparent contact angle 9 and thermodynamic contact angle 9 are then linked by... 

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... 

Figure 6. Difference between the thermodynamic contact angle Sg and the effective contact angle 9 when the solid surface is not vertical.

Figure 13. Predicted force changes for water advancing over a model cavity as a function of the cavity angle iji and the thermodynamic contact angle 9.

A. W. Neumann and J. K. Spelt, eds.. Applied Surface Thermodynamics. Interfacial Tension and Contact Angles, Marcel Dekker, New York, 1996. 

Since both sides of Eq. X-39 can be determined experimentally, from heat of immersion measurements on the one hand and contact angle data, on the other hand, a test of the thermodynamic status of Young s equation is possible. A comparison of calorimetric data for n-alkanes [18] with contact angle data [95] is shown in Fig. X-11. The agreement is certainly encouraging. 

Combination of Eq. 7 or Eq. 8 with the Young-Dupre equation, Eq. 3, suggests that the mechanical work of separation (and perhaps also the mechanical adhesive interface strength) should be proportional to (I -fcos6l) in any series of tests where other factors are kept constant, and in which the contact angle is finite. This has indeed often been found to be the case, as documented in an extensive review by Mittal [31], from which a few results are shown in Fig. 5. Other important studies have also shown a direct relationship between practical and thermodynamic adhesion, but a discussion of these will be deferred until later. It would appear that a useful criterion for maximizing practical adhesion would be the maximization of the thermodynamic work of adhesion, but this turns out to be a serious over-simplification. There are numerous instances in which practical adhesion is found not to correlate with the work of adhesion at ail, and sometimes to correlate inversely with it. There are various explanations for such discrepancies, as discussed below. 

Kom GA, Korn TM (1968) Mathematical handbook. McGraw-Hill, Boston Landau LD, Lifshitz EM (1959) Fluid mechanics, 2nd edn. Pergamon, London Morijama K, Inoue A (1992) The thermodynamic characteristics of two-phase flow in extremely narrow channels (the frictional pressure drop and heat transfer of boiling two-phase flow, analytical model). Heat Transfer Jpn Res 21 838-856 Ngan CD, Dussan EBV (1982) On the nature of the dynamic contact angle an experimental study. JEluidMech 118 27- 0... 

The above considerations show that the interfacial energy is of utmost importance in determining the thermodynamics and kinetics of the nucleation process. Unfortunately, however, there are considerable uncertainities on the values of interfacial free energies. Values determined from contact angle measurements are significantly lower than those determined from the dependence of solubility upon molar surface of the crystallites. Furthermore, reliable data on yes are lacking. 

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