Solid surface tension, contact angle mechanical equilibrium

The surface area expansion process in Figure 3.5 must obey the basic thermodynamic reversibility rules so that the movement from equilibrium to both directions should be so slow that the system can be continually relaxed. For most low-viscosity liquids, their surfaces relax very rapidly, and this reversibility criterion is usually met. However, if the viscosity of the liquid is too high, the equilibrium cannot take place and the thermodynamical equilibrium equations cannot be used in these conditions. For solids, it is impossible to expand a solid surface reversibly under normal experimental conditions because it will break or crack rather than flow under pressure. However, this fact should not confuse us surface tension of solids exists but we cannot apply a reversible area expansion method to solids because it cannot happen. Thus, solid surface tension determination can only be made by indirect methods such as liquid drop contact angle determination, or by applying various assumptions to some mechanical tests (see Chapters 8 and 9). 

Over 150 years ago Thomas Young [104] proposed treating the contact angle of a liquid as the result of the mechanical equilibrium of a drop resting on a plane solid surface under the action of three surface tensions (Figure 1)—Vlv the interface of the liquid and vapor phases, VsL the interface of the solid and the liquid, and Vgv the interface of the solid and vapor. Hence,... 

Three interfaces come into play if a liquid drop is deposited on a solid surface, and three interfacial tensions are involved /sv, Xsi and respectively the solid-vapour, solid-liquid and liquid-vapour interfacial tensions. The mechanical equilibrium of the triple line fixes the value of the contact angle 0 at which the liquid-vapour interface meets the solid plane defined by Young s relationship (Figure 7.2) ... 

The themiod3Tiamic approach to the description of adhesion has many advantages as compared with some other theories. It does not require knowledge of the molecular mechanism of adhesion but considers only the equilibrirun processes at the polymer-solid interface. The approach to the problem developed by Zisman is widely accepted. Zisman introduced the concept of the critical surface tension of wetting as a value which is found by extrapolation of the dependence of cos on y to cos =1, i.e., when liquid fully spreads on the surface. The value Yj found by extrapolation is considered as the critical surface tension of a solid. If the value y is known, the equilibrium contact angle can be predicted for any liquid on any surface. If yj < y, the contact angle equals zero and the liquid spreads on the surface. 

The classical analysis of Young and Laplace of static wetting problems rests on the characterization of each interface by a macroscopic surface tension. At the intersection of three bulk phases, the three phase contact line is at rest only if the capillary forces represented by these surface tensions balance. When the three phases are a solid substrate S, a wetting liquid L and a vapor V, the mechanical equilibrium condition parallel to the solid gives the Young-Dupr6 equation for the contact angle Oq... 

For a static system, solid surface interfacial tensions can be calculated from the measured contact angles by using a mechanical equilibrium relation derived by Young in 1800 [38]. The liquid droplet contact angle on any solid surface can be defined by the mechanical equilibrium of the droplet under the action of three interfacial tensions. The interfacial tension a ij is defined as the amount of work that must be performed in order to separate a unit area of fluid j from k. The term aj is the surface tension between substance j and its own vapor phase (Figure 5.28). The work to separate two phases is expressed as... 

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