Surface Tension Work

A two-dimensional analog of PV work can be recognized in fluid films that exhibit surface tension (tendency of the film surface to contract against an opposing spreading force). The surface tension work wsurf (of, for example, a soap film) can be measured by a rectangular wire-frame device with moveable edge, as shown in Fig. 3.5. 

The film surface tension y= Fsurf/L is the force per unit length exerted by the film on the slide-bar. If the slide-bar is extended by distance dr to stretch the film, the work required is 

This is clearly the two-dimensional analog of PV work. Note that the sign differs in (3.10) and (3.14) because work is performed on the system by reducing the volume in (3.10), but by expanding the area in (3.14). 

Surface tension work can also be characterized analogously  

Surface tension work The transfer of a quantity of area (extensive) through a difference in surface tension (intensive). 

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Figure 3.5 Wire-frame device with sliding edge (length L) for measuring the surface tension work Wsurf of a soap film of area A and surface tension y.

Following Reiss, Frisch, Helfand and Lebowitz, the calculation of the work W follows almost directly from their previous considerations outlined in Section V. For a sufficiently large radius r the work of cavity formation in any fluid is the sum of the volume expansion and surface tension work... 

General hydrodynamic theory for liquid penetrant testing (PT) has been worked out in [1], Basic principles of the theory were described in details in [2,3], This theory enables, for example, to calculate the minimum crack s width that can be detected by prescribed product family (penetrant, excess penetrant remover and developer), when dry powder is used as the developer. One needs for that such characteristics as surface tension of penetrant a and some characteristics of developer s layer, thickness h, effective radius of pores and porosity TI. One more characteristic is the residual depth of defect s filling with penetrant before the application of a developer. The methods for experimental determination of these characteristics were worked out in [4]. 

Now consider some examples of the influence of sedimentation process upon PT sensitivity. Let us consider the application of fine-dispersed magnesia oxide powder as the developer. Using the methods described in [4] we experimentally determined the next characteristics of the developer s layer IT s 0,5, Re s 0,25 pm. We used dye sensitive penetrant Pion , which has been worked out in the Institute of Applied Physics of National Academy of Sciences of Belarus. Its surface tension ct = 2,5 10 N m V It can be shown that minimum width of an indication of magnesia powder zone, imbibed by Pion , which can be registered, is about W s 50 pm. Assume that n = 1. 

Finally, Newmann and co-workers [30] (see also Ref. 31) have argued that while free energy contributions may not be strictly additive as in Eq. IV-11, there should, in principle, be an equation of state relating the work of adhesion to the separate liquid surface tensions such as... 

The film pressure is defined as the difference between the surface tension of the pure fluid and that of the film-covered surface. While any method of surface tension measurement can be used, most of the methods of capillarity are, for one reason or another, ill-suited for work with film-covered surfaces with the principal exceptions of the Wilhelmy slide method (Section II-6) and the pendant drop experiment (Section II-7). Both approaches work very well with fluid films and are capable of measuring low values of pressure with similar precision of 0.01 dyn/cm. In addition, the film balance, considerably updated since Langmuir s design (see Section III-7) is a popular approach to measurement of V. 

A direct measurement of surface tension is sometimes possible from the work of cleaving a crystal. Mica, in particular, has such a well-defined cleavage plane that it can be split into large sheets of fractional millimeter thickness. Orowan... 

Gilman [124] and Westwood and Hitch [135] have applied the cleavage technique to a variety of crystals. The salts studied (with cleavage plane and best surface tension value in parentheses) were LiF (100, 340), MgO (100, 1200), CaFa (111, 450), BaFj (111, 280), CaCOa (001, 230), Si (111, 1240), Zn (0001, 105), Fe (3% Si) (100, about 1360), and NaCl (100, 110). Both authors note that their values are in much better agreement with a very simple estimate of surface energy by Bom and Stem in 1919, which used only Coulomb terms and a hard-sphere repulsion. In more recent work, however, Becher and Freiman [126] have reported distinctly higher values of y, the critical fracture energy. ... 

Referring to Fig. VII-2, assume the surface tension of (10) type planes to be 400 ergs/cm. (a) For what surface tension value of (11) type planes should the stable crystal habit just be that of Fig. Vll-2a and (b) for what surface tension value of (11) type planes should the stable crystal habit be just that of Fig. VII-2i> Explain your work. 

Measuring the electron emission intensity from a particular atom as a function of V provides the work function for that atom its change in the presence of an adsorbate can also be measured. For example, the work function for the (100) plane of tungsten decreases from 4.71 to 4.21 V on adsorption of nitrogen. For more details, see Refs. 66 and 67 and Chapter XVII. Information about the surface tensions of various crystal planes can also be obtained by observing the development of facets in field ion microscopy [68]. 

Water at 20°C rests on solid naphthalene with a contact angle of 90°, while a water-ethanol solution of surface tension 3S dyn/cm shows an angle of 30°. Calculate (a) the work of adhesion of water to naphthalene, (b) the criticd surface tension of naphthalene, and (c) y for naphthalene. 

The interesting implication of Eq. XII-24 is that for a given solid, the work of adhesion goes through a maximum as 7b(a) is varied [69]. For the low-energy surfaces Zisman and co-workers studied, )3 is about 0.04, and Wmax is approximately equal to the critical surface tension yc itself the liquid for this optimum adhesion has a fairly high contact angle. 

It is helpful to consider qualitatively the numerical magnitude of the surface tensional stabilization of a particle at a liquid-liquid interface. For simplicity, we will assume 6 = 90°, or that 7sa = 7SB- Also, with respect to the interfacial areas, J sA = SB, since the particle will lie so as to be bisected by the plane of the liquid-liquid interface, and. AB = rcr - The free energy to displace the particle from its stable position will then be just trr 7AB- For a particle of l-mm radius, this would amount to about 1 erg, for Tab = 40 ergs/cm. This corresponds roughly to a restoring force of 10 dyn, since this work must be expended in moving the particle out of the interface, and this amounts to a displacement equal to the radius of the particle. 

A homogeneous metastable phase is always stable with respect to the fonnation of infinitesimal droplets, provided the surface tension a is positive. Between this extreme and the other thennodynamic equilibrium state, which is inhomogeneous and consists of two coexisting phases, a critical size droplet state exists, which is in unstable equilibrium. In the classical theory, one makes the capillarity approxunation the critical droplet is assumed homogeneous up to the boundary separating it from the metastable background and is assumed to be the same as the new phase in the bulk. Then the work of fonnation W R) of such a droplet of arbitrary radius R is the sum of the... 

The separation of two surfaces in contact is resisted by adhesive forces. As the nonnal force is decreased, the contact regions pass from conditions of compressive to tensile stress. As revealed by JKR theory, surface tension alone is sufficient to ensure that there is a finite contact area between the two at zero nonnal force. One contribution to adhesion is the work that must be done to increase surface area during separation. If the surfaces have undergone plastic defonnation, the contact area will be even greater at zero nonnal force than predicted by JKR theory. In reality, continued plastic defonnation can occur during separation and also contributes to adhesive work. 

An inversion of these arguments indicates that release agents should exhibit several of the following features (/) act as a barrier to mechanical interlocking (2) prevent interdiffusion (J) exhibit poor adsorption and lack of reaction with at least one material at the interface (4) have low surface tension, resulting in poor wettabihty, ie, negative spreading coefficient, of the release substrate by the adhesive (5) low thermodynamic work of adhesion ... 

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