Film surface tension definition

It has been shown (16) that a stable foam possesses both a high surface dilatational viscosity and elasticity. In principle, defoamers should reduce these properties. Ideally a spread duplex film, one thick enough to have two definite surfaces enclosing a bulk phase, should eliminate dilatational effects because the surface tension of an iasoluble, one-component layer does not depend on its thickness. This effect has been verified (17). SiUcone antifoams reduce both the surface dilatational elasticity and viscosity of cmde oils as iUustrated ia Table 2 (17). The PDMS materials are Dow Coming Ltd. polydimethylsiloxane fluids, SK 3556 is a Th. Goldschmidt Ltd. siUcone oil, and FC 740 is a 3M Co. Ltd. fluorocarbon profoaming surfactant. 

There is another point of view from which it is often useful to regard surface phenomena. If the surface of a soap-film in a wire frame is increased by moving outwards against the tension one side of the frame, a quantity of work must be done against the surface tension equal to the product of the surface tension and the increase of area. A definite quantity of potential energy is thus bound up with each unit of surface. The numerical value of the surface energy defined as energy per unit surface is clearly the same as that of the surface tension. The dimensions in each case are... 

When air is exhaled the small alveoli of the lungs could collapse if it were not for the surface active material (surfactant) present in the fluid that coats the lungs. e In fact, the lack of adequate surfactant is the cause of respiratory distress syndrome, a major cause of death among premature infants and a disease that may develop in acute form in adults. The surfactant material forms a thin film of high fluidity at the air-liquid interface and lowers the surface tension from the 72 mN/m of pure water to <10 mN/mfs (Pay attention to the definition of surface tension.11)... 

Devaux2 made numerous experiments between 1903 and 1914. Using a light powder sprinkled on the surface, which is a convenient way of rendering the movements of the oil visible, he confirmed most of the results of Pockels and Rayleigh. He found that the oils spread to a definite maximum extension, which is of course the same as that at which the first fall in surface tension appears. Calculating the thickness of the films, he found it of the same order as the then approximately known dimensions of molecules.8 He was the first to notice that the films may be solid,... 

The definition applies only to a symmetrical film, for which the two bulk phases on either side of the film are the same, and y is the surface tension of a film/bulk interface. 

The initial expansion ratio and dispersity of polyhedral foams are related through the quantitative dependence, given by Eq. (4.9). There at Ap > 103 Pa the content of the liquid phase in the films can be neglected. Thus, the connection of the structure parameters n, a and r can be expressed by the simple relation in Eq. (4.10). It follows from it that under given foaming conditions a definite expansion ratio can be reached by changing the border pressure, foam dispersity and surface tension of the foaming solution. 

Curved surfaces can also be saddle-shaped. Figure 10.20 shows an example. Suppose that a surfactant film is made between the two frames. Surface tension causes the film to assume the smallest surface area possible. In the situation depicted, this surface is saddle-shaped. Moreover, the surface has zero curvature. As drawn for the middle cross section of the film, the principal radii of curvature are equal, but of opposite sign, since the tangent circles are at opposite sides of the film (which is, actually, the definition of a saddle-shaped surface). In other words, = 0 because l/i i + l/(—R2) = 0. This is true for every part of the film surface. 

Now, the surface tension actively assists in reducing the film resistance to mass transfer, while viscous stresses thicken the films. Substituting Eq. (6.7) and using the definition of the capillary number, we obtain... 

Alternatively, surface tension is given by the force per unit length associated with this process. The equivalence of these two definitions can be readily confirmed by a simple example. Consider a liquid film (such as soap film) suspended on a wire frame, which is stretched by moving a slider (Fig. 4.6). The surface tension is the force per unit length, y = F/(2/), where the factor of two arises because the film has two sides. Then the work done for an infinitesimal extension dx is... 

Since the liquid data were obtained at veiy low solute concentrations, can be converted to through = kj c, where c is the molar density of the solvent liquid. There may be an additional effect not included in Eq. (6.72). If concentration changes result in an increase in surface tension as the liquid flows down the column, the liquid film on the packing becomes stabilized and the mass-transfer rate may become larger. If the surface tension decreases, the film may break up into rivulets and the mass-transfer rate decreases [127]. Definite conclusions cannot yet be drawn [16]. 

One of the most popular and simple methods for making a surface tension measurement is the Wilhelmy plate or rod method. Here, either a flat plate (held vertically) or a simple rod is dipped into the fluid and then retracted slowly. The plate is designed to be very hydrophilic, so the water in the trough will wet the plate and be pulled upward as it is retracted. In this method, calculation of the surface tension is easy as the method is analogous to our previous definition of surface tension by pulling out a film from the bulk (Section 3.3). 

Surface tension is strictly defined as the force per unit length that opposes surface area expansion. We can illustrate this definition with a simple experiment shown in Figure 13.1, where the movable bar is pulled with force f to expand a liquid film that is stretched like a soap-bubble film on a wire frame. The surface tension (y) is... 

The quantity 11/ is a measure of the so-called disjoining action , introduced by Derjaguin in 1936 [12]. The disjoining pressure n [8] is determined by the long-range interaction forces between the surfaces of the film (normal to the both surfaces of tension there) and tends to zero when the film thickness is sufficiently large [5]. Eq. (3.15) proposes a more general definition of IT than that for the equilibrium case (Eq. (3.10))... 

In summary, the definition of snrface tension is given by Eqn. 4, of surface energy by Eqn. 5 and the relation between them by Eqn. 7. Note Some authors develop these concepts in terms of the Helmholtz fnnction rather than the Gibbs function, by supposing the soap film to be stretched at constant temperature and volume, rather than pressure.)... 

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