Stable equilibrium thick film

The equilibrium thickness of a (meta-)stable soap film will depend on the strength and range of the repulsive forces in the film. Electrostatic forces are long-range in water and hence give rise to thick (0.2 micron) films, which are highly coloured due to the interference of visible light... 

For a suitably high critical value of A, this theoretical model predicts a lower limit on the equilibrium thickness that can be observed. This lower limit on Z, Z n, is defined by the conditions F= 0 and <1F/<1L = 0 since for a stable film F= 0 and dF/dL > 0 (Clarke, 1987). Various solutions to these conditions have been examined by Knowles and Turan (2000). In the absence of capillary pressure and external pressure, Zmin = 2.58. Using reasonable estimates for Knowles and Turan estimate Zmin to be >6.50 A. That in practice the observed intergranular film thicknesses are typically of the order of 1-2 nm in non-oxide engineering ceramics indicates that the relevant Hamaker constants for ceramics are significantly lower than the critical value. 

By many properties emulsion aqueous films are analogous to foam films. There are several review articles dedicated to properties of emulsion aqueous films [e.g. 320,503-506]. The properties of microscopic emulsion aqueous films (kinetics of thinning, determination of equilibrium thickness, etc.) are studied employing devices quite similar to those used for foam films [503]. Analogous to foam films, stable (metastable) emulsion films are formed only in the presence of surfactants (emulsifiers) at concentrations higher than the critical concentration of formation of black spots C or the concentration, corresponding to... 

Thus, it might be assumed that stabilisation of foam films will depend also on the action of other positive components of disjoining pressure. For example, equilibrium films are obtained from concentrated butyric acid solutions and, therefore, in this concentration range the foam lifetime also increases. On the basis of these concepts it should be expected that a foam consisting of films with equilibrium thicknesses at a constant capillary pressure pa = n, should be infinitely stable. In fact, a real foam decays both in bulk and as a disperse system, due to gas diffusion transfer and certain disturbances (shift of films and borders on structural rearrangement as a result of the collective effects , etc.)... 

As before, the critical thickness her of the film is defined as the smallest value of hf for which a stable equilibrium position rj for the dislocation can be found such that Wd( ) + Ikm(r/) = 0. 

Final equilibrium state. Stable, thick film. c > c.m.c. 

Equation 3.19. In this example we have A < 0, C < 0,. 6 > 0, A > 5, C > 5, and A + C > so that the integral of Equation 3.19 is negative and the generalized entry coefficient positive for films at both thickness h = h and h = fi. These two situations correspond to stable equilibrium and metastable eqnilibrinm films, respectively, where the former is characterized by the highest entry coefficient and the lowest film tension. The classic equilibrium entry coefficient E is concerned with the stable equilibrium so we should have E = E Qi = h. ... 

In the case of pseudo-partial wetting, a condition of stable equilibrium with respect to an oil lens can exist at a film thickness if the disjoining pressure curve is such that we can set = -H owC e) in the approach to the primary maximum on the disjoining pressure isotherm as shown in Figure 3.10a. Here A, B, C, and E represent the indicated areas in the isotherm. The integral in Equation 3.27 with the upper limit set at H owl e) is then equal to the generalized equilibrium spreading... 

The film eventually reaches an equilibrium thickness in which both faces of the film are parallel (Fig. 1.18(c)). In this state there is no variation in intensity over the surface of the film. This is called the common black film. It occurs, typically, at a thickness of 300A (30nm). A further decrease in the film thickness, to another stable equilibrium state with a thickness of about 50A, is often possible and is known as the Newton black film. This film is darker than the first black film, the common black film, as the second of the two split rays, that is refracted into the film, travels through a thinner soap film than in the case of the common black film. Consequently the phase difference between the two split rays of the Newton black film is closer to tt than in the case of the common black film. Some films have only one equilibrium state while others have two or more equilibrium states. 

In a controlled environment a soap film will thin until its thickness becomes appreciably less than the wavelength of light so that it appears black when viewed by reflected light. Commonly it is found that the film reaches a stable thickness, in thermodynamic equilibrium, of about 300 A. This is known as the common black film. If a small amount of evaporation is allowed to take place the film will often thin to a new equilibrium thickness of about 50 A. This is the Newton black film. The thickness of these two equilibrium states can be obtained by measuring the intensity of the reflected light by using photoelectric detectors. The application of Eq. (2.26) will enable the thickness of the film, t, to be determined. 

FIGURE 2.2 Two equilibrium flat films on solid substrates under oversaturation stable film of thickness h, and unstable film of thickness h . 

However, in the case of partial wetting, Equation 2.3 has two solutions (Figure 2.2). According to the stabihty condition of flat films in Equation 2.4, one of them corresponds to the stable equilibrium film of thickness h, and the second one corresponds to the unstable film of thickness (Figure 2.2). This would suggest that equilibrium droplets in the case of partial wetting are sitting on the stable equilibrium film of thickness h. ... 

In the case of thick macroscopic capillaries. Equation 2.42 has three solutions, one of which corresponds to the stable equilibrium a-flhn with thickness h. The excess free energy of a-fllms is equal to zero, according to our choice in Equation 2.38. The second solution of Equation 2.42 in this case, /t , is unstable according to the stability condition (2.4, Section 2.1), and the third solution, h, is P-fllm, which is also stable according to the same stability condition (2.4, Section 2.1). It has been shown in Section 2.1 that P-films have higher excess free energy as compared with a-lihns, that is, P-lilms are less stable and eventually rupture to thinner and absolutely stable a-films. 

Let us assume that the transition zone profile does nof lend asymptotically to the equilibrium thickness but meets the film at the final point x = Xq. In this case, in the vicinity of this point, we approximate the disjoining pressure isotherm by a linear dependency H h) n(/tj - a h - hj, where a = - (/ ) is a positive value is a stable flat liquid film, and the derivative of the disjoining pressure should be negative and n(h ) = Pg. The liquid profile in this region has a low slope, which means Equation 2.23 can be rewritten as... 

There is no simple, direct relationship between elasticity and emulsion or foam stability because additional factors, such as film thickness and adsorption behaviour, are also important [204]. Nevertheless, several researchers have found useful correlations between EM and emulsion or foam stability [131,201,203], The existence of surface elasticity explains why some substances that lower surface tension do not stabilize foams [25]. That is, they do not have the required rate of approach to equilibrium after a surface expansion or contraction as they do not have the necessary surface elasticity. Although greater surface elasticity tends to produce more stable bubbles, if the restoring force contributed by surface elasticity is not of sufficient magnitude, then persistent foams may not be formed due to the overwhelming effects of the gravitational and capillary forces. More stable foams may require additional stabilizing mechanisms. 

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