Critical thickness of film rupture

One more method of blowing a bubble from a strictly defined solution volume is used for studying the properties of stable films [16]. Here the film thickness can be determined from the volumes of the bubble and the liquid which is consumed for its formation. This method is used in the estimation of the critical thickness of film rupture and the minimum adsorption needed to avoid film rupture. 

The final thickness, hp may coincide with the critical thickness of film rupture. Equation 5.273 is derived for tangentially immobile interfaces from Equation 5.259 at a fixed driving force (no disjoining pressure). 

Critical thickness of film rupture Film thickness corresponding to the maximum disjoining pressure... 

The initial distance Hq is large compared with h, the thickness of the film at time t. The change in time, At, is the time it takes to reach a critical thickness for film rupture. Several versions of this equation exist that include internal circulation within the drop, rigid yet deformable interfaces, and complete interface mobility [64, 65]. 

Rupturing (depending on critical thickness of film on solid see text)... 

This device was used in the study of the kinetics of common thin film thinning [16,106], in the determination of the critical thickness of rupture of macroscopic films having an area of about 1 cm2 as well as in the measurement of black film thickness [107]. In equilibrium films this technique does not give reliable results, since there are difficulties in the evaluation of the capillary pressure in the menisci. 

It was first believed that the dimple in foam films decreases and even disappears at small film thickness. Later, experimental investigations of NaDoS aqueous films proved that the rate of thinning is practically equal in both thin and thick film domains, i.e. the difference by thickness between the thinnest and the thickest domains does not decrease up to the critical thickness of rupture. This leads to an increase in the non-uniformity by thickness (Fig. 3.4). 

Treatment of experimental data and their comparison to theoretical predictions are impeded due to the dependence of film lifetime on critical thickness of rupture (see Section 3.2.2.1.). The latter on its turn depends on film radius. In that sense the empirical relation... 

During thinning thermodynamically unstable films keep their shape in a large range of thicknesses until the critical thickness is approached, at which the film ruptures. This thickness is called critical thickness of rupture hcr. Therefore, the thermodynamic instability is a necessary but not a sufficient condition for film instability. There are other factors determining instability which at thicknesses smaller than the critical cease to act. Two are the possible processes involved in film instability - film thinning with retaining film shape, and film rupture. Which of them is realised when thermodynamic instability is reached, requires analysis of the various mechanisms of film rupture. 

Early studies of rupture of unstable thin films have been performed with macroscopic emulsion films [94] and foam films [53]. Very high values for hcr were obtained (of the order of 10 pm). Systematic investigations with microscopic films [e.g. 29,64,73] have shown that their critical thickness is considerably smaller. The probability character of rupture is illustrated by the curves in Fig. 3.12. As it is seen the most probable critical thickness increases with the increase in film radius. The most probable critical thickness of rupture is 30 nm (r = 0.1 mm). Usually such a thickness is reached by films from aqueous solutions of low molecular fatty alcohols at which the surfactant concentration is chosen so that the surface tension is equal in all cases [29,73]. Aniline films exhibit a higher hcr 42 nm. 

The theory of the critical thickness of rupture of thick films cannot be applied to bilayer films (with short-range molecular interactions acting in them) due to their specific structure. Therefore, a new approach is needed to explain the stability of NBF. 

The rupture mechanisms of thin liquid films were considered by de Vries [15] and by Vrij and Overbeek [16]. It was assumed that thermal and mechanical disturbances (having a wavelike nature) cause film thickness fluctuations (in thin films), leading to the rupture or coalescence of bubbles at a critical thickness. Vrij and Overbeek [16] carried out a theoretical analysis of the hydrodynamic interfacial force balance, and expressed the critical thickness of rupture in terms of the attractive van der Waals interaction (characterised by the Hamaker constant A), the surface or interfacial tension y, and the disjoining pressure. The critical wavelength, for the perturbation to grow (assuming that the disjoining pressure just exceeds the... 

Figures 5.37 and 5.38 show the critical thicknesses of rupture, Rp for foam and emulsion films, respectively, plotted vs. the film radius." In both cases the film phase is the aqueous phase, which contains 4.3 x 10 M SDS + added NaCl. The emulsion film is formed between two toluene drops. Curve 1 is the prediction of a simpler theory, which identifies the critical thickness with the transitional one." Curve 2 is the theoretical prediction of Equations 5.270 to 5.272 (no adjustable parameters) in Equation 5.171 for the Hamaker constant the electromagnetic retardation effect has also been taken into account. In addition, Eigure 5.39 shows the experimental dependence of the critical thickness vs. the concentration of surfactant (dodecanol) for aniline films. Figures 5.37 to 5.39 demonstrate that when the film area increases and/or fhe electrolyte concentration decreases the critical film thickness becomes larger.

After the theory of Vrij (1966) surface waves play an important role. The critical thickness for the rupture of thin liquid films derived from the behaviour of surface waves is much smaller than the equilibrium thickness. Fig. 3.17. shows the thinning of a film due to surface waves generated by disturbances with squeesing modes. 

The critical thickness for the rupture of such thin film was formulated by de Feijter (1988) using the Mandelstam s concept,... 

We have studied the mechanisms of rupture of a thin film in crude oil/EOR systems (with or without demulsifier). The results we obtained show that there are three kinds of mechanisms of film rupture. Figure 9 shows the first kind of mechanisms of film rupture in crude oil/EOR systems. The character of the mechanism is that the film keeps thinning to a critical film thickness and ruptures. The film ruptures in this kind of mechanism when the aqueous solution has surfactants that can greatly decrease the interfacial tension and the oil phase has no components that can improve the stability of the film, such as the asphaltenes. 

CRITICAL THICKNESS OF RUPTURE OF CHLOROBENZENE AND ANILINE FILMS. 

Of the three mechanisms, hydrodynamic drainage due to gravity is usually the most rapid and, if the foam is particularly unstable, leads to total collapse before other mechanisms can become important. In those cases, once the loss of liquid from the lamellar layer produces a critical thickness of 5-15 nm, the liquid film can no longer support the pressure of the gas in the bubble, and film rupture occurs. As a model for gravity drainage, a film may be treated as a vertical slit of thickness S (not to be confused with the solubility parameter... 

Systematic experimental studies of the influence of the bulk surfactant concentration, Co, and the film radius, R, on the stability of foam [420,492,545] and emulsion [420,487,546] films are available. The general conclusions are that the critical thickness, hct, increases when R increases and Cq decreases. In Fig. 43, the dependence of the critical thickness of rupture of aniline films on the concentration of dodecanol is shown [420]. 

Figure 43 Experimental dependence of the critical thickness of rupture, ha, of aniline films on the concentration, Cq, of dodecanol, which plays the role of surfactant. (From Ref. 420.)...

If a critical film thickness is not reached during film drainage, the drops separate from each other. Conversely, if the critical film thickness is reached, the film ruptures—as a result of van der Waals forces—and the drops coalesce. This generally occurs at thin spots, because van der Waals forces are inversely proportional to h (Verwey and Overbeek, 1948). The value of bent can be determined by setting the van der Waals forces equal to the driving force for film drainage, giving (Verwey and Overbeek, 1948)... 

When two emulsion drops or foam bubbles approach each other, they hydrodynamically interact which generally results in the formation of a dimple [10,11]. After the dimple moves out, a thick lamella with parallel interfaces forms. If the continuous phase (i.e., the film phase) contains only surface active components at relatively low concentrations (not more than a few times their critical micellar concentration), the thick lamella thins on continually (see Fig. 6, left side). During continuous thinning, the film generally reaches a critical thickness where it either ruptures or black spots appear in it and then, by the expansion of these black spots, it transforms into a very thin film, which is either a common black (10-30 nm) or a Newton black film (5-10 nm). The thickness of the common black film depends on the capillary pressure and salt concentration [8]. This film drainage mechanism has been studied by several researchers [8,10-12] and it has been found that the classical DLVO theory of dispersion stability [13,14] can be qualitatively applied to it by taking into account the electrostatic, van der Waals and steric interactions between the film interfaces [8]. 

Experiments on the stability of water/surfactant films at various pressures were performed by Exerowa et al.2,3 For a dilute aqueous solution of a nonionic surfactant,3 tetraoxyethylene decyl ether (D(EO>4,5 x 10-4 mol/dm3) or eicosaoxyethylene nonylphenol ether (NP(EO)2o, 1 x 10-5 mol/dm3), and electrolyte (KC1), thick films (with thicknesses of the order of 100 A) were observed at low electrolyte concentrations. With an increase of the electrolyte concentration, the film thickness first decreased, which suggests that the repulsion was caused by the double layer. This repulsive force was generated because of the different adsorptions of the two species of ions on the water/ surfactant interface. At a critical electrolyte concentration, a black film was formed, and the further addition of electrolyte did not. modify its thickness, which became almost independent of the external pressure, until a critical pressure was reached, at which it ruptured. While for NP(EO)2o only one metastable equilibrium thickness was found at each electrolyte concentration, in the case of D(EO)4 a hysteresis of the film thickness with increasing and decreasing pressure (i.e., two metastable minima) was observed in the range 5 x 10 4 to 3 x 10 mol/dm3 KC1. The maximum pressure used in these experiments was relatively low, 5 x 104 N/m2, and the Newton black films did not rupture in the range of pressures employed. 

Once formed the unstable waves grow until one of them (the fastest) conforms with Eq. (3.65) and then the film ruptures. During this time the film thins additionally, depending on the conditions under which it is produced. This kinetic part of the theory of critical thicknesses has been formulated and partially solved by Vrij [83]. 

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