Foaming critical thickness

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]. 

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). 

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. 

Critical thickness of rupture and black spot formation in microscopic foam... 

Temperature dependence of the critical concentration Ce of a foam bilayer formation. The Cc concentration (see Eq. (3.129)) of formation of DMPC foam bilayer was determined on the basis of observations of the final state which the foam film reached during its drainage (see Section 3.2), i.e. either rupture at a definite critical thickness without formation of black spots occurs, or formation of foam bilayer via black spots is observed. Rupture at critical thickness occurred at lower DMPC concentrations in the solution (C < Cc) and black spots were formed at higher concentrations (C > Cc). These black spots encountered the film turning it into a foam bilayer of constant radius. At each temperature a series of observations were carried out at various DMPC concentrations for the determination of Cc (the minimum DMPC concentration at which a foam bilayer is formed). This concentration is... 

Phase diagrams of DMPC foam bilayers. The analysis of the experimental results for the foam bilayer thickness and the critical concentration for formation of the foam bilayer... 

The details of the influence that electrostatic surface forces on the stability of foam films is discussed in Section 3.3. As already mentioned, the electrostatic disjoining pressure is determined (at constant electrolyte concentration) by the potential of the diffuse electric layer at the solution/air interface. This potential can be evaluated by the method of the equilibrium foam film (Section 3.3.2) which allows to study the nature of the charge, respectively, the potential. Most reliable results are derived from the dependence foam film thickness on pH of the surfactant solution at constant ionic strength. The effect of the solution pH is clearly pronounced the potential of the diffuse electric layer drops to zero at certain critical pH value. We have named it pH isoelectric (pH ). As already mentioned pH is an intrinsic parameter for each surfactant and is related to its electrochemical behaviour at the solution/air interface. Furthermore, it is possible to find conditions under which the electrostatic interactions in foam films could be eliminated when the ionic strength is not very high. 

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.

FIGURE 5.37 Dependence of the critical thickness, on the radius, R, of foam films. The experimental points are data from Reference 495 the films are formed from a solution of 4.3 x 10 M SDS + 0.25 M NaCl. Curve 1 is the prediction of the simplified theory," whereas Curve 2 is calculated using Equations 5.270 to 5.272 no adjustable parameters. 

For a foam to be persistent, mechanisms must be present to retard the loss of liquid and gas from the foam and to prevent rupture of the lamellae when they are subjected to mechanical shock or when a certain critical thickness is reached. 

The extent and rate of drainage of surplus solution from the interior of the lamellae is one of the important factors determining foam stability, since drainage causes thinning of the film, and when the film reaches a critical thickness (50-100 A), the film may rupture spontaneously. Drainage of the film occurs under two influences gravity and pressure difference. 

Rupture of foams. In [242], the concept of critical thickness is suggested as a criterion of the rupture of foams. This means that polyhedral foam will rupture as soon as the thickness of some films making the faces of the foam polyhedron cells attains a critical value. Adopting the channel model of the foam, i.e., assuming that the liquid completely resides in Plateau borders, and using Eqs. (7.1.21) and (7.1.23), one can represent the volume fraction of the liquid phase, V (the reciprocal of the foam multiplicity K) in the form... 

The fact that the cellular core provides resistance against shear and buckling stresses implies an ideal density for given foam wall thickness (Figure 7.50). This optimum thickness is critically important in designing complex stressed parts. 

Figure 18 Critical thickness, h, vs radius, it, of a foam film formed from aqueous solution of 0.43 mM SDS + 0.1 M NaCl comparison between experimental points, measured by Manev et al. (120), with our theoretical model based on Eqs. (82)-(87) (the solid line) and the model by Malhotra and Wasan (116) (the dashed line).

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... 

Before we proceed further, some features of Eq. (81) need to be noted. The rate (dzi/dt) at which the foam collapses depends strongly on the film velocity (Uf) corresponding to the critical thickness (vp ) at that level, dzi/dt increases as the film velocity corresponding to the critical thickness increases. On the other hand, because dxpjdc < 0, the rate of foam collapse will decrease if the local surfactant concentration increases (i.e., if (8cs/8t) > 0). However, when... 

As we have seen, crude oil foams are usually transient (see, e.g., reference [31]). The absence of significant positive contributions to disjoining pressures means that foam collapse is inevitable when the constituent films drain to their so-called critical thickness. This means that the process of film drainage largely determines foam persistence. In tnrn, that process is usually dominated by the tangential stress boundary condition, Eqnation 1.1, which equates the viscous shear stress to the surface tension gradient in the draining foam film. 

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