Disjoining pressure, in foams

Disjoining pressure in foam films from ABA triblock copolymers... 

V. Bergeron and C.J. Radke Equilibrium Measurements of Oscillatory Disjoining Pressures in Aqueous Foam Films. Langmuir 8, 3020 (1992). 

The thin liquid films bounded by gas on one side and by oil on the other, denoted air/water/oil are referred to as pseudoemulsion films [301], They are important because the pseudoemulsion film can be metastable in a dynamic system even when the thermodynamic entering coefficient is greater than zero. Several groups [301,331,342] have interpreted foam destabilization by oils in terms of pseudoemulsion film stabilities [114]. This is done based on disjoining pressures in the films, which may be measured experimentally [330] or calculated from electrostatic and dispersion forces [331], The pseudoemulsion model has been applied to both bulk foams and to foams flowing in porous media. 

At equilibrium the capillary pressure in the flat horizontal foam film is equal to the disjoining pressure in it... 

The DLVO-theory considers only the molecular van der Waals and electrostatic interactions. A complete analysis of the theory can be found in several monographs [e.g. 3-6] where original and summarised data about the different components of disjoining pressure in thin liquid films, including in foam films are compiled. 

When h r a the contribution of vertexes to the liquid volume fraction of a foam estimated from Eq. (4.4) is smaller compared to that of films, Eq. (4.2) and borders, Eq. (4.3). The relative contribution of borders and films depends on capillary and disjoining pressures. In a foam with thin (black) films at capillary pressures up to 5.103 Pa the border volume is... 

Usually foam column decay begins from the upper layers, because they release more rapidly the excess liquid and the foam films reach the equilibrium thickness faster. Moreover, the highest capillary pressure is in the upper foam layers (and equals the disjoining pressure in the films at equilibrium). Finally, if the vapour pressure over the foam is smaller than the saturated vapour pressure, the probability for surface film rupture increases due to evaporation. 

Bergeron, V. andRadke, C.J., Equilibrium measurements of oscillatory disjoining pressures in aqueous foam films, Langmuir, 8, 3020, 1992. 

Mysels was the first to suggest that micelles can contribute to the disjoining forces in foam films (14, 15). The first treatment describing this phenomena within a theoretical thermodynamic framework was by Pollard and Radke (16), who utilized density functional theory (DFT) to calculate a micellar contribution to the disjoining pressure, Omic. This method sums the force exerted on the interfaces by the micelles in the film, as follows ... 

Foam film stability is, as we have seen, determined in part by the lack of balance between the disjoining pressure and the capillary pressure applied to the films by the Plateau borders. The capillary pressure also drives the process of film thinning, which precedes film rupture. This in turn influences the frequency of foam film rupture. The relative magnitudes of the capillary pressure and the hydrostatic head in the foam also determine the bulk drainage behavior of the foam. If the capillary pressure at the top of the foam balances the hydrostatic head, then bulk drainage will not occur. As we show in later chapters, the stability of the films between antifoam entities and the gas liquid surface—the so-called pseudoemulsion films [60]— may also be determined by the lack of balance between the disjoining pressure in the pseudoemulsion film and the Plateau border capillary pressure. It is therefore important to clearly define the nature of the pressure distribution in the continuous phase of a foam as represented by the system of Plateau border channels. In this, we follow closely the arguments of Princen [61]. 

The disjoining pressures in thin foam films can be as high as 30 kPa (0.3 bar). Such pressures cannot be applied using devices like that shown in Figure 2.8. They can, however, be applied directly to a foam film contained in a cylindrical cell prepared from a porous frit where the menisci in the fine holes in the latter determine the maximum capillary pressure in the Plateau border. In this approach, pressure on the film is directly applied by increasing the surrounding gas pressure. In turn, this produces an enhanced capillary pressure in the liquid trapped in the pores of the frit, presumably as the liquid moves to smaller pore radii. This technique was first used by Mysels and Jones [40] and later refined by Exerowa and Scheludko [41],... 

Another difference between oil spreading on the surface of an aqueous phase and antifoam oil drop entry concerns the nature of any capillary pressure present. Consider then the case of an oil drop already emerged onto the surface of a foaming solution. If the drop is small, the air-oil and oil-foaming liquid surfaces will be hemispherical forms a (convex) lens. In this case, the capillary pressure in the drop will oppose film thinning. A stable film could therefore in principle exist in equilibrium with such a drop even if the disjoining pressure in the film is negative. 

Figure 12.7 (a) A contact formed between two bubbles in a wet foam subject to body forces F. The bubbles shapes are approximated as truncated spheres. A thin film of liquid separates two circular facets, (b) Each facet has a radius ry and an effective overlap 5. A disjoining pressure in the thin film applies a force on the facet. 

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