Disjoining pressure critical

Comparison of the proposed dynamic stability theory for the critical capillary pressure shows acceptable agreement to experimental data on 100-/im permeability sandpacks at reservoir rates and with a commercial a-olefin sulfonate surfactant. The importance of the conjoining/disjoining pressure isotherm and its implications on surfactant formulation (i.e., chemical structure, concentration, and physical properties) is discussed in terms of the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory of classic colloid science. 

Figure 6. Evolution of the lamella thickness as it transports down the periodic pore for the conjoining/disjoining pressure isotherm of Figure 4. Three capillary pressures are considered in curves 1 through 3. These capillary-pressure values are also labelled in Figure 4. Curve 2 defines the critical or marginally...

Since monodisperse creams of a range of droplet sizes can readily be prepared, it is possible to study the effect of droplet size on the critical osmotic pressure required for film rupture, n. This was found to increase with increasing droplet size. The critical osmotic pressure is, in effect, the disjoining pressure as smaller droplets have higher disjoining pressures (due to a smaller radius of curvature),... 

A stable film can be obtained only if the hydration repulsion is stronger than the above critical value, hence if Aj > A, and the maximum disjoining pressure occurs at a distance d < d = 3A,. 

Other discrepancies between the black film behaviour and DLVO-theory are related to the difference in the critical electrolyte concentration, corresponding to the transition between the two black films types (see Section 3.4.2) the existence of a second minimum in the 11(A) isotherm the sharp rise in the disjoining pressure (after the second minimum). All this is evidenced by the measurements of contact angles between the film and bulk phase. 

Recently a new method for formation of monodisperse emulsions that creates high capillary pressures, involving osmotic stress technique, has been introduced [73]. It proves to be most reliable for the purpose. Preliminary calculations showed that the emulsion films in such monodisperse systems rupture in a narrow range of critical disjoining pressure. For example, NaDoS emulsion films rupture in the range from 1 to 1.3-105 Pa, which is analogous to foam films from the same surfactant solution. Unfortunately, the foam film type has not been considered. 

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. 

The basic mechanism of foam degradation in porous medium is film coalescence. It depends on film thickness and capillary pressure. In the process of advancement the film thickness changes considerably thickens in the narrow parts (pore throats) and thins in the wider parts (pore bodies). Visual observations of such a stretching-squeezing mechanism are reported by Huh et al. [178]. Therefore, the film thickness would depend on the liquid/gas ratio, the rate of movement and the ratio of pore-body to pore-throat. When the critical capillary (disjoining) pressure is reached, the film will rupture. 

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... 

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). 

Basu, S. and Sharma, M.M., Measurement of critical disjoining pressure for dewetting of solid surfaces, J. Colloid Interface Sci., 181, 443, 1996. 

Thus, it is deduced that effective adhesion depends critically on the liquid adhesive displacing the third phase and spreading into all the space between the two solid surfaces to be attached to one another. The angle of contact, the hquid surface tension and the disjoining pressure are the appropriate measurable properties that enable quantitative values of the free energy of spreading to be assessed. 

Let us reexamine the condition for foam collapse within the framework of this assumption. Because film rupture can occur only if the capillary pressure (ff/j-p) exceeds the maximum disjoining pressure (i7m v), it is possible to define a critical Plateau border radius (/-pc) given by ... 

If the short-range repulsive disjoining pressure is large enough, the black foam films are stable. There are two types of black foam films common and Newtonian. While the common black films are the thicker type of black films (from about 5 to 20 nm in thickness), the Newtonian black (NB) films are bimolecular thin films (less than 5 mn in thickness). A mechanism of rupture of NB films is considered as a process of new phase nucleation in a two-dimensional system [105 108]. There exist in the film elementary vacancies (unoccupied positions of surfactant molecules) moving randomly, which associate to form clusters of vacancies called holes. A hole can grow up by fluctuations to a critical size and become a nucleus of a hypothetical two-dimensional phase of vacancies. Further spontaneous growth of the nucleus leads irreversibly to the rupture of the film. When the rupture of NB film is due to formation of holes in it by a nucleation mechanism, it has been shown that the mean film lifetime r depends on the monomer surfactant concentration C as ... 

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