Stability of a Liquid Film

Consider a thin liqmd Aim in air for which the Hamaker constant Ah is 5 x K)- erg and electrical double-layer effects are negligible. If viscosity is 1 cp, density is 1 g/cm. Aim thickness is 50 nm, and surface tension is 40 mN/m, And the wavenumbers and of the critical and fastest growing disturbances and the time factor (3 for growth of the latter using the inextmisible interface results given above. Compare with the corresponding results for a free interface in the inviscid approximation. 

The disjoining pressure is -A I6rch, according to Equation 5.111. Hence, from Equations 5.119 through 5.121, we have, for inextensible Aim surfaces. 

In the examples of interfacial stability considered thus far, the systems have been at rest in their initial states. Hence the predictions of when instability can be expected are, in fact, conditions for thermodynamic stability. We have chosen not to emphasize this point and to carry out the analyses in terms of perturbations of the general equations of change because we obtain in this way not only the stability condition but also the rates of growth of unstable perturbations and the appropriate frequencies of oscillation and damping factors for stable perturbations. Also, the basic method of analysis used above is applicable to systems not initially in equilibrium, as we shall see later in this chapter and in Chapter 6. 

Nevertheless, there may be situations where information on growth rates and the characteristics of the fastest growing disturbance is not of prime importance. In this case the energy and force methods, when they are applicable, can be used to determine the condition for thermodynamic stability with less effort than required for the more general analysis presented above (Miller and Scriven, 1970). 

The energy method can be used whenevCT an energy function such as the free energy exists that is known to have a local minimum at any state of stable equihbrium. Basically the change in this function is calculated for all possible perturbations from the equifibrimn state. If all such changes are positive, the initial state is stable. But if any possible perturbation produces a decrease in the energy fimction, instability can be expected. 

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Feldman (F3), 1957 Mathematical consideration of stability of a liquid film on a wall with a cocurrent gas stream above it. 

Interactions between the opposing film surfaces are important for the stability of a liquid film like foam films, emulsion films, etc. Related to this, the adsorption of ions at the film interfaces plays a decisive role. 

Together with the ansatz Eq. (1.1), Eq. (1.5) describes the response of a liquid film to an applied pressure p. The resulting differential equation is usually solved in the limit of small amplitudes q < h hv and only terms linear in f are kept ( linear stability analysis ). This greatly simplifies the differential equation. The pressure inside the film p = Pl + Tex consists of the Laplace pressure pL = —ydxxh, minimizing the surface area of the film, and an applied destabilizing pressure pex, which does not have to be specified at this point. This leads to the dispersion relation... 

Stability of isolated liquid films soap films foams. Pure liquids rarely, if ever, foam, but most solutions of capillary active substances do so to a greater or less extent, and long-chain colloidal electrolytes, particularly the soaps, have an almost miraculous power of rendering liquid films stable. Dewar1 has maintained soap films unbroken for over a year (one for three years ), with due precautions against evaporation, mechanical and thermal shocks, and absorption of carbon dioxide. 

By using the concept of nanoconfined liquids it is possible to improve both the stability of supported liquid films (a critical problem in all catalysts previously discussed) and the catalytic performances, because ... 

This inequality is the most severe condition of the hydrodynamic stability of the liquid film [241]. Therefore, an instability and rupture of the film are considered to occur when the film thickness attains a critical value /icr, as the liquid flows out of the film. The critical thickness is determined by the condition... 

Several colloidal interaction forces can act between particles dispersed in a liquid. If these particles attract each other, they will aggregate, which means that the dispersion is unstable. The interaction forces can also affect the stability of a thin film (e.g., between air bubbles) and the rheological properties of particle gels. 

Chapters 10 and 11 are dedicated to nex concepts of flotation and microflotation. As a main act of these processes the formation and stability of thin liquid films are discussed in Appendix 2D. 

In one approach, the stability of pseudoemulsion films can be predicted by calculating the total interaction energy for the thinning of a liquid film bounded by an air—water and a water-oil interface along the lines described earlier in Chapters 1 and 2. From this interaction energy, the disjoining pressure, which is the net pressure difference normal to the surface between the gas and oil phases and the bulk liquid from which the lamellae extend, can be calculated. Estimates of the disjoining and capil-... 

The reactants in SILP catalysis are preferentially processed in gaseous form. Processing of solid SILP catalysts in a liquid reaction phase as a slurry requires extremely low solubility of the ionic liquid film in the liquid reaction mixture and affords special constraints upon the mechanical stability of the liquid film. In contrast, for the - by r more attractive - gas-phase applications of SILP catalysts the extremely low volatility of the ionic liquids is the key success fector. It is noteworthy that earlier attempts to apply supported liquid catalysts in continuous gas phase reactions - using organic liquid phases [32] or water [33] as the immobilized liquid phase - resulted in catalyst systems too unstable for technical use due to evaporation of the liquid film with time. In contrast, SILP systems have been... 

Garrett, P. R. (1980). Preliminary considerations concerning the stability of a liquid heterogeneity in a plane-paraUel hquid film. Journal of Colloid Interface Science, 76(2), 587-590. 

The behavior of disperse systems, such as foams and emulsions, is very complex and there have been only few attempts to derive qualitative and quantitative relationships between their stability and physicochem-ical parameters of the stabilizing adsorption layers. The starting point of most of these approaches is the hydrodynamic theory of thinning of a liquid film between two bubbles or drops according to Reynolds (1) and Levich (2). A simplified picture of the general scenario in an emulsion is the following. When two... 

The disjoining pressure n is the major thermodynamic stabilizing factor against drop coalescence. A stable equilibrium state of a liquid film can exist only if the following two conditions are satisfied (3) ... 

Fig. 8.13. Schematic representation of conditions for the stability of thin liquid films. Thermal fluctuations of the free liquid-air interface are (a) diminished and (b) amplified, resulting in stable film or decomposition of the film in liquid drops and dry patches, respectively. Left schematic representation of the disjoining pressure middle uniform film and a sketch of a capillary wave with a disjoining pressure indicating the sign and the magnitude right resulting film profile.

The microscopic processes of crude oil displacement by immmis-cible surfactant solutions and, therefore, the efficiency of tertiary oil recovery are determined by static and dynamic wetting as well as by the stability of the liquid film adjacent to the solid surface. All these properties are connected also with the liquid/ liquid interfacial tension and the flow conditions. The two-liquid flow influences dynamic wetting via the shear force exerted on the liquid/liquid interface (1-5), and it affects also the film stability by those forces that act directly at the film of liquid jS/bulk liquid A boundary (6-7). 

Miles, J. W., The Hydrodynamic Stability of a Thin Film of Liquid in Uniform Shearing Motion, J. Fluid Mech., Vol. 8, pp. 593-610 (I960). 

Figure 5. Illustration of the Gihhs-Marangoni effect in a thin liquid film. Reaction of a liquid film to a surface disturbance, (a) Low surfactant concentration yields only low differential tension in film. The thin film is poorly stabilized, (b) Intermediate surfactant concentration yields a strong Gibbs-Marangoni effect which restores the film to its original thickness. The thin film is stabilized, (c) High surfactant concentration (> cmc) yields a differential tension which relaxes too quickly due to diffusion of surfactant. The thinner film is easily ruptured. (From Pugh [109]. Copyright 1996 Elsevier, Amsterdam.)...

Charwat A.F., Kelly R.E. and Gazley C. (1972). The flow and stability of thin liquid films on a rotating disk. J. Fluid Mech., 53, part2,227-255. 

Franke and Pahl [49] have made a study of the effect of inherent liquid drop impact on the stability of horizontal liquid films. Their experimental observations... 

Effect of External Aqueous Phase Composition. The properties of the extracting emulsion may be varied by altering the composition of the external, continuous phase which influences its viscosity and polarity. An increase in viscosity can provide a certain kinetic stability for the emulsion as a/result of the decrease in rate at which the thickness of a liquid film between two surfaces diminishes (i). This factor can play a significant role in reverse emulsions (ie. oil-in-water-in-oil emulsions). 

Several breakdown processes may occur on storage depending on (i) Particle size distribution and density difference between the droplets and the medium, (ii) Magnitude of the attractive versus repulsive forces which determine flocculation, (iii) Solubility of the disperse droplets and the particle size distribution which determine Ostwald ripening, (iv) Stability of the liquid film between the droplets that determines coalescence. (v) Phase inversion. The various breakdown processes are illustrated in the Fig. 3.32. This is followed by a description of each of the breakdown processes and methods that can be applied to prevent such instability. 

Finally, we consider the hydrodynamic theory of thin liquid film rupture. The stability of the liquid films to a great extent is ensured by the property of the adsorbed surfactant to damp the thermally excited fluctuation capillary waves representing peristaltic variations in the film thickness [6]. In addition to the theory of stability of free foam and emulsion films, we consider also the drainage and stability of wetting films, which find application in various coating technologies [7]. 

The authors review the theoretical analysis of the hydrodynamic stability of fluid interfaces under nonequilibrium conditions performed by themselves and their coworkers during the last ten years. They give the basic equations they use as well as the associate boundary conditions and the constraints considered. For a single interface (planar or spherical) these constraints are a Fickean diffusion of a surface-active solute on either side of the interface with a linear or an erfian profile of concentration, sorption processes at the interface, surface chemical reactions and electrical or electrochemical constraints for charged interfaces. General stability criteria are given for each case considered and the predictions obtained are compared with experimental data. The last section is devoted to the stability of thin liquid films (aqueous or lipidic films). 

Evidence for the high stability of the liquid film between emulsion droplets when using HMI was obtained by Exerowa et al. [10] using disjoining pressure measurements. This is illustrated in Figure 15.7, which shows a plot of disjoining pressure versus separation... 

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