Horizontal Foam Films

Let us consider a horizontal foam film between two bubbles or an emulsion film between two drops of another immiscible liquid. We neglect gravitation and assume an axisymmetric symmetry. When two bubbles or drops approach each other, the liquid in between is squeezed out. Thus, drainage and hydrodynamic forces are 

For fluid interfaces, it is appropriate to replace the force in Eq. (6.42) by the pressure AP = Jtif  

rf is the radius of the film. We replaced the distance D, conveniently used to describe the separation between rigid objects, with the film thickness h. The pressure AP = Pc—n contains two contributions the capillary pressure. Pc = 2YL/rb. caused by the curvature of the bubble and the disjoining pressure caused by interfacial forces, n(b). 

For a bubble interacting with a planar solid surface, Scheludko replaced the noslip boundary conditions used to derive Eq. (6.42) with a boundary condition for an ideal mobile surface. As a result, he obtained a higher drainage rate [686, 759]  

One might assume that for a foam film we should apply the mobile boundary condition to both surfaces. In that case, any film would immediately rupture. In fact, however, as discussed in Section 6.5 gradients in the surface concentration of surfactants usually lead to an effective no-slip boundary condition [714,721,724,760). 

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The measuring cell of Scheludko and Exerowa [e.g. 15-20] has proven to be a suitable and reliable tool for formation of microscopic horizontal foam films. It is presented in Fig. 2.2, variants A, B and C. The foam film c is formed in the middle of a biconcave drop b, situated in a glass tube a of radius R, by withdrawing liquid from it (variants A and B) and in the hole of porous plate g (variant C). Photographs of formation of black foam film via black spots taken under a microscope are presented in Fig. 2.3. 

The measuring cells for the study of microscopic horizontal foam films (especially variant A, Fig. 2.2 and variant D, Fig. 2.4) have been widely used in [e.g. 26-47]. 

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

Elasticity can be measured either with macroscopic vertical or horizontal foam films [94-97] or with individual foam bubbles [98]. 

The question of the ( -potential value at the electrolyte solution/air interface in the absence of a surfactant in the solution is very important. It can be considered a priori that it is not possible to obtain a foam film without a surfactant. In the consideration of the kinetics of thinning of microscopic horizontal foam films (Section 3.2) a necessary condition, according to Reynolds relation, is the adsorption of a surfactant at both film surfaces. A unique experiment has been performed [186] in which an equilibrium microscopic horizontal foam film (r = 100 pm) was obtained under very special conditions. A quartz measuring cell was employed. The solutions were prepared in quartz vessels which were purified from surface impurities by a specially developed technique. The strong effect of the surfactant on the rate of thinning and the initial film thickness permitted to control the solution purity with respect to surfactant traces. Hence, an equilibrium thick film with initial thickness of about 120 nm was produced (in the ideal case such a film should be obtained right away). Due to the small film size it was possible to produce thick (100 - 80 nm) equilibrium films without a surfactant. In many cases it ruptured when both surfaces of the biconcave drop contacted. Only very precise procedure led to formation of an equilibrium film. 

We will consider only some more interesting aspects of stratification of microscopic horizontal foam films, giving an example of the role of stratified films in foam stability (see Chapter 7). 

Deryaguin and Titijevskaya [37] measured the isotherms of disjoining pressure of microscopic foam films (common thin films) in a narrow range of pressures. At equilibrium, the capillary pressure in the flat horizontal foam film is equal to the disjoining pressure n in it,... 

Film Thickness. The measurement of the thickness of the horizontal foam films formed from DMS show that in the sodium chloride concentration region, 4 X 10 4-10 2 mole/dm3, black films are formed with a... 

Figure 9 Image of a horizontal foam film in the concentration range of precipitation PAMPS/DTAB solutions. The size of the film is about 1 mm...

Figure 14. Stratification of horizontal foam film from 0.1 mol/L sodium dodecyl sulfate surfactant solution.

Figure 20. Effect of temperature on the drainage time of horizontal foam films from ethoxylated alcohols 4 wt% Enordet AE1215-30 (m) and 2 wt% Enordet AE1215-9.4 (A), with 12-15 C-atom chains and 30 and 9.4 ethoxy groups, respectively (54). Film radius was 0.3 mm.

Most quantitative studies on foams have been carried out using foam films. As discussed above, microscopic horizontal films were studied by Scheludko and coworkers [2-4]. A schematic representation of the set-up used to study horizontal foam films is given in Figure 8.2. The foam thickness was determined by interferometry. Studies on vertical films were carried out by Mysels and collaborators... 

Dynamics and stability of thin foam films have been and continue to be an object of intensive research [e.g. 28-35]. Model studies with vertical large macroscopic films with linear sizes of the order of centimeters as well as with horizontal circular microscopic films with radius of the order of millimeters were performed. The kinetics of thinning of vertical macroscopic films in described in detail in [33]. Some of the results presenting an interpretation of the dynamic properties of films and foam are considered in Chapter 7. Microscopic foam films offer certain advantages with respect to treatment of stability of foams and foam films, since the systems studied behave under strictly defined conditions. 

Under certain conditions aqueous electrolyte solutions form foam films of equilibrium thickness. For a microscopic horizontal film this thickness is determined by the positive component of disjoining pressure (FU) which depends on the potential of the diffuse electric layer at the foam film/air(gas) interface. 

The most suitable technique ensuring the formation of black films is the one that operates with horizontal microscopic films. It allows to work with the lowest possible surfactant concentration and to study in detail the very interesting stage of appearance of black films, including of foam bilayers (NBF). The microscopic foam films provide information about formation and stability of black foam films. On the other hand, as it will be demostrated, the microscopic film is a suitable model to measure several quantitative parameters characterising black film behaviour. 

Additional data about the structure of black films are obtained by X-ray diffraction method. The first steps [336,338] have been performed with vertical foam films in a frame in a horizontal scanning diffractometer. Black films from decyltrimethyl ammonium decyl sulphate and NaBr solutions have been studied. The film thickness was calculated using a model of the mean electron density projection on the film normal. However, there was no indication whether the films were CBF or NBF. Platikanov et al. [339,340] used a new device for investigation of a horizontal black films from aqueous NaDoS solution (see Section 2.2.6). They found essentially different X-ray diffraction traces for the three types of black films CBF, NBF and stratified black films. This indicates their different structure. Precise X-ray reflectivity measurements with CBF and NBF films from NaDoS and NaCl aqueous solutions [341-343] provided more details about their structure. The data obtained for the thicknesses of the respective layers which detail the film structure are given below... 

The model approach implies bearing in mind that the foam is not a sum of individual films and the results obtained on model films cannot be directly applied to foams. Moreover, the different types of foam films (macroscopic, microscopic, horizontal and vertical, as well as foam bubbles) yield very different information about foam stability that has to be considered when the respective foam properties are compared. 

Black Liquor from Soda-pulp Mills.—One ton of pulp will produce about 3,300 gal. of 5 deg. liquor, and this is concentrated to 35 deg. in multiple-effect evaporators of the horizontal and film type, with a capacity of from 2 to 2K gal. per square foot, according to the steam pressure, which will be from 10 to 25 lb., with a vacuum of from 27 to 28 in. Special construction and separators are necessary on account of the excessive foaming. Evaporators must have cast-iron or steel shells with wrought-iron or steel tubes, as the liquors are strongly alkaline. 

Most quantitative studies on foams have been carried out using foam films. As discussed above, microscopic horizontal films were studied by Scheludko and... 

At high surfactant concentrations (i.e., much above the CMC), thin foam films were observed (48—53) to become thinner in a stepwise fashion that is, thinning foam films formed from micellar surfactant solutions exhibit a number of metastable states before attaining an equilibrium film thickness. This process can be followed in Figure 13, which shows a photocurrent (film thickness)—time interferogram of a horizontal flat film... 

FIGURE 4.36 Plot of disjoining pressure, II, vs. film thickness, h comparison of experimental data for a foam film from Ref. [461] (thin-film pressure balance) with the theoretical curve (the solid line) calculated by means of Equation 4.230. The film is formed from 200 mM aqueous solution of the nonionic surfactant Tween 20. The volume fraction of the micelles (cj) = 0.334) is determined from the film contact angle the micelle diameter id = 1.2 nm) is determined by dynamic light scattering. The points on the horizontal axis denote the respective values of h for the stratification steps measured by a thin-film pressure balance. 

Most quantitative studies on film drainage have been carried out using small, horizontal films, as described in detail by Scheludko and co-workers [2-4]. Figure 8.2 illustrates the measuring cell for studying microscopic foam films. 

A related phenomenon to asymmetric drainage in horizontal cylindrical foam films is that of the so-called marginal regeneration. This process occurs in vertical foam films subject to both capillary suction from the Plateau borders and gravity. It is manifest as an apparent turbulent motion on the margin of foam films where thin elements of film are drawn out of the Plateau border and thick elements are sucked... 

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