Foams spherical

Foam is a disperse system, consisting of gas bubWes, separated by liquid layers. Dispersion of gas in liquid in which the gas cortect is low and the thickness of liquid layers is commensurable to gas bubble size is called gas emulsion or spherical foam ( kugelsctiaiim by Manegold l l ). The shape of bubbles in die gas emulsion is spherical (if their size is not very big) and there is no contact between them. 

The spherical foam films can be obtained by blowing a bubble from a vertical capillary tube. The principle of formation of such a bubble is illustrated in Fig. 2.22. A vertical capillary tube is placed in a vessel with the surfactant solution so that its upper orifice is close to the solution surface. When a gas (air) with a definite pressure is introduced into the tube over the solution surface a foam film is formed acquiring the shape of a hemisphere. 

The same principle of formation of a spherical foam film is used in the device (Fig. 2.23) for direct measurement of the film tension y in static [126] and dynamic [127] conditions. The lower part of the capillary is placed in a closed space filled up with a gas, whose pressure can be measured precisely and by means of a special pump can be varied at different rates. The manometer registers the difference with the atmospheric pressure Ap, which is equal to the capillary pressure pa of the spherical foam film... 

Fig. 2.25 illustrates a device for the study of the deformation of a spherical foam film in an electric field, proposed in [130]. The surfactant solution is fed into the glass cell through the tube 2, so that its level reaches the porous plate 4. When air is blown through the tube 3, a foam bubble forms at the capillary orifice. An electric field is created between electrode 1 and 6, which deforms the foam film (bubble). The bubble transforms from spherical to ellipsoidal shape. The value of the deformation A/ depends on the surface tension of the film... 

A spherical foam film can be formed at the top of a foam bubble floating freely at the solution surface during the process of film thinning. Under gravity such a microscopic bubble,... 

However, the VL F value for a spherical foam is substantial and amounts to 48% of the total foam volume for a simple cubic packing and to 26% for a hexagonal close packing. For the latter the foam expansion ratio varies from 2.01 to 3.85 which may introduce large errors into the calculation of the //IIlln value. In a polyhedral foam the liquid volume can be neglected with respect to the foam volume but for the determination of //min( ) more detailed information on the structure of the foam is needed. 

A necessary and sufficient condition for the principal possibility of foam separation is that a substance should be concentrated in the foam, i.e. condition Mrnm > 1 is fulfilled. From Eqs. (10.7) and (10.11) it follows that condition F mm > 1 is valid for a spherical foam when... 

Spherical foam ( Kugel-Schaum ), consisting of gas bubbles separated by thick films of viscous Hquid produced in freshly prepared systems. This may be considered as a temporary dilute dispersion of bubbles in the liquid. 

Laplace pressure than the larger bubbles, but as the gas solubility increases with pressure the gas molecules will difTuse from the smaller to the larger bubbles. This process only occurs with spherical foam bubbles, and may be opposed by the Gibbs elasticity effect. Alternatively, rigid films produced using polymers may resist Ostwald ripening as a result of their high surface viscosity. 

Polydispersity. If a liquid is injected into polydisperse cellular foam (a process which decreases the foam multiplicity) until the foam becomes spherical with the same size distribution of bubbles, then the obtained spherical foam is said to be equivalent. The equivalent foam is characterized by the multiplicity called the minimum multiplicity Kmjn. Obviously, the minimum multiplicity of polydisperse foam is larger than that of monodisperse foam, since in gaps between densely packed spheres of the same largest size, spheres of smaller sizes can be located. Thus the value K a can be used as a quantitative measure of polydispersity [214], While K a = 3.86 for monodisperse foam, for actual polydisperse foam we have 10 to 15 in practice Kma never exceeds 20 [480],... 

On the interface between the foam and the ambient liquid medium, one can set the local multiplicity equal to the multiplicity Kmn of the spherical foam. On the interface between the foam and a porous filter, one can set the value of the volume moisture content provided by this filter [246],... 

Foam consists of gas dispersed in a relatively small amount of liquid Two extremes and a continuum of intermediate stages are possible. An example of one extreme is a freshly poured glass of beer Which besides the carbon dioxide already has a significant amount of liquid present. The foam bubbles have no connection to each other and are ball shaped. Because of its much higher specific weight the liquid drains down between the bubbles wile the gas bubbles concentrate on top and by the time become dry . The two stages are therefore called wet or spherical foam and dry or polyhedral foam, see Fig. 2. 

Figure 2 (a) Wei (spherical) foam, (b) transition state and (c) dry (polyhedral) foam Foams are thermodynamically unstable l The Gibbs equation for a system is given by dG = VdP + SdT + ffdA ( +iMdn,+. ..)... 

The structure of a foam depends on the relative proportions of the gas and liquid. Bubbles are spherical in foams containing a large amount of liquid (>25%). As the percentage of liquid decreases, the bubbles become less spherical. Foams with less than 2% liquid are almost completely polyhedral. For monodispersed foams (composed of identical bubbles), a gas volume fraction of 0.74 is considered to be the limit beyond which the bubbles cease to be spherical. This is because the highest volume fraction that identical... 

Two main types of foams may be distinguished (1) spherical foam ( Kugel Schaum ), consisting of gas bubbles separated by thick films of viscous liquid produced in freshly prepared systems. This may be considered as a temporary dilute dispersion of bubbles in the liquid. (2) Polyhedral gas cells produced on aging thin fiat walls are produced with junction points of the interconnecting channels (plateau borders). Due to the interfacial curvature, the pressure is lower and the film is thicker in the plateau border. A capillary suction effect of the liquid occurs from the centre of the film to its periphery. 

Near the surface, a high (>70 vol.%) gas content structure, polyhedral foam is usually formed. Below the surface is a low (<70 vol.%) gas content structure called a spherical foam (or kugelschaum or gas emulsion). 

Figure 13.7 Stages in a foam lifetime, (a) Spherical foam (independent gets bubbles), (b) gravity drainage period, (c) lamella thinning period and (d) film rupture. Berg (2010). Reproduced with permission from World Scientific...

Figure 13.9 Pressure inside air bubbles in a spherical foam. Adapted from Pugh (1996), with permission from Elsevier...

Explain the difference between a spherical foam and a polyhedral foam. 

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