Real foam

A real foam has further degrees of freedom available for estabHshing local mechanical equiHbrium the films and Plateau borders may curve. In fact, curvature can be readily seen in the borders of Figure 1. In order to maintain such curvature, there must be a pressure difference between adjacent bubbles given by Laplace s law according to the surface free energy of the film and the principle radii of curvature of the film AP = ) Note that the... 

Real foams are well described by this formula. Note that foaming offers a vast range of modulus p/Ps can be varied from 0.5 to 0.005, a factor of 10, by processing, allowing E to be varied over a factor of 10 . ... 

The probability of formation of polyhedra (cells) of a definite shape was studied with the methods of statistical mechanics applying two variants of calculations [52], These theoretical considerations were done for a monolayer of a polydisperse foam. Both variants gave a probability curve the maximum of which was at 6 side faces of the polyhedron. The theoretical dependence fits well with the curve of probability for distribution of cell faces in a real foam monolayer [53],... 

The geometry of three-dimensional polyhedral foam is more complex. Plateau experimented with soap bubbles and found that in equilibrium polyhedral structure (first law of Plateau) at each vertex of the polyhedron (cell) six faces (films) and four Plateau borders meet. The angle between borders equals lOO (second law of Plateau). This has been proved by Matzke who studied real foams [61-63], Plateau borders meet at the so-called vertex. Other configurations of the borders are unstable. ... 

Dispersity of gas emulsions and polyhedral foams is a very important parameter which determines many of their properties and processes occurring in them (diffusion transfer, drainage, etc.) and, therefore, their technological characteristics and areas of application. The kinetics of changes in dispersity indicates the rate of foam inner destruction resulting from coalescence and diffusion transfer. In real foams bubble size varies in a wide range (from micrometers to centimetres). Only by means of special methods it is possible to obtain foam in which bubble size varies in a narrow interval, i.e. foam that can be regarded as monodisperse. 

The borders in a real foam form a network that is represented as a system of independent capillaries (Plateau borders) along the whole foam column that follow the direction of the shortest path flow. It is assumed that the liquid flow is in the direction of gravitational field. 

In contrast to the behaviour of free foam films which has been studied in details, the process of liquid outflow from foam films constituting the real foam is still largely overlooked. The reason is that film thinning in a real foam (compared to thinning of free foam films) is a very complex process which is related to the non-homogeneity of film thickness, to the presence of films of different size and orientation, as well as to technical difficulties, etc. 

Thus, it might be assumed that stabilisation of foam films will depend also on the action of other positive components of disjoining pressure. For example, equilibrium films are obtained from concentrated butyric acid solutions and, therefore, in this concentration range the foam lifetime also increases. On the basis of these concepts it should be expected that a foam consisting of films with equilibrium thicknesses at a constant capillary pressure pa = n, should be infinitely stable. In fact, a real foam decays both in bulk and as a disperse system, due to gas diffusion transfer and certain disturbances (shift of films and borders on structural rearrangement as a result of the collective effects , etc.)... 

It should also be noted that in real foams as a result of reduced pressure in borders pa 1 kPa) films become relatively thin, while the electrostatic component (IX,/ - p ) strongly decreases. Furthermore, it has been shown [37] that with the increase in surfactant concentration while keeping the ionic strength constant, the transition from unstable to stable... 

As already mentioned the real foam is not a simple sum of films. Its behaviour and response to different disturbances is much more complex than the behaviour of individual foam films. This is so because the films in the foam have different size and shape, and the kinetics of establishing film equilibrium is more complicated since the process of foam drainage exerts significant influence. 

Let us consider the simplest model of a real foam built up of different by size bubbles but having equilibrium films. If the diffusion expansion of bubbles runs slowly, then the real (aggregative) stability with respect to coalescence will be preserved but the column height and dispersity will decrease as a result of gas diffusion transfer between bubbles in the foam and from the upper bubbles to the surrounding medium (if the foam is open). 

A qualitative evidence of the above are the data reported in [52]. It has been established that there is a correlation between the calculated rate of internal diffusion foam collapse and the experimentally determined rate. To obtain a stable foam from poor surfactants (alcohols, acids, etc.) under these conditions is hardly possible because of either insufficient dynamic elasticity of foam films or the lack of equilibrium elasticity (for films from insoluble surfactants). Furthermore, the n barrier for films from acid or alcohol solutions is low and the typical capillary pressures for a real foam are sufficient to induce disturbance of the film equilibrium and, respectively, foam collapse. 

It is believed [10] that for real foams and emulsions the value of t0 can be expressed with the general relation... 

The products thereby obtained are anionic silane surfactants exhibiting excellent surfactant properties dependent on the ammonium counter ion. Some specimen are real foam boosters, too. For example an 1 wt. % aqueous solution of isopropylammonium sulfatohexyl trimetyl silane shows a surface tension of 21 mN m and a spreading ability of 65 mm. As being familiar for the nonionics the aqueous solution of... 

The films and Plateau borders of real foams have finite thicknesses. However, this... 

Nevertheless, some of the predictions of simple regular foam models are relevant to real foams. One such property is the linear modulus Go, which is the slope of the stress-strain curve at zero strain. From Eq. (9-57a), we obtain... 

For a few decades now cellular and porous systems have been classified in morphological terms by simulating the real systems by one or another imaginary, and always simplified, geometrical or stereometrical scheme using an artificially ordered-structure model. Such classifications have always been based on the concept that in any cellular or porous system it is possible to isolate a structural element (cell or pore). However, the diversity of pore and cell types even in small-sized real foamed systems does, in most cases, not permit a definition by only one single geometrical structural parameter, as for other types of solids (type and volume of elementary cell, interplanar or interatomic distances, etc.)... 

Theoretical premises for the determination of the physicomechanical properties by the acoustic pulse method were derived from the following three models of real foam structures... 

As with cell shapes of a real foam, cell sizes in this material can also be characterized only by nominal (effective) values. The actual effective values depend, first, on the observation method (whether direct — macroscopic, or indirect — adsorption, volumetric, picnometric, etc.). Secondly, they depend on the particular simplified model of the structure and cell shape and thirdly on the method of processing the measured data. 

However, a real foam structure is composed of cells having differing shapes, sizes and volumes. In studying the properties of foamed polymers as well as in developing and elaborating preparative processes, it is necessary to find out cell size, shape and volume distribution. The methods for calculating the respective distribution functions will be discussed in Sect. 9.2, 9.3 here, we only note that the cell size distribution function is a most comprehensive and valuable characteristic of plastic foam structures. 

Aleksandrova et al. [197] have continued to report progress in studying the reactions of diisocyanates in systems simulating real foam systems. 

For real foams, the value of can be expressed by the general expression,... 

Real foams are typically polydisperse2, which results in changes in the shape of foam cells. The Plateau rules (three films form a border four borders meet at a node) remain valid in all cases. The degree of dispersion in foam may be characterized by its specific surface area. One, however, usually measures some mean values of foam cell geometrical parameters, such as the average number of cells per unit volume, n, or the mean equivalent radius,7,... 

The formation of ordered microstructure in thin liquid films offers a new mechanism for the stabilization of foams. As a proof of microstructuring in real foams, Figure 17 shows a photograph of an aqueous foam system stabilized because of the stratification in the foam bubble lamellae. The practical importance of the film microstructuring is that the lifetimes of foams with stratifying films are much longer. 

According to the adsorption theory (97), the solid particles are the real foam breakers in the mixed antifoams, and the role of the oil is that it shields the particles from adsorption inside the solution. When the particle, which is shielded by the oil, enters the foam surface, the oil spreads and releases the particles. The problems with this mechanism are similar to those with the adsorption with solid particles alone (88). Moreover,... 

Foam is a disperse system in which the dispersed phase is a gas (most commonly air) and the dispersion medium is a liquid (for aqueous foams, it is water). Foam structure and foam properties have been a subject of a number of comprehensive reviews [6, 17, 18]. From the viewpoint of practical applications, aqueous foams can be, provisionally, divided into two big classes dynamic (bubble) foams which are stable only when gas is constantly being dispersed in the liquid 2) medium and high-expansion foams capable of maintaining the volume during several hours or even days. In general, the basic surface science rules are established in foam models foam films, monodisperse foams in which the dispersed phase is in the form of spheres (bubble foams) or polyhedral (high-expansion foams). Meanwhile, real foams are considerably different from these models. First of all, the main foam structure parameters (dispersity, expansion, foam film thickness, pressure in the Plateau-Gibbs boarders) depend... 

A number of fundamental works are dedicated to the investigation of foam stability [6, 17] but the interest of the investigators in this problem is persistent, which is evidenced by recent review papers, e.g. [20]. In this section data are given which can be of interest for the practical application of foams. First of all, several processes take place simultaneously in real foams, which lead to foam collapse. The main processes are redistribution of the disperse medium in differently high foam column layers and the change of the mean radius of the foam cells [12]. 

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