Structural Parameters of Foams

The polyhedral foam consists of gas bubbles with a polyhedral shape, the faces of which are flat or sHghtly bent liquid films, the edges are the plateau borders, and the edge crosspoints are the vortexes. Several techniques can be applied to obtain the analytical dependence of these characteristics and the structural parameters of 

The foam expansion ratio can be characterised by the liquid volume fraction in the foam, which is the sum of the volume fractions of the films, plateau borders and vertexes. Alternatively, the foam density can be used as a measure of the foam expansion ratio. The reduced pressure in the foam plateau border can be measured using a capillary manometer [4], while the bubble size and shape distribution in a foam can be determined by microphotography of the foam. Information about the liquid distribution between films and plateau borders is obtained from the data on the border radius of curvature, the film thickness, and the film-to-plateau border number ratio obtained in an elementary foam cell. 

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Usually the estimation of structural parameters of foam formed by dispersion through gauzes is done on the basis of liquid and gas material balance [36,38]. Such calculations do not account for the properties of foaming solution and capillary pressures during the process of foam formation. That is why they cannot give reliable results. 

The theory of luminous flux extinction by a foam, introduced by Krotov and Kruglyakov [63] (see Section 8.4.), gives the relation between optical density and structural parameters of foam (for border foam )... 

Fig. 3. Relationship between moisture sorption and structural parameters of foamed polymers, see Eq. (14) (1) rigid polyurethane foam grade PPU-3 (2) unfoamed polyurethane, the same grade...

The direct measurement of the various important parameters of foam films (thickness, capillary pressure, contact angles, etc.) makes it possible to derive information about the thermodynamic and kinetic properties of films (disjoining pressure isotherms, potential of the diffuse electric layer, molecular characteristics of foam bilayer, such as binding energy of molecules, linear tension, etc.). Along with it certain techniques employed to reveal foam film structure, being of particular importance for black foam films, are also considered here. These are FT-IR Spectroscopy, Fluorescence Recovery after Photobleaching (FRAP), X-ray reflectivity, measurement of the lateral electrical conductivity, measurement of foam film permeability, etc. 

Relation between the Geometrical (Structural) Parameters of a Foam and its Physicochemical Characteristics... 

In order to compare the structural parameters of the foam model studied by Kruglyakov et al. [18] with the respective parameters of a real polydisperse foam (individual bubbles of different degree of polyherdisity) Kachalova et. al. [19] performed measurements of the average border radius of curvature of foams with variable expansion ratio. The foam studied, generated by the set-up shown in Fig. 1.4, was obtained from a nonionic surfactant solution of Triton-X-100 (a commercial product) to which NaCl (0.4 mol dm 3) was added. The expansion ratio was determined conductometrically with correction of the change in electrolyte concentration due to the internal foam destruction. The electrolyte concentration... 

This constant wo characterises the initial volumetric flow rate referring to a unit cross-sectional foam area. A rigorous analytical dependence of the constant wq on the structural parameters of a low expansion ratio foam and the properties of the solution (dp IdH, H, r, R, n, a) has not been derived, so that this constant cannot be calculated. 

The relation between the structural parameters of low expansion ratio foams is given by Eqs. (4.24) and (4.26)... 

Equations connecting the accumulation ratio to parameters of foam structure (dispersity, expansion ratio, radius of curvature of Plateau borders) can be derived from the balance equations of the surfactant and the liquid phase, and the data on foam structure. 

As mentioned in Chapter 5, the analytical dependence of the initial volumetric rate of drainage w0 on the structural parameters of a foam is unknown. Therefore, a semi-quantitative estimation of the effect of both the structural parameters of a foam and the properties of a foaming solution can be done using the Eq. (5.60) of the flow rate in a homogeneous polyhedral border foam [59]. 

A detail analysis of Eqs. (10.21) and (10.22) and identification of the relationship between the characteristics of foam separation and the structural parameters of the foam are possible on the basis of the material balance equations for the substance in the foam and in the solution, including those taking into account the foam breakdown [51]. The material balance of a substance participating in foam separation is given by... 

For the process of foam accumulation involving capillary drying, an equation relating the water flooding coefficient to the structural parameters of the foam can be derived [67]. 

Relation between the geometrical (structural) parameters of a foam 345... 

Physicochemical studies of the regularities of foaming and formation of cellular structure in foams, studies of rheological and thermodynamic parameters of foaming and of the mechanism of interactions between components, etc. 

A further elucidation of tte nature of foamed plastics requires an even more extensive use of methods of physics and physical chemistry of polymers. In this way, a quantitative estimation of the oligomeric specificity of foam morphology will be possibte and especially the relationship between chemical and supetmolecular organizations of walls and struts in gas-structure dements and the morphological parameters of foams could be established. 

This survey deals with the fundamental morphological parameters of foamed polymers including size, shape and number of cells, closeness of cells, cellular structure anisotropy, cell size distribution, surface area etc. The methods of measurement and calculation of these parameters are discussed. Attempts are made to evaluate the effect and the contribution of each of these parameters to the main physical properties of foamed polymers namely apparent density, strength and thermoconductivity. The cellular structure of foamed polymers is considered as a particular case of porous statistical systems. Future trends and tasks in the study of the morphology and cellular structure-properties relations are discussed. 

A promising method of controlling and evaluating the structural parameters of plastic foams is the acoustic (ultrasonic) pulse method This method is based on the propagation of elastic waves in a porous medium depending on shape, distribution and volumetric content of the GSE. 

A preliminary stndy on the viscoelastic behaviour of polyolefin foam sheets with different chemical (PE and PP) and cellular structure by DMA, in the low freqnency and low compression ranges, is presented. DSC and SEM are also used to determine the morphological parameters of the samples. A connection between the morphological properties (apparent degree of crystallinity), type of cellular structure, homogeneity, cell size and shape, cell wall thickness) and the viscoelastic behavionr, a basic key for the development of mechanical and insnlating applications, has been established. 9 refs. 

The method of structural foam moulding permits the manufacture of foams with a compact skin and a cellular core. The properties of such mouldings depend, among other parameters, on the structure of the foam. This article reports on a study of the influence of density, specimen thickness, orientation and ambient temp, on mechanical properties and chemical resistance of injection monlded structural foams made from PP. Results are discussed with reference to relationships between structnre and properties. 5 refs. 

Along with all the advantages, the refined blend structure is more sensitive towards the foaming parameters as foaming temperature and time. The higher number of cells and the elastomeric PB block promote rapid cell coalescence and collapse at elevated foaming temperatures and times. These phenomena can result in an increase in foam density and open-celled or inhomogeneous foam structures. 

Combined measurement techniques were successfully applied in the study of surface forces in microscopic foam films such as study of longitudinal electrical condictivity, study of black films with X-rays forced rupture of films by a-particles irradiation, etc. They permit to find the relation between surface forces and parameters of film structure. It is important also surface forces measurements to be performed at controlled state of the adsorption layer. As far as surface forces act normally to film surface, it is interesting to understand the role of... 

Optical techniques for measurement of foam film thickness involve different models and plotting the optical parameters it is possible to find the real film structure. In this sense it is interesting to compare h(Cei) dependence of lyso PC films in the presence of CaCl2 depicted by two independent optical techniques microinteferometric (Fig. 3.50) and FT-IR spectroscopy [193,292]. In this case the thickness of the aqueous core d2 is determined from... 

A semi-quantitative estimation of the influence of the structural parameters and physicochemical properties of the foaming solution on the initial drainage rate can be obtained from the equation describing the drainage in a homogenous polyhedral foam, the liquid of which flows out only through the borders [7]... 

The critical analysis of the results on foam rheology, proposed by Heller and Kuntamukkula [16], has shown that in most of the experiments the structural viscosity depends on the geometrical parameters of the device used to study foam flow. This means that incorrect data about flow regime and boundary conditions, created at the tube and capillary walls, etc., are introduced in the calculation of viscosity (slip or zero flow rate). Most unclear remains the problem of the effect of the kind of surfactant and its surface properties on foam viscosity and on the regime of foam flow (cross section rate profile and condition of inhibition of motion at the wall surface). 

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