Foamed cell volume

Cell si has been characterized by measurements of the cell diameter in one or more of the three mutually perpendicular directions (143) and as a measurement of average cell volume (144,145). Mechanical, optical, and thermal properties of a foam are all dependent upon the cell size. 

CellgeometTy is governed predominantly by the final foam density and the external forces exerted on the cellular stmcture prior to its stabilization in the expanded state. In a foam prepared without such external forces, the cells tend to be spherical or ellipsoidal at gas volumes less than 70—80% of the total volume, and they tend toward the shape of packed regular dodecahedra at greater gas volumes. These shapes have been shown to be consistent with surface chemistry arguments (144,146,147). Photographs of actual foam cells (Fig. 2) show a broad range of variations in shape. 

During synthesis of a polymer, particularly of polyurethane, gaseous products can appear. Therefore, a complete model of the process must take into account (at least in some cases) the possibility of local evaporation and condensation of a solvent or other low-molecular-weight products. Such a complex model is discussed for chemical processing of polyurethane that results in formation of integral foams in a stationary mold.50 In essence, the model is an analysis of the effects of temperature in a closed cell containing a solvent and a monomer. An increase in temperature leads to an increase in pressure which influences the boiling temperature of the solvent and results in an increase in cell volume. The kinetics of polymerization is described by a simple second-order equation. The... 

The volume and shape of Plateau borders depend on the expansion ratio of the foam. In a spherical monodisperse foam with close packing of bubbles all air/liquid interfaces are spherical and the liquid volume which belongs to one cell can be derived from the difference between the volumes of the corresponding polyhedron (for example, a dodecahedron) and the inscribed in it sphere, having in mind the co-ordination number of the foam cell. 

The edges of this dodecahedron sized a - 8.5 cm. When the volume of the rubber balloon at inflation became bigger than the volume of the sphere inscribed in the dodecahedron, the balloon was deformed by the dedecahedron faces and took a shape close to the respective shape of a bubble in a monodisperse dodecahedral foam with a definite expansion ratio. The expansion ratio of the foam was determined by the volume of liquid (surfactant solution or black ink in the presence of sodium dodecylsulphate) poured into the dodecahedron. An electric bulb fixed in the centre of the balloon was used to take pictures of the model of the foam cell obtained. The film shape and the projection of the borders and vertexes on the dodecahedron face are clearly seen in Fig. 1.10. 

Complete information about the liquid distribution between films and Plateau borders is supplied from the data about the border radius curvatures, the film thickness and the films to Plateau borders number ratio in an elementary foam cell. For a polyhedral foam consisting of pentagonal dodecahedron cells the ratio of film liquid volume and border volume can be expressed by the formulae (see Eqs. (4.7) - (4.9))... 

A complete knowledge of the cell structure of a particular polymer would require the size, shape, and location of each cell. Because this is impractical, approximations are employed. Cell size has been characterized by measurements of cell diameter [25] and of average cell volume [26,27]. Mechanical, optical, and thermal foam properties depend on cell size. 

As can be seen from the differential curves of the cell volume fraction distribution (Curves 1 in Fig. 2a, b), the microcells occupy a relatively small volume of the foam 5% for y = 40 kg/m and 11% for y = 500 kg/m. They are, however, the most numerous group of cells (Curves 3,... 

V3 wave propagation velocities wave propagation velocity in gas phase wave propagation velocity in polymer phase packed volume cell volume volume of dry foam effective cell volume volume of gas phase... 

G is the gas-filling (porosity) of the foam, being equal to the ratio of the cell volume to the total material volume. 

The foam cell diameter depends on the number of faces (Fig. 16) and, on the average, is proportional to their volume cubed. The cell size distribution in a cut-off section is never symmetrical, and the maximum value of this distribution will be a diameter larger than the mean cell diameter. It must be noted that the above distribution law depends on the assumed range of cell sizes which manifests itself in the numerical value of the factor k in Eq. (37). 

Fig. 18 allows to calculate by optical bar charts of plastic foams, the morphological term effective specific pore (cell) volume, V ff it can be expressed by as follows... 

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. 

Dispersity. Foam cells usually have the shape of rounded polyhedra. Therefore, it is convenient to choose the radius a of the volume-equivalent bubble, that is, of a spherical bubble of the same volume as the cell as the single linear dimension characterizing the interior scale of foam. Foam consisting of cells of the same size is said to be monodisperse. This kind of foam is extremely rare. Usually, there exists a spectrum of radii ai,..., a in this case, the foam dispersity characterizes the mean linear dimension of the cell [214] ... 

Sometimes, the term osmotic dispersion pressure [378, 383] is used instead of capillary rarefaction. The osmotic pressure is defined as the excessive external pressure that must be applied to the semipermeable membrane interface between foam and fluid to stop the flux of the fluid sucked into the foam from the free volume. In this case, it is assumed that foam cell faces are flat, and therefore, the capillary pressure in foam bubbles is zero. 

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 result of these processes is a gradual decrease in the foam column height (H) in a layer-wise foam collapse or a avalanche -like decay of the foam volume when reaching a critical size of the polyhedral foam cells. 

In foamed products, the blown-cell volume displaces resin to make consumer products less costly and less wasteful when discarded. A foam s shockabsorbing, heat-insulating, and compression properties are key added benefits for certain packaging applications (see Case 13.1). 

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