Structure of foams

Let us discuss the structure of a metastable polyhedral foam in a bit more detail. In pioneering experimental studies Joseph Plateau5 established some simple rules in the second half of the 19th century. Three of these 

When the number and volume of the polyhedral compartments are given, the optimal structure of the foam is the one that creates the smallest total film area. This condition constitutes a formidable but straightforward mathematical optimization problem. Solution as an average, the polyhedra consist of 13.4 sides. Experimentally it was indeed found that the polyhedra most commonly found in foams have 14 sides, followed by 12 sides as a second choice. 

FIC U RE 1.1 Aged polydisperse foam with dry polyhedral foam (polyederschaum) at top of column and spherical bubbles (kugelschaum) at bottom of column. 

Plateau borders form a hexagonal cross section at plane of observation 

Kelvin bubble is bisected to form a bubble that can still tessellate despite touching the wall of the retaining vessel 

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A cellular or porous structure of foam plastics is produced with gas- or foam-forming agents. The quality of the resulting material depends on choosing the right agent,... 

The first area covers low volumetric flow rates, and entrance pressures below Pcr. This sector of two-phase flow in the molding machine is characterized by a complex non-linear dependence of reduced pressure on reduced volumetric flow rate. The structure of foam plastics obtained in this way was called shell structure by the authors in [20, 21] — the extrudate contains huge shell bubbles which are comparable to its section. As CBA concentration increases, or medium volumetric flow rate is increased at low CBA concentration, small bubbles materialize in the melt around the shell bubbles, and the structure becomes shell-bubble . Increase of the volumetric flow rate and the concentration of flowing agent neutralizes the difference in bubble size their lateral dimensions become smaller than their longitudinal ones. 

Fig. 12 Cell structure of foamed TPVs formed by various blowing agents at 1 wt% concentration at 160°C...

Chapter 1 Formation and Structure of Foams. Pressure in the Liquid l... 

This classification of foamed materials only formally resembles the classification based on the cell concept proposed by A. A. Berlin more than a quarter of a century ago it is based on quite different morphological notions about the spatial structure of foamed polymers. 

Nevertheless, in the field of physical chemistry of foamed polymers the transition from quantity to quality has not yet occurred practically no generalizations, even of semi-empirical nature, are available which relate the kinetics of moisture and water absorption to the main morphological parameters of polymeric foams (specific gravity, portion of open ceUs, etc.) Very little is known about molecular mechanisms of vapor and moisture transfer taking into account the chemical and physical structure of foams. 

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. 

At present, there are at least two approaches to the investigation of the cellular structure of foamed polymers. In the first one, which may formally be called a graphical approach, attempts are made to draw conclusions on the macroscopic properties of foamed polymers from morphological parameters such as the geometry and stereometry of cells of various sizes, shapes and types. The second approach, which may be referred to as physicochemical, attempts to explain and predict polymer morphology from the data on the chemical composition of the polymer matrix and the mechanisms of foaming... 

Both continuous and batch i ocesses can be used for foamed-composite preparation, depending upon the jn oducts desired and market demand. The structure of foamed composites can be classified as shown in Figure 52, that is, imidirectional (or monoaxial), two-dimensional, and three-dimensional reinforcements can also be employed. In addition, combinations of these structures can be used (2). 

Figure 52. Schematic diagram of reinforced structure of foamed composites. (1) Unidirectional, (2) Continuous-strand mat, (3) Chopped-strand mat, (4) Uni-directional skin layer, (5) Three-dimensional.

A complicated many-layer structure of foam cells is formed when gas bubbles are sparged into solutions of surfactants. According to [429], each bubble has a two-sided envelope which is a layer of the solvent containing hydrophilic polar parts of surfactant molecules (see Figure 7.2). Nonpolar hydrophobic parts of molecules on the inner surface of the envelope are oriented toward the bubble, and on the outer surface, outward the envelope. Between two cells, each of which is a capsule with envelope, there is a lamella, that is, an interlayer of a complicated structure. In the middle of the lamella, there is a liquid layer that is a continuous phase. On each of two surfaces of this layer, there is a monolayer of the surfactant. The hydrophobic parts ( tails ) of surfactants molecules in each monolayer and the tails of the envelope form two direct plate micellae [413], which separate the envelope and the continuous liquid film at the center. Thus, gas bubbles in foam are separated at least by five distinct layers. The multilayer structure of a foam lamella is well seen in photographs (e.g., see [429], p. 54). This fact is also confirmed by the ladder-type shape of the disjoining pressure... 

From the above remarks follow applications of investigation of the states of minimal surfaces and possible changes in their shapes (catastrophes) on altering some control parameters. For example, foams may be formed at a phase boundary, thus determining the rate and character of reagent transport at the interface. Some small marine animals, such a Radiolaria, are built of skeletons covered with membranes. Thus, the structure of foam at the phase boundary or the shape of a radiolarian result from the same condition of a minimal surface area of the foam stretched at the interface or the membrane stretched on the skeleton of a radiolarian. 

Mechanisms of Single-Foam Film Stability. Soap bubbles and soap films have been the focus of scientific interest since the days of Hooke and Newton (2—9). The stability and structure of foams are determined primarily by the relative rate of coalescence of the dispersed gas bubbles (10). The process of coalescence in foams is controlled by the thinning and rupture of the foam films separating the air bubbles. Experimental observations suggest that the lifetime (stability) of foam films is determined primarily by the thinning time rather than by the rupture time. Hence, if the approaching bubbles have equal size, the process of coalescence can be split into three stages ... 

Foams play an important role in several fields of human Hfe in food technology, medicine, cosmetics, oceanography, environmental technology, fire extinguishing technology, etc. Therefore, foams were investigated very early by natural scientists. Foam films and Plateau borders were characterized, and the formation and structure of foams were described. The mechanical, optical and electrical properties of foams and theories for foam stability were presented [1]. 

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