Three-dimensional foam

The situation becomes more complex in the case of a three-dimensional foam. Since the septa should all be identical, again three should meet at 120° angles to form borders or lines, and four lines should meet at a point, at the tetrahedral angle of 109°28. This was observed to be the case by Matzke [179] in his extensive statistical study of the geometric features of actual foams. 

Shear stress for three-dimensional foams using the Kelvin s tetrakaidecahedron model is given in [29], The value of Young s modulus (modulus of extension) was calculated to be... 

Unfortunately, for three-dimensional foams, no analog of von Neumann s law has been discovered, and theory of coarsening is much less developed. A review of the work on this problem can be found in Glazier and Weaire (1992).-------------------------------... 

Foam is a disperse system with a high surface area, and consequently foams tend to collapse spontaneously. Ordinarily, three-dimensional foams of surfactant solutes persist for a matter of hours in closed vessels. Gas slowly diffuses from the small bubbles to the large ones (since the pressure and hence thermodynamic activity of the gas within the bubbles is inversely proportional to bubble radius). Diffusion of gas leads to a rearrangement of the foam stmctures and this is often sufficient to rupture the thin lamellae in a well-drained film. 

Metals fi om all three groups according to Winand classification of metals [1] can be obtained in the honeycomb-like or the 3D (three dimensional) foam forms under the appropriate electrodeposition conditions. 

Panizza M, Solisio C, Cerisola G (1999) Electrochemical remediation of copper (II) from an industrial effluent Part II. Three-dimensional foam electrode. Resour Conserv Recy 27 299-307... 

With three bubbles, the septa must meet at 120° if the system is to be mechanically stable. A fourth bubble could now be added as shown in Fig. XIV-14, but this would not be stable. The slightest imbalance or disturbance would suffice to move the septa around until an arrangement such as in Fig. XIV-14h resulted. Thus a two-dimensional foam consists of a more or less uniform hexagonal type of network. 

Stabilization of the Cellular State. The increase in surface area corresponding to the formation of many ceUs in the plastic phase is accompanied by an increase in the free energy of the system hence the foamed state is inherently unstable. Methods of stabilizing this foamed state can be classified as chemical, eg, the polymerization of a fluid resin into a three-dimensional thermoset polymer, or physical, eg, the cooling of an expanded thermoplastic polymer to a temperature below its second-order transition temperature or its crystalline melting point to prevent polymer flow. 

Flexible foams are three-dimensional agglomerations of gas bubbles separated from each other by thin sections of polyurethanes and polyureas. The microstmetures observed in TDI- and MDI-based flexible foams are different. In TDI foams monodentate urea segments form after 40% conversion, foUowed by a bidentate urea phase, which is insoluble in the soft segment. As the foam cures, annealing of the precipitated discontinuous urea phase... 

Polyurethane foams are generally made using a polyalcohol rather than a diol as the monomer, so the polymer has a high amount of three-dimensional cross-linking. The result is a rigid but very light foam suitable for use as thermal insulation in building construction and portable ice chests. 

The structure of whipped cream is quite complex. A coating of milk protein surrounds small globules of milk fat containing both solid and liquid fats. These globules stack into chains and nets around air bubbles. The air bubbles are also formed from the milk proteins, which create a thin membrane around the air pockets. The three-dimensional network of joined fat globules and protein films stabilizes the foam, keeping the whipped cream stiff. 

When performing catalytic reactions or reactions with immobilized reactants, a bed or support has to be fiUed into a tube or capillary. The fiUing may be a bed of powder, a bed of granules or a three-dimensional material network (e.g. a polymerized foam). By special choice of the filling, e.g. very regularly sized particles, it is attempted to improve the flow characteristics. 

To be semisolid, a system must have a three-dimensional structure that is sufficient to impart solidlike character to the undistributed system that is easily broken down and realigned under an applied force. The semisolid systems used pharmaceutically include ointments and solidified w/o emulsion variants thereof, pastes, o/w creams with solidified internal phases, o/w creams with fluid internal phases, gels, and rigid foams. The natures of the underlying structures differ remarkably across all these systems, but all share the property that their structures are easily broken down, rearranged, and reformed. Only to the extent that one understands the structural sources of these systems does one understand them at all. 

Successful development of such systems will lead to foamed materials having useful stress-absorbing characteristics in addition to controlled physics properties. Although our work in this area is currently in a very early stage, prototype materials have been successfully synthesized and assessed structurally using three-dimensional (3D) X-ray microtomography. The technique offers a unique insight into the internal microstructure of cellular materials (see Fig. 3). The diameter of the mainly open cell pores varies from approximately 100 to 250 pm (the resolution of the instrument is 5 pm), with cell walls of variable thickness. 

Self contained dual agent systems, (foam/water and dry chemical), are provided for manual fire fighting efforts against three dimensional pressure leaks and large diameter pool fires. The design affords fast fire knockdown, extinguishment and sealant against re-flash. A skid... 

Three-dimensional electrode materials that fit well into parallel-plate [75,91, 92,93] reactors are (i) reticulated metals [75,91-93], (ii) metalized plastics (metalization of polyurethane foams) [94] and (iii) carbon [95]. 

Three-dimensional Cu or Ni foam and reticulated carbon (for the recovery of noble metals) cathodes are used. Between each pair of cathodes an inert,... 

Dong, X., et al., Synthesis of graphene-carbon nanotube hybrid foam and its use as a novel three-dimensional electrode for electrochemical sensing. Journal of Materials Chemistry,... 

In order to extend the effective electrode area in principle three-dimensional electrodes are possible, for example, by using a packed particle bed, a sintered or foamed metal, or a graphite fiber felt. But the depth of the working electrode volume usually is only small (it is dependent on the ratio of the electrode and electrolyte conductivity, for example, [45]). 

---