About foam

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overview

… a foam is a substance that is formed by trapping pockets of gas in a liquid or solid …

… in most foams, the volume of gas is large …

… with thin films of liquid or solid separating the regions of gas …

… foams are examples of dispersed media …

… in general, gas is present in large amount so it will be divided into gas bubbles of many different sizes (the material is polydisperse) …

open-cell foam + closed-cell foam

… an important division of solid foams is into closed-cell foams and open-cell foams …

… in a closed-cell foam, the gas forms discrete pockets, each completely surrounded by the solid material …

… in an open-cell foam, the gas pockets connect with each other …

… a bath sponge is an example of an open-cell foam: water can easily flow through the entire structure, displacing the air …

… a camping mat is an example of a closed-cell foam: the gas pockets are sealed from each other, and so the mat cannot soak up water …

foam as multiscale system

… a foam is in many cases a multiscale system …

… one scale is the bubble …

… material foams are typically disordered and have a variety of bubble sizes …

… at larger sizes, the study of idealized foams is closely linked to the mathematical problems of minimal surfaces and three-dimensional tessellations, also called honeycombs …

… the weaire-phelan structure is believed to be the best possible (optimal) unit cell of a perfectly ordered foam[citation needed] …

… while plateau's laws describe how soap-films form structures in foams …

… at lower scale than the bubble is the thickness of the film for metastable foams …

… which can be considered as a network of interconnected films called lamellae …

… ideally, the lamellae are connected in triads and radiate 120° outward from the connection points, known as plateau borders …

… an even lower scale is the liquid-air interface at the surface of the film. most of the time this interface is stabilized by a layer of amphiphilic structure …

… often made of surfactants, particles (pickering emulsion), or more complex associations …

formation

… to create foam, work (w) is needed to increase the surface area (δa) …

… several conditions are needed to produce foam … there must be …

  1. mechanical work …

  2. surface active components (surfactants) that reduce the surface tension, and …

  3. the formation of foam faster than its breakdown …

stabilisation

… stabilization of foam is caused by …

  1. van der waals forces between the molecules in the foam …

  2. electrical double layers created by dipolar surfactants, and …

  3. the marangoni effect, which acts as a restoring force to the lamellae …

… the marangoni effect is dependent on the liquid that is foaming usually not being pure. generally, there are surfactants in the solution which will decrease the surface tension in the liquid

foam applications

… liquid foams can be used in fire retardant foam, such as those that are used in extinguishing fires, especially oil fires …

… solid foams form an important class of lightweight cellular engineering material …

… shape memory foams have many possible applications, such as dynamic structural support, flexible foam core, and expandable foam fill …

kelvin problem and the weaire-phelan structure

… in geometry, the weaire–phelan structure is a complex 3-dimensional structure representing an idealised foam of equal-sized bubbles …

… the kelvin problem … in 1887, lord kelvin asked how space could be partitioned into cells of equal volume with the least area of surface between them, i.e., what was the most efficient bubble foam? …

… he proposed a foam, based on the bitruncated cubic honeycomb, which is called the kelvin structure …

… to conform to plateau's laws governing the structures of foams, the hexagonal faces of kelvin's variant are slightly curved …

… the weaire–phelan structure differs from kelvin's in that it uses two kinds of cells, though they both have equal volume …

…the weaire–phelan structure is the inspiration for the design of the beijing national aquatics centre for the 2008 olympics in beijing …

… the resulting structural support system is inherently strong and lightweight. as all joints in the structure are close to tetrahedral angles …

…the framework fills a large volume of space with a reduced amount of material, similar to a hexagon in two dimensions …

[weaire-phelan - visualised filling a container]

stretched grid method

… the stretched grid method (sgm) is a numerical technique for finding approximate solutions of various mathematical and engineering problems that can be related to an elastic grid behavior …

… in particular, meteorologists use the stretched grid method for weather prediction …

… and engineers use the stretched grid method to design tents and other tensile structures …