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Foams are materials formed by trapping pockets of gas in a
liquid A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure. As such, it is one of the four fundamental states of matter (the others being solid, gas, a ...
or solid. A bath sponge and the head on a glass of beer are examples of foams. In most foams, the volume of gas is large, with thin films of liquid or solid separating the regions of gas. Soap foams are also known as suds. Solid foams can be closed-cell or open-cell. In closed-cell foam, the gas forms discrete pockets, each completely surrounded by the solid material. In open-cell foam, gas pockets connect to each other. A bath sponge is an example of an open-cell foam: water easily flows through the entire structure, displacing the air. A sleeping mat is an example of a closed-cell foam: gas pockets are sealed from each other so the mat cannot soak up water. Foams are examples of dispersed media. In general, gas is present, so it divides into gas
bubbles Bubble, Bubbles or The Bubble may refer to: Common uses * Bubble (physics), a globule of one substance in another, usually gas in a liquid ** Soap bubble * Economic bubble, a situation where asset prices are much higher than underlying fundame ...
of different sizes (i.e., the material is polydisperse)—separated by liquid regions that may form films, thinner and thinner when the liquid phase drains out of the system
films A film also called a movie, motion picture, moving picture, picture, photoplay or (slang) flick is a work of visual art that simulates experiences and otherwise communicates ideas, stories, perceptions, feelings, beauty, or atmosphere ...
. When the principal scale is small, i.e., for a very fine foam, this dispersed medium can be considered a type of
colloid A colloid is a mixture in which one substance consisting of microscopically dispersed insoluble particles is suspended throughout another substance. Some definitions specify that the particles must be dispersed in a liquid, while others extend ...
. ''Foam'' can also refer to something that is analogous to foam, such as quantum foam.


Structure

A foam is, in many cases, a multi-scale 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 A honeycomb is a mass of hexagonal prismatic wax cells built by honey bees in their nests to contain their larvae and stores of honey and pollen. Beekeepers may remove the entire honeycomb to harvest honey. Honey bees consume about of hone ...
. The Weaire–Phelan structure is considered the best possible (optimal) unit cell of a perfectly ordered foam, 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 a network of interconnected films called lamellae. Ideally, the lamellae connect 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
surfactant Surfactants are chemical compounds that decrease the surface tension between two liquids, between a gas and a liquid, or interfacial tension between a liquid and a solid. Surfactants may act as detergents, wetting agents, emulsifiers, foaming ...
s, particles ( Pickering emulsion), or more complex associations.


Mechanical properties of solid foams

Solid foams, both open-cell and closed-cell, are considered as a sub-class of cellular structures. They often have lower nodal connectivity as compared to other cellular structures like honeycombs and truss lattices, and thus, their failure mechanism is dominated by bending of members. Low nodal connectivity and the resulting failure mechanism ultimately lead to their lower mechanical strength and stiffness compared to honeycombs and truss lattices.


Formation

Several conditions are needed to produce foam: there must be mechanical work, surface active components (surfactants) that reduce the
surface tension Surface tension is the tendency of liquid surfaces at rest to shrink into the minimum surface area possible. Surface tension is what allows objects with a higher density than water such as razor blades and insects (e.g. water striders) to f ...
, and the formation of foam faster than its breakdown. To create foam, work (W) is needed to increase the
surface area The surface area of a solid object is a measure of the total area that the surface of the object occupies. The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the definition of arc ...
(ΔA): : W = \gamma \Delta A \,\! where γ is the surface tension. One of the ways foam is created is through dispersion, where a large amount of gas is mixed with a liquid. A more specific method of dispersion involves injecting a gas through a hole in a solid into a liquid. If this process is completed very slowly, then one bubble can be emitted from the orifice at a time as shown in the picture below. One of the theories for determining the separation time is shown below; however, while this theory produces theoretical data that matches with the experimental data, detachment due to capillarity is accepted as a better explanation. The buoyancy force acts to raise the bubble, which is : F_b = Vg(\rho_2-\rho_1)\! where V is the volume of the bubble, g is the acceleration due to gravity, and ρ1 is the density of the gas ρ2 is the density of the liquid. The force working against the buoyancy force is the
surface tension Surface tension is the tendency of liquid surfaces at rest to shrink into the minimum surface area possible. Surface tension is what allows objects with a higher density than water such as razor blades and insects (e.g. water striders) to f ...
force, which is : F_s = 2r \pi\gamma\!, where γ is the surface tension, and r is the radius of the orifice. As more air is pushed into the bubble, the buoyancy force grows quicker than the surface tension force. Thus, detachment occurs when the buoyancy force is large enough to overcome the surface tension force. : Vg(\rho_2-\rho_1)> 2r \pi\gamma\! In addition, if the bubble is treated as a sphere with a radius of R and the volume V is substituted in to the equation above, separation occurs at the moment when : R^3=\frac\! Examining this phenomenon from a capillarity viewpoint for a bubble that is being formed very slowly, it can be assumed that the pressure p inside is constant everywhere. The hydrostatic pressure in the liquid is designated by p_0. The change in pressure across the interface from gas to liquid is equal to the capillary pressure; hence, : p-p_0=\gamma\left (\frac+\frac\right)\! where R1 and R2 are the radii of curvature and are set as positive. At the stem of the bubble, R3 and R4 are the radii of curvature also treated as positive. Here the hydrostatic pressure in the liquid has to take in account z, the distance from the top to the stem of the bubble. The new hydrostatic pressure at the stem of the bubble is ''p''0(''ρ''1 − ''ρ''2)''z''. The hydrostatic pressure balances the capillary pressure, which is shown below: : p-p_0-(\rho_2-\rho_1)gz=\gamma\left (\frac+\frac\right)\! Finally, the difference in the top and bottom pressure equal the change in hydrostatic pressure: : (\rho_2-\rho_1)gz=\gamma\left (\frac+\frac-\frac-\frac\right)\! At the stem of the bubble, the shape of the bubble is nearly cylindrical; consequently, either R3 or R4 is large while the other radius of curvature is small. As the stem of the bubble grows in length, it becomes more unstable as one of the radius grows and the other shrinks. At a certain point, the vertical length of the stem exceeds the circumference of the stem and due to the buoyancy forces the bubble separates and the process repeats.Bikerman, J.J. "Formation and Structure" in ''Foams'' New York, Springer-Verlag, 1973. ch 2. sec 24–25


Stability


Stabilization

The stabilization of a foam is caused by van der Waals forces between the molecules in the foam,
electrical double layer A double layer (DL, also called an electrical double layer, EDL) is a structure that appears on the surface of an object when it is exposed to a fluid. The object might be a solid particle, a gas bubble, a liquid droplet, or a porous body. The D ...
s created by dipolar surfactants, and the Marangoni effect, which acts as a restoring force to the lamellae. The Marangoni effect depends on the liquid that is foaming being impure. Generally, surfactants in the solution decrease the surface tension. The surfactants also clump together on the surface and form a layer as shown below. For the Marangoni effect to occur, the foam must be indented as shown in the first picture. This indentation increases local surface area. Surfactants have a larger diffusion time than the bulk of the solution—so the surfactants are less concentrated in the indentation. Also, surface stretching makes the surface tension of the indented spot greater than the surrounding area. Consequentially—since diffusion time for the surfactants is large—the Marangoni effect has time to take place. The difference in surface tension creates a gradient, which instigates fluid flow from areas of lower surface tension to areas of higher surface tension. The second picture shows the film at equilibrium after the Marangoni effect has taken place.


Destabilization

Witold Rybczynski and Jacques Hadamard developed an equation to calculate the velocity of bubbles that rise in foam with the assumption that the bubbles are spherical with a radius r. : u=\frac(\rho_2-\rho_1)\left (\frac\right)\! with velocity in units of centimeters per second. ρ1 and ρ2 is the density for a gas and liquid respectively in units of g/cm3 and ῃ1 and ῃ2 is the viscosity of the gas and liquid g/cm·s and g is the acceleration in units of cm/s2. However, since the density and viscosity of a liquid is much greater than the gas, the density and viscosity of the gas can be neglected, which yields the new equation for velocity of bubbles rising as: : u=\frac(\rho_2)\! However, through experiments it has been shown that a more accurate model for bubbles rising is: : u=\frac(\rho_2-\rho_1)\! Deviations are due to the Marangoni effect and capillary pressure, which affect the assumption that the bubbles are spherical. For laplace pressure of a curved gas liquid interface, the two principal radii of curvature at a point are R1 and R2. With a curved interface, the pressure in one phase is greater than the pressure in another phase. The capillary pressure Pc is given by the equation of: : P_c=\gamma\left (\frac+\frac\right)\!, where \gamma is the surface tension. The bubble shown below is a gas (phase 1) in a liquid (phase 2) and point A designates the top of the bubble while point B designates the bottom of the bubble. At the top of the bubble at point A, the pressure in the liquid is assumed to be p0 as well as in the gas. At the bottom of the bubble at point B, the hydrostatic pressure is: : P_B,1=p_0+g\rho_1z\! : P_B,2=p_0+g\rho_2z\! where ρ1 and ρ2 is the density for a gas and liquid respectively. The difference in hydrostatic pressure at the top of the bubble is 0, while the difference in hydrostatic pressure at the bottom of the bubble across the interface is ''gz''(''ρ''2 − ''ρ''1). Assuming that the radii of curvature at point A are equal and denoted by RA and that the radii of curvature at point B are equal and denoted by RB, then the difference in capillary pressure between point A and point B is: : P_c=2\gamma\left (\frac-\frac\right)\! At equilibrium, the difference in capillary pressure must be balanced by the difference in hydrostatic pressure. Hence, : gz(\rho_2-\rho_1)=2\gamma\left (\frac-\frac\right)\! Since, the density of the gas is less than the density of the liquid the left hand side of the equation is always positive. Therefore, the inverse of RA must be larger than the RB. Meaning that from the top of the bubble to the bottom of the bubble the radius of curvature increases. Therefore, without neglecting gravity the bubbles cannot be spherical. In addition, as z increases, this causes the difference in RA and RB too, which means the bubble deviates more from its shape the larger it grows. Foam destabilization occurs for several reasons. First,
gravitation In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stron ...
causes drainage of liquid to the foam base, which Rybczynski and Hadamar include in their theory; however, foam also destabilizes due to
osmotic pressure Osmotic pressure is the minimum pressure which needs to be applied to a solution to prevent the inward flow of its pure solvent across a semipermeable membrane. It is also defined as the measure of the tendency of a solution to take in a pure ...
causes drainage from the lamellas to the Plateau borders due to internal concentration differences in the foam, and Laplace pressure causes diffusion of gas from small to large bubbles due to pressure difference. In addition, films can break under disjoining pressure, These effects can lead to rearrangement of the foam structure at scales larger than the bubbles, which may be individual ( T1 process) or collective (even of the "avalanche" type).


Experiments and characterizations

Being a multi-scale system involving many phenomena, and a versatile medium, foam can be studied using many different techniques. Considering the different scales, experimental techniques are diffraction ones, mainly light scattering techniques ( DWS, see below, static and dynamic light scattering, X-rays and neutron scattering) at sub-micrometer scales, or microscopic ones. Considering the system as continuous, its ''bulk'' properties can be characterized by light transmittance but also conductimetry. The correlation between structure and bulk is evidenced more accurately by acoustics in particular. The organisation between bubbles has been studied numerically using sequential attempts of evolution of the minimum surface energy either at random (Pott's model) or deterministic way (surface evolver). The evolution with time (i.e., the dynamics) can be simulated using these models, or the ''bubble model'' (Durian), which considers the motion of individual bubbles. Observations of the small-scale structure can be made by shining the foam with laser light or x-ray beams and measuring the reflectivity of the films between bubbles. Observations of the global structure can be done using neutron scattering. A typical light scattering (or diffusion) optical technique, multiple light scattering coupled with vertical scanning, is the most widely used technique to monitor the dispersion state of a product, hence identifying and quantifying destabilization phenomena. It works on any concentrated dispersions without dilution, including foams. When light is sent through the sample, it is backscattered by the bubbles. The backscattering intensity is directly proportional to the size and volume fraction of the dispersed phase. Therefore, local changes in concentration (drainage, syneresis) and global changes in size (ripening, coalescence) are detected and monitored.


Applications


Liquid foams

Liquid foams can be used in fire retardant foam, such as those that are used in extinguishing fires, especially oil fires. In some ways, leavened
bread Bread is a staple food prepared from a dough of flour (usually wheat) and water, usually by baking. Throughout recorded history and around the world, it has been an important part of many cultures' diet. It is one of the oldest human-made f ...
is a foam, as the yeast causes the bread to rise by producing tiny bubbles of gas in the dough. The dough has traditionally been understood as a closed-cell foam, in which the pores do not connect with each other. Cutting the dough releases the gas in the bubbles that are cut, but the gas in the rest of the dough cannot escape. When dough is allowed to rise too far, it becomes an open-cell foam, in which the gas pockets are connected. Cutting the dough or the surface otherwise breaking at that point would cause a large volume of gas to escape, and the dough would collapse. The open structure of an over-risen dough is easy to observe: instead of consisting of discrete gas bubbles, the dough consists of a gas space filled with threads of the flour-water paste. Recent research has indicated that the pore structure in bread is 99% interconnected into one large vacuole, thus the closed-cell foam of the moist dough is transformed into an open cell solid foam in the bread. The unique property of gas-liquid foams having very high specific surface area is exploited in the chemical processes of froth flotation and
foam fractionation Foam fractionation is a chemical process in which hydrophobic molecules are preferentially separated from a liquid solution using rising columns of foam. It is commonly used, albeit on a small scale, for the removal of organic waste from aquariums ...
.


Solid foams

Solid foams are a class of lightweight cellular engineering materials. These foams are typically classified into two types based on their pore structure: open-cell-structured foams (also known as reticulated foams) and closed-cell foams. At high enough cell resolutions, any type can be treated as continuous or "continuum" materials and are referred to as cellular solids, with predictable mechanical properties. Open-cell-structured foams contain pores that are connected to each other and form an interconnected network that is relatively soft. Open-cell foams fill with whatever gas surrounds them. If filled with air, a relatively good insulator results, but, if the open cells fill with water, insulation properties would be reduced. Recent studies have put the focus on studying the properties of open-cell foams as an insulator material. Wheat gluten/TEOS bio-foams have been produced, showing similar insulator properties as for those foams obtained from oil-based resources. Foam rubber is a type of open-cell foam. Closed-cell foams do not have interconnected pores. The closed-cell foams normally have higher compressive strength due to their structures. However, closed-cell foams are also, in general more dense, require more material, and as a consequence are more expensive to produce. The closed cells can be filled with a specialized gas to provide improved insulation. The closed-cell structure foams have higher dimensional stability, low moisture absorption coefficients, and higher strength compared to open-cell-structured foams. All types of foam are widely used as core material in
sandwich-structured composite A sandwich-structured composite is a special class of composite materials that is fabricated by attaching two thin but stiff skins to a lightweight but thick core. The core material is normally low strength material, but its higher thickness provid ...
materials. The earliest known engineering use of cellular solids is with wood, which in its dry form is a closed-cell foam composed of lignin, cellulose, and air. From the early 20th century, various types of specially manufactured solid foams came into use. The low density of these foams makes them excellent as thermal insulators and flotation devices and their lightness and compressibility make them ideal as packing materials and stuffings. An example of the use of azodicarbonamide as a blowing agent is found in the manufacture of vinyl (PVC) and EVA-PE foams, where it plays a role in the formation of air bubbles by breaking down into gas at high temperature. The random or "stochastic" geometry of these foams makes them good for energy absorption, as well. In the late 20th century to early 21st century, new manufacturing techniques have allowed for geometry that results in excellent strength and stiffness per weight. These new materials are typically referred to as engineered cellular solids.


Syntactic foam

A special class of closed-cell foams, known as syntactic foam, contains hollow particles embedded in a matrix material. The spheres can be made from several materials, including glass, ceramic, and polymers. The advantage of
syntactic foam Syntactic foams are composite materials synthesized by filling a metal, polymer, or ceramic matrix with hollow spheres called microballoons or cenospheres or non-hollow spheres (e.g. perlite). In this context, "syntactic" means "put together." ...
s is that they have a very high strength-to-weight ratio, making them ideal materials for many applications, including deep-sea and space applications. One particular syntactic foam employs
shape memory polymer Shape-memory polymers (SMPs) are polymeric smart materials that have the ability to return from a deformed state (temporary shape) to their original (permanent) shape when induced by an external stimulus (trigger), such as temperature change. P ...
as its matrix, enabling the foam to take on the characteristics of shape memory resins and composite materials; i.e., it has the ability to be reshaped repeatedly when heated above a certain temperature and cooled. Shape memory foams have many possible applications, such as dynamic structural support, flexible foam core, and expandable foam fill.


Integral skin foam

''Integral skin foam'', also known as ''self-skin foam'', is a type of foam with a high-density skin and a low-density core. It can be formed in an ''open-mold process'' or a ''closed-mold process''. In the open-mold process, two reactive components are mixed and poured into an open mold. The mold is then closed and the mixture is allowed to expand and cure. Examples of items produced using this process include arm rests, baby seats, shoe soles, and
mattress A mattress is a large, usually rectangular pad for supporting a lying person. It is designed to be used as a bed, or on a bed frame as part of a bed. Mattresses may consist of a quilted or similarly fastened case, usually of heavy cloth, conta ...
es. The closed-mold process, more commonly known as '' reaction injection molding'' (RIM), injects the mixed components into a closed mold under high pressures.


Defoaming

Foam, in this case meaning "bubbly liquid", is also produced as an often-unwanted
by-product A by-product or byproduct is a secondary product derived from a production process, manufacturing process or chemical reaction; it is not the primary product or service being produced. A by-product can be useful and marketable or it can be consid ...
in the manufacture of various substances. For example, foam is a serious problem in the
chemical industry The chemical industry comprises the companies that produce industrial chemicals. Central to the modern world economy, it converts raw materials (oil, natural gas, air, water, metals, and minerals) into more than 70,000 different products. The ...
, especially for
biochemical Biochemistry or biological chemistry is the study of chemical processes within and relating to living organisms. A sub-discipline of both chemistry and biology, biochemistry may be divided into three fields: structural biology, enzymology an ...
processes. Many biological substances, for example proteins, easily create foam on agitation or aeration. Foam is a problem because it alters the liquid flow and blocks oxygen transfer from air (thereby preventing microbial respiration in aerobic
fermentation Fermentation is a metabolic process that produces chemical changes in organic substrates through the action of enzymes. In biochemistry, it is narrowly defined as the extraction of energy from carbohydrates in the absence of oxygen. In food ...
processes). For this reason, anti-foaming agents, like
silicone A silicone or polysiloxane is a polymer made up of siloxane (−R2Si−O−SiR2−, where R = organic group). They are typically colorless oils or rubber-like substances. Silicones are used in sealants, adhesives, lubricants, medicine, cooking ...
oils, are added to prevent these problems. Chemical methods of foam control are not always desired with respect to the problems (i.e., contamination, reduction of mass transfer) they may cause especially in food and pharmaceutical industries, where the product quality is of great importance. Mechanical methods to prevent foam formation are more common than chemical ones.


Speed of sound

The acoustical property of the speed of sound through a foam is of interest when analyzing failures of hydraulic components. The analysis involves calculating total hydraulic cycles to fatigue failure. The speed of sound in a foam is determined by the mechanical properties of the gas creating the foam: oxygen, nitrogen, or combinations. Assuming that the speed of sound is based on the liquid's fluid properties leads to errors in calculating fatigue cycles and failure of mechanical hydraulic components. Using acoustical transducers and related instrumentation that set low limits (0–50,000 Hz with roll-off) causes errors. The low roll-off during measurement of actual frequency of acoustic cycles results in miscalculation due to actual hydraulic cycles in the possible ranges of 1–1000 MHz or higher. Instrumentation systems are most revealing when cycle bandwidths exceed the actual measured cycles by a factor of 10 to 100. Associated instrumentation costs also increase by factors of 10 to 100. Most moving hydro-mechanical components cycle at 0–50 Hz, but entrained gas bubbles resulting in a foamy condition of the associated
hydraulic fluid A hydraulic fluid or hydraulic liquid is the medium by which power is transferred in hydraulic machinery. Common hydraulic fluids are based on mineral oil or water. Examples of equipment that might use hydraulic fluids are excavators and backhoe ...
results in actual hydraulic cycles that can exceed 1000 MHz even if the moving mechanical components do not cycle at the higher cycle frequency.


Gallery

Image:Plankton creates sea foam 2.jpg, Close-up of sea foam ( decomposing plankton) on a tide pool Image:Aluminium foam.jpg, Foamed aluminium Image:FoamedPlastic.jpg, Micrograph of temper (memory) foam Image:Silikonschaum riesenblase verfuellungsversuch.jpg,
Silicone foam Silicone foam is a synthetic rubber product used in gasketing, sheets and firestops. It is available in solid, cured form as well as in individual liquid components for field installations. Uses *Gaskets *Sheets *High temperature tubes for autoc ...
penetration seal Image:Diet Coke Mentos.jpg, Diet Coke and Mentos foam "geyser" Image:Foam ball.png, Industrial CT scanning of a foam ball Image:Expanded polystyrene foam dunnage.jpg, Polystyrene foam cushioning


Foam scales and properties


See also

*
Aluminium foam sandwich Aluminium foam sandwich (AFS) is a sandwich panel product which is made of two metallic dense face sheets and a metal foam core made of an aluminium alloy. AFS is an engineering structural material owing to its stiffness-to-mass ratio and energy a ...
*
Ballistic foam Ballistic foam is a foam that sets hard. It is widely used in the manufacture and repair of aircraft to form a light but strong filler for aircraft wings. The foam is used to surround aircraft fuel tanks to reduce the chance of fires caused by the ...
*
Chaotic bubble Chaotic bubbles within physics and mathematics, occur in cases when there are any dynamic processes that generate bubbles that are nonlinear. Many exhibit mathematically chaotic patterns consistent with chaos theory. In most systems, they arise ou ...
* Metal foam * Nanofoam * Sea foam *
Reversibly assembled cellular composite materials Reversibly assembled cellular composite materials (RCCM) are three-dimensional lattices of modular structures that can be partially disassembled to enable repairs or other modifications. Each cell incorporates structural material and a reversible ...
*
Foam party A foam party is a social event at which participants dance to music on a dance floor covered in several feet of suds or bubbles, dispensed from a foam machine. History Foam parties can be dated back to ''A Rhapsody in Black and Blue'', a 1932 sh ...


References


Further reading

* Thomas Hipke, Günther Lange, René Poss: Taschenbuch für Aluminiumschäume. Aluminium-Verlag, Düsseldorf 2007, . * Hannelore Dittmar-Ilgen: Metalle lernen schwimmen. In: Dies.: Wie der Kork-Krümel ans Weinglas kommt. Hirzel, Stuttgart 2006, , S. 74.


External links

* Andrew M. Kraynik, Douglas A. Reinelt, Frank van Swo
Structure of random monodisperse foam
* D. L. Weaire, Stefan Hutzler (1999
The Physics of Foams
* {{Patterns in nature Colloids