Foams
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Foams are two-phase
material A material is a matter, substance or mixture of substances that constitutes an Physical object, object. Materials can be pure or impure, living or non-living matter. Materials can be classified on the basis of their physical property, physical ...
systems where a gas is dispersed in a second, non-gaseous material, specifically, in which gas cells are enclosed by a distinct
liquid Liquid is a state of matter with a definite volume but no fixed shape. Liquids adapt to the shape of their container and are nearly incompressible, maintaining their volume even under pressure. The density of a liquid is usually close to th ...
or
solid Solid is a state of matter where molecules are closely packed and can not slide past each other. Solids resist compression, expansion, or external forces that would alter its shape, with the degree to which they are resisted dependent upon the ...
material. Note, this source focuses only on liquid foams. Note, this source also focuses on liquid foams. Foam "may contain more or less liquid r solidaccording to circumstances", although in the case of gas-liquid foams, the gas occupies most of the volume. In most foams, the volume of gas is large, with thin films of liquid or solid separating the regions of gas.


Etymology

The word derives from the medieval German and otherwise obsolete ''veim'', in reference to the "frothy head forming in the glass once the beer has been freshly poured" (cf. ''ausgefeimt'').


Structure

A foam is, in many cases, a multi-scale system. One scale is the bubble:
material A material is a matter, substance or mixture of substances that constitutes an Physical object, object. Materials can be pure or impure, living or non-living matter. Materials can be classified on the basis of their physical property, physical ...
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 reported in one primary philosophical source to be 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 In chemistry and physics, metastability is an intermediate energetic state within a dynamical system other than the system's state of least energy. A ball resting in a hollow on a slope is a simple example of metastability. If the ball is onl ...
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 or interfacial tension between two liquids, a liquid and a gas, or a liquid and a solid. The word ''surfactant'' is a Blend word, blend of "surface-active agent", coined in ...
s, particles ( Pickering emulsion), or more complex associations. Foams are examples of dispersed media. In general, gas is present, so it divides into gas bubbles 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 known as a movie or motion picture, is a work of Visual arts, visual art that simulates experiences and otherwise communicates ideas, stories, perceptions, emotions, or atmosphere through the use of moving images that are gen ...
. 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 exte ...
.


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 (physics), tension is what allows objects with a higher density than water such as razor blades and insects (e.g. Ge ...
, and the formation of foam faster than its breakdown. To create foam, work (W) is needed to increase the
surface area The surface area (symbol ''A'') 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 d ...
(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 the experimental data, detachment due to capillarity is accepted as a better explanation. The
buoyancy Buoyancy (), or upthrust, is the force exerted by a fluid opposing the weight of a partially or fully immersed object (which may be also be a parcel of fluid). In a column of fluid, pressure increases with depth as a result of the weight of t ...
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 (physics), tension is what allows objects with a higher density than water such as razor blades and insects (e.g. Ge ...
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 into 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 equals 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 foam is caused by
van der Waals force In molecular physics and chemistry, the van der Waals force (sometimes van der Waals' force) is a distance-dependent interaction between atoms or molecules. Unlike ionic or covalent bonds, these attractions do not result from a chemical elec ...
s between the molecules in the foam,
electrical double layer Electricity is the set of physical phenomena associated with the presence and motion of matter possessing an electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnetism, as described by Maxwel ...
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 the 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 the 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. Curing a foam solidifies it, making it indefinitely stable at STP.


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 dynamic viscosity of the gas and liquid respectively in units of g/cm·s and g is the acceleration of gravity 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 (), also known as gravitation or a gravitational interaction, is a fundamental interaction, a mutual attraction between all massive particles. On Earth, gravity takes a slightly different meaning: the observed force b ...
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 (chemistry), 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 soluti ...
causes drainage from the lamellas to the Plateau borders due to internal concentration differences in the foam, and
Laplace pressure The Laplace pressure is the pressure difference between the inside and the outside of a curved surface that forms the boundary between two fluid regions. The pressure difference is caused by the surface tension of the interface between liquid and ...
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).


Mechanical properties


Liquid foams


Solid foams

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. 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. The strength of foams can be impacted by the density, the material used, and the arrangement of the cellular structure (open vs closed and pore isotropy). To characterize the mechanical properties of foams, compressive stress-strain curves are used to measure their strength and ability to absorb energy since this is an important factor in foam based technologies.


Elastomeric foam

For elastomeric cellular solids, as the foam is compressed, first it behaves elastically as the cell walls bend, then as the cell walls buckle there is yielding and breakdown of the material until finally the cell walls crush together and the material ruptures. This is seen in a stress-strain curve as a steep linear elastic regime, a linear regime with a shallow slope after yielding (plateau stress), and an exponentially increasing regime. The stiffness of the material can be calculated from the linear elastic regime where the modulus for open celled foams can be defined by the equation: \left ( \frac \right )_f = C_f\left ( \frac \right )^2 where E_s is the modulus of the solid component, E^* is the modulus of the honeycomb structure, C_f is a constant having a value close to one, \rho^* is the density of the honeycomb structure, and \rho_s is the density of the solid. The elastic modulus for closed cell foams can be described similarly by: \left ( \frac \right )_f = C_f\left ( \frac \right )^3 where the only difference is the exponent in the density dependence. However, in real materials, a closed-cell foam has more material at the cell edges which makes it more closely follow the equation for open-cell foams. The ratio of the density of the honeycomb structure compared with the solid structure has a large impact on the modulus of the material. Overall, foam strength increases with density of the cell and stiffness of the matrix material.


Energy of deformation

Another important property which can be deduced from the stress strain curve is the energy that the foam is able to absorb. The area under the curve (specified to be before rapid densification at the peak stress), represents the energy in the foam in units of energy per unit volume. The maximum energy stored by the foam prior to rupture is described by the equation: \frac = 0.05\left ( \frac \right )^2\left .975-1.4 \left ( \frac \right ) \right/math> This equation is derived from assuming an idealized foam with engineering approximations from experimental results. Most energy absorption occurs at the plateau stress region after the steep linear elastic regime.


Directional dependence

The
isotropy In physics and geometry, isotropy () is uniformity in all orientations. Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefix ' or ', hence ''anisotropy''. ''Anisotropy'' is also u ...
of the cellular structure and the absorption of fluids can also have an impact on the mechanical properties of a foam. If there is anisotropy present, then the materials response to stress will be directionally dependent, and thus the stress-strain curve, modulus, and energy absorption will vary depending on the direction of applied force. Also, open-cell structures which have connected pores can allow water or other liquids to flow through the structure, which can also affect the rigidity and energy absorption capabilities.


Differences between liquid and solid foams

Theories regarding foam formation, structure, and properties—in
physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...
and
physical chemistry Physical chemistry is the study of macroscopic and microscopic phenomena in chemical systems in terms of the principles, practices, and concepts of physics such as motion, energy, force, time, thermodynamics, quantum chemistry, statistical mech ...
—differ somewhat between liquid and solid foams in that the former are dynamic (e.g., in their being "continuously deformed"), as a result of gas diffusing between cells, liquid draining from the foam into a bulk liquid, etc. Theories regarding liquid foams have as direct analogs theories regarding
emulsion An emulsion is a mixture of two or more liquids that are normally Miscibility, immiscible (unmixable or unblendable) owing to liquid-liquid phase separation. Emulsions are part of a more general class of two-phase systems of matter called colloi ...
s, two-phase
material A material is a matter, substance or mixture of substances that constitutes an Physical object, object. Materials can be pure or impure, living or non-living matter. Materials can be classified on the basis of their physical property, physical ...
systems in which one
liquid Liquid is a state of matter with a definite volume but no fixed shape. Liquids adapt to the shape of their container and are nearly incompressible, maintaining their volume even under pressure. The density of a liquid is usually close to th ...
is enclosed by another.


Examples of foams and foam examples

* Bath sponge - A bath sponge is an example of an open-cell foam; water easily flows through the entire structure, displacing the air. * The head on a glass of beer * Soap foam (also known as ''suds'') * Sleeping mat - A sleeping mat is an example of a product composed of closed-cell foam. ''Foam'' can also refer to something that is analogous to foam, such as quantum foam.


Applications


Liquid foams

Liquid foams can be used in fire retardant foam, such as those that are used in extinguishing fires, especially oil fires. The dough of leavened
bread Bread is a baked food product made from water, flour, and often yeast. It is a staple food across the world, particularly in Europe and the Middle East. Throughout recorded history and around the world, it has been an important part of many cu ...
has traditionally been understood as a closed-cell foam—
yeast Yeasts are eukaryotic, single-celled microorganisms classified as members of the fungus kingdom (biology), kingdom. The first yeast originated hundreds of millions of years ago, and at least 1,500 species are currently recognized. They are est ...
causing bread to rise via tiny bubbles of gas that become the bread pores—where the cells 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 surface at that point would cause a large volume of gas to escape, and the dough to collapse. 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.


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 foams can be used to filter air. For example, a foam embedded with catalyst has been shown to catalytically convert formaldehyde to benign substances when formaldehyde polluted air passes through the open cell structure. 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 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 Density (volumetric mass density or specific mass) is the ratio of a substance's mass to its volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' (or ''d'') can also be u ...
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


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 person Lying (position), lying down, especially for sleeping. It is designed to be used as a bed, or on a bed frame as part of a bed. Mattresses may consist of a Quilting, quilted o ...
es. The closed-mold process, more commonly known as '' reaction injection molding'' (RIM), injects the mixed components into a closed mold under high pressures.


Gallery

Image:FoamedPlastic.jpg,
Micrograph A micrograph is an image, captured photographically or digitally, taken through a microscope or similar device to show a magnify, magnified image of an object. This is opposed to a macrograph or photomacrograph, an image which is also taken ...
of temper (memory) foam Image:Silikonschaum riesenblase verfuellungsversuch.jpg, Silicone foam penetration seal Image:Foam ball.png, Industrial CT scanning of a foam ball Image:Expanded polystyrene foam dunnage.jpg, Polystyrene foam cushioning Image:Aluminium foam.jpg, Foamed
aluminum Aluminium (or aluminum in North American English) is a chemical element; it has chemical symbol, symbol Al and atomic number 13. It has a density lower than that of other common metals, about one-third that of steel. Aluminium has ...


Foam scales and properties


See also

* Aluminium foam sandwich * Ballistic foam * Chaotic bubble * Defoamer * Foam glass * Metal foam *
Nanofoam Nanofoams are a class of nanostructured, porous medium, porous materials (foams) containing a significant population of pores with diameters less than 100 nanometer, nm. Aerogels are one example of nanofoam. Metal Overview Metallic nanofoams ...
* Sea foam * Reversibly assembled cellular composite materials * Foam party *
Soft matter Soft matter or soft condensed matter is a type of matter that can be deformed or structurally altered by thermal or mechanical stress which is of similar magnitude to thermal fluctuations. The science of soft matter is a subfield of condensed ...


References


Further reading

* A modern treatise almost exclusively focused on liquid foams. * A treatise termed a classic by Weaire & Hutzler (1999), on solid foams, and the reason they limit their focus to liquid foams. * Note, this source also focuses on liquid foams. * 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
* {{Patterns in nature Colloids