Foam - Knowledge (XXG)

4299: 3074: 4668: 4028:—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. 4700: 394: 1981: 4322: 2557: 5260:, the term refers to "a light frothy mass of fine bubbles formed in or on the surface of a liquid or from a liquid", giving the examples of those produced by "salivating or sweating", ones stably produced to fight fires, ones that are the product of gas bubbles introduced during manufacturing, and then the further broad examples of sea foam, and then anything resembling the foregoing. Finally, the general definition includes actions to produce all of the above. See 6490: 1967: 413: 3750: 3005: 804: 4649: 4715: 4530: 4385: 4173: 3787: 3623: 1904: 887: 97: 4685: 3884: 693: 4111: 4070: 3709: 592: 551: 199: 56: 3688:

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.

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The general use of the term, which includes both noun and verb forms, is both narrower and broader than the one from material science described here. In general use, it is narrower, in that it most often refers to liquid foams; it is broader in that it includes all manners of such, and the actions to

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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

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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

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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

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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

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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

462:—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 3683:

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

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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

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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

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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

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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

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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

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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

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Being a multi-scale system involving many phenomena, and a versatile medium, foam can be studied using many different techniques. 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

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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

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One optical technique involves the use of multiple light scattering coupled with vertical scanning along the height of the sample vessel. When light is sent through the sample, it is backscattered by the bubbles. Therefore, local changes in scattering and light transmission can detected and

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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

1007: 2220: 1876: 500:. 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 2016:

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.

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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

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Schematic stress-strain curve of an elastomeric foam, demonstrating the three regions which are linear elastic, cell-wall buckling, and cell-wall fracture, where the area under the curve specified represents the energy per unit volume the foam can

2942: 3591: 4465:; 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. 1212:

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.

2955:. 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 R 3609:

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.

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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

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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.

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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.

1551: 2827: 2527: 5415: 4488:. 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 2715:

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

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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

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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.

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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:

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Reyes-Labarta, J.A.; Marcilla, A. (2012). "Thermal Treatment and Degradation of Crosslinked Ethylene Vinyl Acetate-Polyethylene-Azodicarbonamide-ZnO Foams. Complete Kinetic Modelling and Analysis".

4637:) 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. 4445:

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

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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

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or foaming is a means of mass killing farm animals by spraying foam over a large area to obstruct breathing and ultimately cause suffocation. It is usually used to attempt to stop disease spread.

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Reyes-Labarta, J.A.; Marcilla, A. (2008). "Differential Scanning Calorimetry Analysis of the Thermal Treatment of Ternary Mixtures of Ethylene Vinyl Acetate, Polyethylene and Azodicarbonamide".

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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 R

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Reyes-Labarta, J.A.; Olaya, M.M.; Marcilla, A. (2006). "DSC Study of the Transitions Involved in the Thermal Treatment of Foamable Mixtures of PE and EVA Copolymer with Azodicarbonamide".

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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.

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lead fails to summarise, instead presenting novel content (dispersed media, quantum foam, and allusions to foam as polydisperse, colloidal, and as suds, beer head, bath sponges, etc., all

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material. The foam "may contain more or less liquid according to circumstances", although in the case of gas-liquid foams, the gas occupies most of the volume. The word derives from the

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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.

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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

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Kooistra, Gregory W.; Deshpande, Vikram S.; Wadley, Haydn N.G. (August 2004). "Compressive behavior of age hardenable tetrahedral lattice truss structures made from aluminium".

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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

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the formal and key matter of defining what this form of material is, with distinction between liquid and solid foams, is not accomplished by the current unsourced essay.

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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.

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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.

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connectivity and the resulting failure mechanism ultimately lead to their lower mechanical strength and stiffness compared to honeycombs and truss lattices.

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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

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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.

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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 R

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results in actual hydraulic cycles that can exceed 1000 MHz even if the moving mechanical components do not cycle at the higher cycle frequency.

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Reyes-Labarta, J.A.; Marcilla, A. (2008). "Kinetic Study of the Decompositions Involved in the Thermal Degradation of Commercial Azodicarbonamide".

4749: 4291:) and closed-cell foams. At high enough cell resolutions, any type can be treated as continuous or "continuum" materials and are referred to as 6314: 6303: 6144: 5309: 2339: 4298: 5452: 4699: 3691:

Most moving hydro-mechanical components cycle at 0–50 Hz, but entrained gas bubbles resulting in a foamy condition of the associated

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Examining this phenomenon from a capillarity viewpoint for a bubble that is being formed very slowly, it can be assumed that the pressure

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causes drainage of liquid to the foam base, which Rybczynski and Hadamar include in their theory; however, foam also destabilizes due to

2215:{\displaystyle u={\frac {2gr^{2}}{9\eta _{2}}}(\rho _{2}-\rho _{1})\left({\frac {3\eta _{1}+3\eta _{2}}{3\eta _{1}+2\eta _{2}}}\right)\!} 1871:{\displaystyle (\rho _{2}-\rho _{1})gz=\gamma \left({\frac {1}{R_{1}}}+{\frac {1}{R_{2}}}-{\frac {1}{R_{3}}}-{\frac {1}{R_{4}}}\right)\!} 6665: 4742: 861:

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

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oils, are added to prevent these problems. Chemical methods of foam control are not always desired with respect to the problems (i.e.,

4614:. Foam is a problem because it alters the liquid flow and blocks oxygen transfer from air (thereby preventing microbial respiration in 3761: with: a much more thorough presentation of the variety of techniques used to characterise liquid and solid foams. You can help by 6267: 5218: 612: 5899: 5658:"A rate-sensitive constitutive model for anisotropic cellular materials - Application to a transversely isotropic polyurethane foam" 5581: 5462: 5293: 4577: 4432: 4274: 4256: 4154: 4097: 3967: 3852: 3834: 3736: 3670: 1943: 926: 819:

and have a variety of bubble sizes. At larger sizes, the study of idealized foams is closely linked to the mathematical problems of

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A treatise termed a classic by Weaire & Hutzler (1999), on solid foams, and the reason they limit their focus to liquid foams.

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Wu, Qiong; Andersson, Richard L.; Holgate, Tim; Johansson, Eva; Gedde, Ulf W.; Olsson, Richard T.; Hedenqvist, Mikael S. (2014).

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are used to measure their strength and ability to absorb energy since this is an important factor in foam based technologies.

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Hannelore Dittmar-Ilgen: Metalle lernen schwimmen. In: Dies.: Wie der Kork-Krümel ans Weinglas kommt. Hirzel, Stuttgart 2006,

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Open-cell foams can be used to filter air. For example, a foam embedded with catalyst has been shown to catalytically convert

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deterministic way (surface evolver). The evolution with time (i.e., the dynamics) can be simulated using these models, or the

6221: 6178: 5163: 4822: 4555: 4410: 4194: 3812: 3648: 1925: 908: 718: 118: 6150: 5270: 2982:, These effects can lead to rearrangement of the foam structure at scales larger than the bubbles, which may be individual ( 2441:. With a curved interface, the pressure in one phase is greater than the pressure in another phase. The capillary pressure P 5023: 4331: 4907: 4838: 4031:

The unique property of gas-liquid foams having very high specific surface area is exploited in the chemical processes of

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At equilibrium, the difference in capillary pressure must be balanced by the difference in hydrostatic pressure. Hence,

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is that they have a very high strength-to-weight ratio, making them ideal materials for many applications, including

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Observations of the small-scale structure can be made using various light scattering and image capturing techniques.

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causes drainage from the lamellas to the Plateau borders due to internal concentration differences in the foam, and

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causes diffusion of gas from small to large bubbles due to pressure difference. In addition, films can break under

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and flotation devices and their lightness and compressibility make them ideal as packing materials and stuffings.

4183: 4132: 3894: 3816: 3801: 3652: 3637: 1914: 897: 220: 107: 4209: 3920: 2641: 2574: 733: 133: 5917:"Catalytic Surgical Smoke Filtration Unit Reduces Formaldehyde Levels in a Simulated Operating Room Environment" 6350: 6479: 5761:

Wang, Shuo; Austin, Peter; Chakrabati-Bell, Sumana (2011). "It's a maze: The pore structure of bread crumbs".

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Thomas Hipke, Günther Lange, René Poss: Taschenbuch für Aluminiumschäume. Aluminium-Verlag, Düsseldorf 2007,

5964:"Highly porous flame-retardant and sustainable biofoams based on wheat gluten and in situ polymerized silica" 5079: 4216: 3927: 3429:{\displaystyle \left({\frac {E^{*}}{E_{s}}}\right)_{f}=C_{f}\left({\frac {\rho ^{*}}{\rho _{s}}}\right)^{3}} 3182:{\displaystyle \left({\frac {E^{*}}{E_{s}}}\right)_{f}=C_{f}\left({\frac {\rho ^{*}}{\rho _{s}}}\right)^{2}} 1998: 1463:. The change in pressure across the interface from gas to liquid is equal to the capillary pressure; hence, 740: 140: 5491:

Queheillalt, Douglas T.; Wadley, Haydn N.G. (January 2005). "Cellular metal lattices with hollow trusses".

1719:{\displaystyle p-p_{0}-(\rho _{2}-\rho _{1})gz=\gamma \left({\frac {1}{R_{3}}}+{\frac {1}{R_{4}}}\right)\!} 1148: 961: 4690: 4358: 44: 4998: 4919: 4551: 4406: 4190: 4083: 3808: 3722: 3644: 3046: 1921: 904: 854:. Ideally, the lamellae connect in triads and radiate 120° outward from the connection points, known as 649:

that states a Knowledge (XXG) editor's personal feelings or presents an original argument about a topic.

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that states a Knowledge (XXG) editor's personal feelings or presents an original argument about a topic.

114: 69: 33: 5697:"The effect of moisture absorption on thephysical properties of polyurethane shapememory polymer foams" 4361:, where it plays a role in the formation of air bubbles by breaking down into gas at high temperature. 4223: 3934: 3326:

is the density of the solid. The elastic modulus for closed cell foams can be described similarly by:

747: 393: 147: 6256:; Cohen-Addad, S; Elias, F; Graner, F; Höhler, R; Pitois, O; Rouyer, F & Saint-Jalmes, A (2013). 5708: 5622: 5535: 5500: 5373: 5207:; Cohen-Addad, S; Elias, F; Graner, F; Höhler, R; Pitois, O; Rouyer, F & Saint-Jalmes, A (2013). 4714: 4458: 828: 4292: 2937:{\displaystyle gz(\rho _{2}-\rho _{1})=2\gamma \left({\frac {1}{R_{A}}}-{\frac {1}{R_{B}}}\right)\!} 447:, in reference to the "frothy head forming in the glass once the beer has been freshly poured" (cf. 6713: 6673: 6457: 4883: 4615: 4462: 4006: 2979: 2556: 1994: 851: 5597:

M. Liu et al. Multiscale modeling of effective elastic properties of fluid-filled porous materials

1980: 6651: 6551: 6388: 6284: 6238: 6195: 5944: 5815: 5677: 5638: 5551: 5363: 5319: 5235: 5180: 4622: 4607: 4354: 4343: 4205: 4036: 3916: 3586:{\displaystyle {\frac {W_{max}}{E_{s}}}=0.05\left({\frac {\rho ^{*}}{\rho _{s}}}\right)^{2}\left} 2333:

However, through experiments it has been shown that a more accurate model for bubbles rising is:

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Finally, the difference in the top and bottom pressure equal the change in hydrostatic pressure:

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At the stem of the bubble, the shape of the bubble is nearly cylindrical; consequently, either R

3302: 3275: 6739: 6678: 6578: 6573: 6514: 6504: 6442: 6310: 6299: 6263: 6217: 6174: 6140: 5936: 5895: 5862: 5835: 5734: 5577: 5458: 5305: 5214: 5159: 4939: 4595: 4047: 855: 840: 812: 467: 424: 40: 2536: 6529: 6113: 6105: 6076: 6068: 6041: 6012: 6004: 5975: 5928: 5827: 5770: 5724: 5716: 5669: 5630: 5543: 5508: 5381: 5297: 5045: 5040: 5016: 5002: 4898: 4894: 4850: 4829: 4480:, is a type of foam with a high-density skin and a low-density core. It can be formed in an 4310:

to benign substances when formaldehyde polluted air passes through the open cell structure.

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as well as in the gas. At the bottom of the bubble at point B, the hydrostatic pressure is:

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as its matrix, enabling the foam to take on the characteristics of shape memory resins and

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systems where a gas is disbursed in a second, non-gaseous material, specifically, in which

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This article is about the substance formed from trapped gas bubbles. For other uses, see

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in the manufacture of various substances. For example, foam is a serious problem in the

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inside is constant everywhere. The hydrostatic pressure in the liquid is designated by

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How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension

3749: 3004: 6728: 6630: 6625: 5948: 5681: 5642: 4992: 4673: 4634: 4630: 4350: 4025: 824: 482: 5916: 5555: 39:"Foaming" and "Foamy" redirect here. For a method of mass killing farm animals, see 6541: 6464: 6447: 5696: 5673: 4842: 4599: 4307: 1546:{\displaystyle p-p_{0}=\gamma \left({\frac {1}{R_{1}}}+{\frac {1}{R_{2}}}\right)\!} 952: 534: 516: 501: 5547: 5512: 4590:

Foam, in this case meaning "bubbly liquid", is also produced as an often-unwanted

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At the top of the bubble at point A, the pressure in the liquid is assumed to be p

1598:. The hydrostatic pressure balances the capillary pressure, which is shown below: 1138:

is the density of the liquid. The force working against the buoyancy force is the

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is reported in one primary philosophical source to be the best possible (optimal)

754: 154: 6257: 6216:. Cambridge Solid State Science. Cambridge, England: Cambridge University Press. 6211: 6168: 6134: 5657: 5262: 5208: 5153: 2522:{\displaystyle P_{c}=\gamma \left({\frac {1}{R_{1}}}+{\frac {1}{R_{2}}}\right)\!} 6659: 6617: 6536: 6432: 6427: 6346: 5855:"'They're cooking them alive': calls to ban 'cruel' killing methods on US farms" 5124: 5031: 4931: 4879: 4658: 4529: 4384: 4172: 3883: 3786: 3622: 2967: 1903: 1564:

are the radii of curvature and are set as positive. At the stem of the bubble, R

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too, which means the bubble deviates more from its shape the larger it grows.

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is substituted in to the equation above, separation occurs at the moment when

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Several conditions are needed to produce foam: there must be mechanical work,

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is large, with thin films of liquid or solid separating the regions of gas. A

5940: 5932: 5866: 4734: 4510:(RIM), injects the mixed components into a closed mold under high pressures. 2734:). Assuming that the radii of curvature at point A are equal and denoted by R 6708: 6611: 5301: 5036: 5019: 4957: 4888: 4867: 4497: 4493: 4089: 3728: 3062: 2742:, then the difference in capillary pressure between point A and point B is: 2242: 836: 570: 486: 75: 5839: 5738: 5831: 5788: 3448:

energy stored by the foam prior to rupture is described by the equation:

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Measurement by multiple light scattering, coupled with vertical scanning.

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foams, which can be considered a network of interconnected films called

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is the density for a gas and liquid respectively in units of g/cm and ῃ

1928: in this section. Unsourced material may be challenged and removed. 947:, and the formation of foam faster than its breakdown. To create foam, 911: in this section. Unsourced material may be challenged and removed. 524: 455: 401: 6109: 6072: 6045: 6008: 2419:{\displaystyle u={\frac {2gr^{2}}{9\eta _{2}}}(\rho _{2}-\rho _{1})\!} 335:

is written like draft academic essay/treatment, from sources unstated,

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and that the radii of curvature at point B are equal and denoted by R

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causing bread to rise via tiny bubbles of gas that become the bread

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Benson, E.R.; Alphin, R.L.; Dawson, M.D.; Malone, G.W. (May 2009).

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of the gas and liquid respectively in units of g/cm·s and g is the

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In addition, if the bubble is treated as a sphere with a radius of

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International Journal of Solids and Structures (2019) 162, 36-44

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At lower scale than the bubble is the thickness of the film for

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Theories regarding foam formation, structure, and properties—in

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can also refer to something that is analogous to foam, such as

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Yu, Y. J.; Hearon, K.; Wilson, T. S.; Maitland, D. J. (2011).

5354:

Morgan, F. (2008). "Existence of Least-perimeter Partitions".

4523: 4457:

and space applications. One particular syntactic foam employs

4378: 4166: 4104: 4063: 3877: 3780: 3743: 3702: 3616: 2998: 1897: 880: 686: 631: 585: 544: 478: 428: 319: 254: 192: 90: 49: 6206:

A modern treatise almost exclusively focused on liquid foams.

5915:

Carroll, Gregory T.; Kirschman, David L. (January 23, 2023).

5341:

Anionic Surfactants – Physical Chemistry of Surfactant Action

3870:(Durian), which considers the motion of individual bubbles. 2027:

a foam solidifies it, making it indefinitely stable at STP.

647:

is written like student essay summarising an unstated source

5477:

Wilson, A.J, "Principles of Foam Formation and Stability."

2323:{\displaystyle u={\frac {gr^{2}}{3\eta _{2}}}(\rho _{2})\!} 1277:{\displaystyle Vg(\rho _{2}-\rho _{1})>2r\pi \gamma \!} 601:

needs attention from an expert in physics or chemistry

504:

is an example of a product composed of closed-cell foam.

6136:

Polyurethane and related foams: chemistry and technology

4020:

has traditionally been understood as a closed-cell foam—

2966:

Foam destabilization occurs for several reasons. First,

4128: 3762: 3070:

for open celled foams can be defined by the equation:

3017: 714: 652: 340: 285: 216: 6330:

Andrew M. Kraynik, Douglas A. Reinelt, Frank van Swol

5339:

Lucassen, J. (1981). Lucassen-Reijnders, E. H. (ed.).

3456: 3334: 3305: 3278: 3251: 3224: 3197: 3087: 2841: 2751: 2644: 2577: 2539: 2454: 2342: 2262: 2064: 2041: 1738: 1607: 1472: 1442: 1422: 1336: 1313: 1293: 1222: 1198: 1151: 1116: 1096: 1027: 964: 511:. In general, gas is present, so it divides into gas 5290:

Compendium of Chemical Terminology (The "Gold Book")

489:

are examples of foams; soap foams are also known as

6696: 6589: 6497: 6395: 5147: 5145: 5143: 5141: 5139: 4602:processes. Many biological substances, for example 2225:

with velocity in units of centimeters per second. ρ

2009:, which acts as a restoring force to the lamellae. 121:. Unsourced material may be challenged and removed. 5199: 5197: 4504:. The closed-mold process, more commonly known as 3585: 3428: 3318: 3291: 3264: 3237: 3210: 3181: 2936: 2821: 2696: 2629: 2545: 2521: 2418: 2322: 2214: 2047: 1870: 1718: 1545: 1455: 1428: 1405: 1319: 1299: 1276: 1204: 1180: 1122: 1102: 1079: 984: 843:describe how soap-films form structures in foams. 710: 5115:Reversibly assembled cellular composite materials 2933: 2818: 2693: 2626: 2518: 2415: 2319: 2211: 1867: 1715: 1542: 1402: 1273: 1177: 1076: 981: 5405:New York, Springer-Verlag, 1973. ch 2. sec 24–25 5397: 5395: 5324:: CS1 maint: bot: original URL status unknown ( 2986:) or collective (even of the "avalanche" type). 800:A foam is, in many cases, a multi-scale system. 6295:Note, this source also focuses on liquid foams. 6034:Industrial & Engineering Chemistry Research 5454:Foam Engineering: Fundamentals and Applications 5314:. Archived from the original on March 10, 2012. 5246:Note, this source also focuses on liquid foams. 5191:Note, this source focuses only on liquid foams. 4349:An example of the use of azodicarbonamide as a 4342:of these foams makes them excellent as thermal 3299:is the density of the honeycomb structure, and 1080:{\displaystyle F_{b}=Vg(\rho _{2}-\rho _{1})\!} 807:Order and disorder of bubbles in a surface foam 5662:International Journal of Solids and Structures 5611:"The Mechanical Properties of Cellular Solids" 6373: 5894:. Cambridge, UK: Cambridge University Press. 5789:"New weapon in war on bird flu: tiny bubbles" 4750: 8: 6289:: CS1 maint: multiple names: authors list ( 6262:. Oxford, England: Oxford University Press. 6243:: CS1 maint: multiple names: authors list ( 6200:: CS1 maint: multiple names: authors list ( 6173:. Oxford, England: Oxford University Press. 5656:Li, Pei; Guo, Y. B.; Shim, V. P. W. (2020). 5401:Bikerman, J.J. "Formation and Structure" in 5240:: CS1 maint: multiple names: authors list ( 5213:. Oxford, England: Oxford University Press. 5185:: CS1 maint: multiple names: authors list ( 5158:. Oxford, England: Oxford University Press. 719:introducing citations to additional sources 4558:. Unsourced material may be challenged and 4413:. Unsourced material may be challenged and 4365:referred to as engineered cellular solids. 4098:Learn how and when to remove these messages 3815:. Unsourced material may be challenged and 3737:Learn how and when to remove these messages 3651:. Unsourced material may be challenged and 3272:is a constant having a value close to one, 3245:is the modulus of the honeycomb structure, 2697:{\displaystyle P_{B},2=p_{0}+g\rho _{2}z\!} 2630:{\displaystyle P_{B},1=p_{0}+g\rho _{1}z\!} 579:Learn how and when to remove these messages 84:Learn how and when to remove these messages 6380: 6366: 6358: 4976:Giant bubbles, coloured bubbles, freezing 4757: 4743: 4735: 4295:, with predictable mechanical properties. 1890:bubble separates and the process repeats. 515:of different sizes (i.e., the material is 6213:Cellular Solids: Structure and Properties 6117: 6080: 6016: 5979: 5892:Cellular Solids: Structure and Properties 5885: 5883: 5728: 5576:. Waveland Press, Inc. pp. 686–713. 5367: 4578:Learn how and when to remove this message 4433:Learn how and when to remove this message 4275:Learn how and when to remove this message 4257:Learn how and when to remove this message 4155:Learn how and when to remove this message 3968:Learn how and when to remove this message 3853:Learn how and when to remove this message 3835:Learn how and when to remove this message 3684:foam: oxygen, nitrogen, or combinations. 3671:Learn how and when to remove this message 3566: 3556: 3550: 3526: 3514: 3504: 3498: 3479: 3463: 3457: 3455: 3420: 3408: 3398: 3392: 3381: 3368: 3356: 3346: 3340: 3333: 3310: 3304: 3283: 3277: 3256: 3250: 3229: 3223: 3202: 3196: 3173: 3161: 3151: 3145: 3134: 3121: 3109: 3099: 3093: 3086: 2920: 2911: 2900: 2891: 2868: 2855: 2840: 2805: 2796: 2785: 2776: 2756: 2750: 2684: 2668: 2649: 2643: 2617: 2601: 2582: 2576: 2538: 2505: 2496: 2485: 2476: 2459: 2453: 2406: 2393: 2377: 2362: 2349: 2341: 2310: 2294: 2279: 2269: 2261: 2198: 2182: 2167: 2151: 2141: 2128: 2115: 2099: 2084: 2071: 2063: 2040: 1993:The stabilization of a foam is caused by 1944:Learn how and when to remove this message 1854: 1845: 1834: 1825: 1814: 1805: 1794: 1785: 1759: 1746: 1737: 1702: 1693: 1682: 1673: 1647: 1634: 1618: 1606: 1529: 1520: 1509: 1500: 1483: 1471: 1447: 1441: 1421: 1390: 1377: 1350: 1341: 1335: 1312: 1292: 1249: 1236: 1221: 1197: 1156: 1150: 1130:is the acceleration due to gravity, and ρ 1115: 1095: 1067: 1054: 1032: 1026: 1018:force acts to raise the bubble, which is 999:at a time as shown in the picture below. 980: 963: 927:Learn how and when to remove this message 788:Learn how and when to remove this message 675:Learn how and when to remove this message 381:Learn how and when to remove this message 363:Learn how and when to remove this message 308:Learn how and when to remove this message 243:Learn how and when to remove this message 181:Learn how and when to remove this message 5479:Foams: Physics, Chemistry, and Structure 4772: 3072: 709:Relevant discussion may be found on the 6153:from the original on February 17, 2017. 5481:. New York, Springer-Verlag, 1989, ch 1 5135: 4644: 3218:is the modulus of the solid component, 6282: 6236: 6193: 5317: 5273:from the original on December 9, 2014. 5233: 5178: 3904:Please improve this section by adding 615:may be able to help recruit an expert. 6332:Structure of random monodisperse foam 5853:Bolotnikova, Marina (March 8, 2022). 5567: 5565: 1181:{\displaystyle F_{s}=2r\pi \gamma \!} 985:{\displaystyle W=\gamma \Delta A\,\!} 7: 4556:adding citations to reliable sources 4411:adding citations to reliable sources 4195:adding citations to reliable sources 3813:adding citations to reliable sources 3649:adding citations to reliable sources 1926:adding citations to reliable sources 1192:where γ is the surface tension, and 909:adding citations to reliable sources 119:adding citations to reliable sources 6666:The Chemical Basis of Morphogenesis 6210:Gibson, LJ & Ashby, MF (1997). 6167:Weaire, D & Hutzler, S (1999). 5451:Stevenson, Paul (January 3, 2012). 5152:Weaire, D & Hutzler, S (1999). 1997:between the molecules in the foam, 839:of a perfectly ordered foam, while 6098:Journal of Applied Polymer Science 6061:Journal of Applied Polymer Science 5997:Journal of Applied Polymer Science 5256:produce them, hence, according to 974: 496:Solid foams can be closed-cell or 25: 5294:Blackwell Scientific Publications 4791:Experiments and characterization 4079:This section has multiple issues. 3718:This section has multiple issues. 873:), or more complex associations. 560:This section has multiple issues. 431:cells are enclosed by a distinct 65:This article has multiple issues. 6488: 5968:Journal of Materials Chemistry A 5921:ACS Chemical Health & Safety 5574:Mechanical Behavior of Materials 4713: 4698: 4683: 4666: 4647: 4528: 4383: 4171: 4109: 4068: 3882: 3785: 3748: 3707: 3621: 3003: 1979: 1965: 1902: 995:where γ is the surface tension. 885: 702:relies largely or entirely on a 691: 636: 590: 549: 324: 259: 197: 95: 54: 4353:is found in the manufacture of 4182:needs additional citations for 4087:or discuss these issues on the 3726:or discuss these issues on the 2560:Bubble for hydrostatic pressure 1913:needs additional citations for 896:needs additional citations for 568:or discuss these issues on the 106:needs additional citations for 73:or discuss these issues on the 5701:Smart Materials and Structures 5674:10.1016/j.ijsolstr.2020.08.007 5425:. January 2009. Archived from 5356:Philosophical Magazine Letters 2874: 2848: 2412: 2386: 2316: 2303: 2134: 2108: 1986:Marangoni effect of a film (2) 1765: 1739: 1653: 1627: 1396: 1370: 1255: 1229: 1073: 1047: 951:(W) is needed to increase the 943:(surfactants) that reduce the 1: 6259:Foams: Structure and Dynamics 6139:. CRC Press. pp. 79–81. 5721:10.1088/0964-1726/20/8/085010 5548:10.1016/j.actamat.2004.05.039 5513:10.1016/j.actamat.2004.09.024 5210:Foams: Structure and Dynamics 4621:processes). For this reason, 4332:sandwich-structured composite 3906:secondary or tertiary sources 2445:is given by the equation of: 1110:is the volume of the bubble, 477:In most foams, the volume of 5572:Courtney, Thomas H. (2005). 4005:Liquid foams can be used in 4135:the claims made and adding 1134:is the density of the gas ρ 603:. The specific problem is: 223:the claims made and adding 6756: 6133:Ashida, Kaneyoshi (2006). 5615:Metallurgical Transactions 4765:Foam scales and properties 4731:Foam scales and properties 4517: 4507:reaction injection molding 4372: 4057: 2429:Deviations are due to the 1972:Marangoni effect of a film 1010:Rising bubble from orifice 38: 31: 6646:D'Arcy Wentworth Thompson 6486: 6337:Moriarty, Philip (2010). 5775:10.1016/j.jcs.2011.05.004 5763:Journal of Cereal Science 5457:. John Wiley & Sons. 5386:10.1080/09500830801992849 5343:. NY, USA: Marcel Dekker. 4770: 3319:{\displaystyle \rho _{s}} 3292:{\displaystyle \rho ^{*}} 2951:must be larger than the R 941:surface active components 865:structure, often made of 811:One scale is the bubble: 6351:University of Nottingham 5933:10.1021/acs.chas.2c00071 4606:, easily create foam on 4325:A closed-cell metal foam 1999:electrical double layers 474:is enclosed by another. 273:may need to be rewritten 5302:10.1351/goldbook.E02065 5080:Aluminium foam sandwich 4302:An open-cell metal foam 2546:{\displaystyle \gamma } 2247:acceleration of gravity 833:Weaire–Phelan structure 487:head on a glass of beer 443:and otherwise obsolete 275:. The reason given is: 5890:Gibson, Ashby (1999). 4691:Industrial CT scanning 4326: 4303: 4016:The dough of leavened 3985: 3893:relies excessively on 3600:Directional dependence 3587: 3430: 3320: 3293: 3266: 3239: 3212: 3183: 3079: 3049:of foams, compressive 2938: 2823: 2698: 2631: 2561: 2547: 2523: 2420: 2324: 2216: 2049: 1872: 1720: 1547: 1457: 1430: 1407: 1321: 1301: 1278: 1206: 1182: 1124: 1104: 1081: 1011: 986: 823:and three-dimensional 808: 655:by rewriting it in an 507:Foams are examples of 417: 409: 398: 343:by rewriting it in an 45:Foamy (disambiguation) 43:. For other uses, see 6480:Widmanstätten pattern 5832:10.3382/ps.2008-00268 5684:– via Elsevier. 5609:Ashby, M. F. (1983). 4920:double bubble theorem 4794:Transport properties 4324: 4301: 4058:Further information: 3983: 3588: 3443:Energy of deformation 3431: 3321: 3294: 3267: 3265:{\displaystyle C_{f}} 3240: 3238:{\displaystyle E^{*}} 3213: 3211:{\displaystyle E_{s}} 3184: 3076: 3047:mechanical properties 2990:Mechanical properties 2939: 2824: 2699: 2632: 2559: 2548: 2524: 2421: 2325: 2217: 2050: 2005:surfactants, and the 1873: 1721: 1548: 1458: 1456:{\displaystyle p_{0}} 1431: 1408: 1322: 1302: 1279: 1207: 1183: 1125: 1105: 1082: 1009: 987: 806: 613:WikiProject Chemistry 470:systems in which one 415: 404: 396: 34:Foam (disambiguation) 6170:The Physics of Foams 5432:on December 12, 2013 5155:The Physics of Foams 4971:double bubble theory 4552:improve this section 4459:shape memory polymer 4407:improve this section 4191:improve this article 3809:improve this section 3645:improve this section 3454: 3332: 3303: 3276: 3249: 3222: 3195: 3085: 3051:stress-strain curves 2839: 2749: 2642: 2575: 2537: 2452: 2340: 2260: 2062: 2039: 1995:van der Waals forces 1922:improve this article 1736: 1605: 1470: 1440: 1420: 1334: 1311: 1291: 1220: 1196: 1149: 1114: 1094: 1025: 962: 905:improve this article 815:foams are typically 715:improve this article 397:Top of a foamy drink 115:improve this article 6714:Mathematics and art 6704:Pattern recognition 6674:Aristid Lindenmayer 5974:(48). 20996–21009. 5713:2011SMaS...20h5010Y 5627:1983MTA....14.1755A 5540:2004AcMat..52.4229K 5505:2005AcMat..53..303Q 5378:2008PMagL..88..647M 4884:disjoining pressure 4623:anti-foaming agents 4486:closed-mold process 4463:composite materials 4449:. The advantage of 4007:fire retardant foam 2980:disjoining pressure 2243:dynamic viscosity 609:WikiProject Physics 6652:On Growth and Form 6552:Logarithmic spiral 6389:Patterns in nature 5981:10.1039/C4TA04787G 5635:10.1007/bf02645546 4474:Integral skin foam 4469:Integral skin foam 4327: 4304: 4120:possibly contains 4037:foam fractionation 3986: 3583: 3426: 3316: 3289: 3262: 3235: 3208: 3179: 3080: 2934: 2819: 2694: 2627: 2562: 2543: 2519: 2416: 2320: 2249:in units of cm/s. 2212: 2045: 1868: 1716: 1543: 1453: 1426: 1403: 1317: 1297: 1274: 1202: 1178: 1120: 1100: 1077: 1012: 982: 871:Pickering emulsion 809: 657:encyclopedic style 460:physical chemistry 418: 410: 399: 345:encyclopedic style 208:possibly contains 6722: 6721: 6679:Benoît Mandelbrot 6579:Self-organization 6515:Natural selection 6505:Pattern formation 6315:978-3-7776-1440-3 6304:978-3-87017-285-5 6146:978-1-58716-159-9 6110:10.1002/app.23969 6073:10.1002/app.28802 6046:10.1021/ie3006935 6040:(28): 9515–9530. 6009:10.1002/app.26922 5534:(14): 4229–4237. 5362:(9–10): 647–650. 5311:978-0-9678550-9-7 5070: 5069: 5065: 5064: 4908:Thin film balance 4705:Polystyrene foam 4598:, especially for 4596:chemical industry 4588: 4587: 4580: 4482:open-mold process 4443: 4442: 4435: 4289:reticulated foams 4285: 4284: 4277: 4267: 4266: 4259: 4241: 4165: 4164: 4157: 4122:original research 4102: 4048:Foam depopulation 3978: 3977: 3970: 3952: 3863: 3862: 3855: 3845: 3844: 3837: 3779: 3778: 3741: 3681: 3680: 3673: 3572: 3520: 3485: 3414: 3362: 3167: 3115: 3034: 3033: 2926: 2906: 2811: 2791: 2511: 2491: 2384: 2301: 2205: 2106: 2048:{\displaystyle r} 1954: 1953: 1946: 1860: 1840: 1820: 1800: 1708: 1688: 1535: 1515: 1429:{\displaystyle p} 1400: 1320:{\displaystyle V} 1300:{\displaystyle R} 1205:{\displaystyle r} 1123:{\displaystyle g} 1103:{\displaystyle V} 937: 936: 929: 798: 797: 790: 780: 779: 765: 685: 684: 677: 630: 629: 583: 391: 390: 383: 373: 372: 365: 318: 317: 310: 290:lead layout guide 253: 252: 245: 210:original research 191: 190: 183: 165: 88: 41:Foam depopulation 16:(Redirected from 6747: 6530:Sexual selection 6492: 6382: 6375: 6368: 6359: 6354: 6294: 6288: 6280: 6278: 6276: 6248: 6242: 6234: 6232: 6230: 6205: 6199: 6191: 6189: 6187: 6155: 6154: 6130: 6124: 6123: 6121: 6104:(3): 2015–2025. 6093: 6087: 6086: 6084: 6067:(5): 3217–3224. 6056: 6050: 6049: 6029: 6023: 6022: 6020: 5992: 5986: 5985: 5983: 5959: 5953: 5952: 5912: 5906: 5905: 5887: 5878: 5877: 5875: 5873: 5850: 5844: 5843: 5811: 5805: 5804: 5802: 5800: 5785: 5779: 5778: 5758: 5752: 5749: 5743: 5742: 5732: 5692: 5686: 5685: 5653: 5647: 5646: 5621:(9): 1755–1769. 5606: 5600: 5594: 5588: 5587: 5569: 5560: 5559: 5523: 5517: 5516: 5488: 5482: 5475: 5469: 5468: 5448: 5442: 5441: 5439: 5437: 5431: 5420: 5412: 5406: 5399: 5390: 5389: 5371: 5351: 5345: 5344: 5336: 5330: 5329: 5323: 5315: 5281: 5275: 5274: 5253: 5247: 5245: 5239: 5231: 5229: 5227: 5201: 5192: 5190: 5184: 5176: 5174: 5172: 5149: 5046:light scattering 5041:light scattering 5030:, bubble model, 5017:light scattering 4899:surface rheology 4851:surface rheology 4830:Surface rheology 4773: 4759: 4752: 4745: 4736: 4717: 4702: 4687: 4677:penetration seal 4670: 4651: 4583: 4576: 4572: 4569: 4563: 4532: 4524: 4476:, also known as 4438: 4431: 4427: 4424: 4418: 4387: 4379: 4280: 4273: 4262: 4255: 4251: 4248: 4242: 4240: 4199: 4175: 4167: 4160: 4153: 4149: 4146: 4140: 4137:inline citations 4113: 4112: 4105: 4094: 4072: 4071: 4064: 3973: 3966: 3962: 3959: 3953: 3951: 3910: 3886: 3878: 3874:Light scattering 3858: 3851: 3840: 3833: 3829: 3826: 3820: 3789: 3781: 3774: 3771: 3752: 3744: 3733: 3711: 3710: 3703: 3699:Characterization 3676: 3669: 3665: 3662: 3656: 3625: 3617: 3592: 3590: 3589: 3584: 3582: 3578: 3577: 3573: 3571: 3570: 3561: 3560: 3551: 3531: 3530: 3525: 3521: 3519: 3518: 3509: 3508: 3499: 3486: 3484: 3483: 3474: 3473: 3458: 3435: 3433: 3432: 3427: 3425: 3424: 3419: 3415: 3413: 3412: 3403: 3402: 3393: 3386: 3385: 3373: 3372: 3367: 3363: 3361: 3360: 3351: 3350: 3341: 3325: 3323: 3322: 3317: 3315: 3314: 3298: 3296: 3295: 3290: 3288: 3287: 3271: 3269: 3268: 3263: 3261: 3260: 3244: 3242: 3241: 3236: 3234: 3233: 3217: 3215: 3214: 3209: 3207: 3206: 3188: 3186: 3185: 3180: 3178: 3177: 3172: 3168: 3166: 3165: 3156: 3155: 3146: 3139: 3138: 3126: 3125: 3120: 3116: 3114: 3113: 3104: 3103: 3094: 3057:Elastomeric foam 3029: 3026: 3007: 2999: 2976:Laplace pressure 2972:osmotic pressure 2943: 2941: 2940: 2935: 2932: 2928: 2927: 2925: 2924: 2912: 2907: 2905: 2904: 2892: 2873: 2872: 2860: 2859: 2828: 2826: 2825: 2820: 2817: 2813: 2812: 2810: 2809: 2797: 2792: 2790: 2789: 2777: 2761: 2760: 2703: 2701: 2700: 2695: 2689: 2688: 2673: 2672: 2654: 2653: 2636: 2634: 2633: 2628: 2622: 2621: 2606: 2605: 2587: 2586: 2552: 2550: 2549: 2544: 2528: 2526: 2525: 2520: 2517: 2513: 2512: 2510: 2509: 2497: 2492: 2490: 2489: 2477: 2464: 2463: 2431:Marangoni effect 2425: 2423: 2422: 2417: 2411: 2410: 2398: 2397: 2385: 2383: 2382: 2381: 2368: 2367: 2366: 2350: 2329: 2327: 2326: 2321: 2315: 2314: 2302: 2300: 2299: 2298: 2285: 2284: 2283: 2270: 2221: 2219: 2218: 2213: 2210: 2206: 2204: 2203: 2202: 2187: 2186: 2173: 2172: 2171: 2156: 2155: 2142: 2133: 2132: 2120: 2119: 2107: 2105: 2104: 2103: 2090: 2089: 2088: 2072: 2054: 2052: 2051: 2046: 2007:Marangoni effect 1983: 1969: 1949: 1942: 1938: 1935: 1929: 1906: 1898: 1877: 1875: 1874: 1869: 1866: 1862: 1861: 1859: 1858: 1846: 1841: 1839: 1838: 1826: 1821: 1819: 1818: 1806: 1801: 1799: 1798: 1786: 1764: 1763: 1751: 1750: 1725: 1723: 1722: 1717: 1714: 1710: 1709: 1707: 1706: 1694: 1689: 1687: 1686: 1674: 1652: 1651: 1639: 1638: 1623: 1622: 1552: 1550: 1549: 1544: 1541: 1537: 1536: 1534: 1533: 1521: 1516: 1514: 1513: 1501: 1488: 1487: 1462: 1460: 1459: 1454: 1452: 1451: 1435: 1433: 1432: 1427: 1412: 1410: 1409: 1404: 1401: 1399: 1395: 1394: 1382: 1381: 1362: 1351: 1346: 1345: 1326: 1324: 1323: 1318: 1306: 1304: 1303: 1298: 1283: 1281: 1280: 1275: 1254: 1253: 1241: 1240: 1211: 1209: 1208: 1203: 1187: 1185: 1184: 1179: 1161: 1160: 1142:force, which is 1129: 1127: 1126: 1121: 1109: 1107: 1106: 1101: 1086: 1084: 1083: 1078: 1072: 1071: 1059: 1058: 1037: 1036: 991: 989: 988: 983: 932: 925: 921: 918: 912: 889: 881: 821:minimal surfaces 793: 786: 775: 772: 766: 764: 723: 695: 687: 680: 673: 669: 666: 660: 640: 639: 632: 625: 622: 616: 594: 593: 586: 575: 553: 552: 545: 386: 379: 368: 361: 357: 354: 348: 328: 327: 320: 313: 306: 302: 299: 293: 286:improve the lead 263: 262: 255: 248: 241: 237: 234: 228: 225:inline citations 201: 200: 193: 186: 179: 175: 172: 166: 164: 123: 99: 91: 80: 58: 57: 50: 21: 6755: 6754: 6750: 6749: 6748: 6746: 6745: 6744: 6725: 6724: 6723: 6718: 6692: 6585: 6493: 6484: 6391: 6386: 6336: 6327: 6321: 6281: 6274: 6272: 6270: 6252: 6235: 6228: 6226: 6224: 6209: 6192: 6185: 6183: 6181: 6166: 6163: 6161:Further reading 6158: 6147: 6132: 6131: 6127: 6095: 6094: 6090: 6058: 6057: 6053: 6031: 6030: 6026: 5994: 5993: 5989: 5961: 5960: 5956: 5914: 5913: 5909: 5902: 5889: 5888: 5881: 5871: 5869: 5852: 5851: 5847: 5820:Poultry Science 5813: 5812: 5808: 5798: 5796: 5795:. June 10, 2007 5787: 5786: 5782: 5760: 5759: 5755: 5750: 5746: 5694: 5693: 5689: 5655: 5654: 5650: 5608: 5607: 5603: 5595: 5591: 5584: 5571: 5570: 5563: 5528:Acta Materialia 5525: 5524: 5520: 5493:Acta Materialia 5490: 5489: 5485: 5476: 5472: 5465: 5450: 5449: 5445: 5435: 5433: 5429: 5418: 5414: 5413: 5409: 5400: 5393: 5353: 5352: 5348: 5338: 5337: 5333: 5316: 5312: 5283: 5282: 5278: 5267:Merriam-Webster 5261: 5258:Merriam-Webster 5254: 5250: 5232: 5225: 5223: 5221: 5203: 5202: 5195: 5177: 5170: 5168: 5166: 5151: 5150: 5137: 5133: 5076: 5071: 5066: 5028:Surface Evolver 4989:Liquid fraction 4876:Surface tension 4839:Langmuir trough 4766: 4763: 4733: 4726: 4718: 4709: 4703: 4694: 4693:of a foam ball 4688: 4679: 4671: 4662: 4652: 4643: 4633:, reduction of 4584: 4573: 4567: 4564: 4549: 4533: 4522: 4516: 4471: 4451:syntactic foams 4439: 4428: 4422: 4419: 4404: 4388: 4377: 4371: 4293:cellular solids 4281: 4270: 4269: 4268: 4263: 4252: 4246: 4243: 4200: 4198: 4188: 4176: 4161: 4150: 4144: 4141: 4126: 4114: 4110: 4073: 4069: 4062: 4056: 4045: 4033:froth flotation 4003: 3998: 3974: 3963: 3957: 3954: 3911: 3909: 3903: 3899:primary sources 3887: 3876: 3859: 3848: 3847: 3846: 3841: 3830: 3824: 3821: 3806: 3790: 3775: 3769: 3766: 3759:needs expansion 3753: 3712: 3708: 3701: 3693:hydraulic fluid 3677: 3666: 3660: 3657: 3642: 3626: 3615: 3602: 3562: 3552: 3546: 3536: 3532: 3510: 3500: 3494: 3493: 3475: 3459: 3452: 3451: 3445: 3404: 3394: 3388: 3387: 3377: 3352: 3342: 3336: 3335: 3330: 3329: 3306: 3301: 3300: 3279: 3274: 3273: 3252: 3247: 3246: 3225: 3220: 3219: 3198: 3193: 3192: 3157: 3147: 3141: 3140: 3130: 3105: 3095: 3089: 3088: 3083: 3082: 3059: 3039: 3030: 3024: 3021: 3014:needs expansion 3008: 2997: 2992: 2962: 2958: 2954: 2950: 2916: 2896: 2890: 2886: 2864: 2851: 2837: 2836: 2801: 2781: 2775: 2771: 2752: 2747: 2746: 2741: 2737: 2733: 2726: 2714: 2710: 2680: 2664: 2645: 2640: 2639: 2613: 2597: 2578: 2573: 2572: 2567: 2535: 2534: 2501: 2481: 2475: 2471: 2455: 2450: 2449: 2444: 2440: 2436: 2402: 2389: 2373: 2369: 2358: 2351: 2338: 2337: 2306: 2290: 2286: 2275: 2271: 2258: 2257: 2240: 2236: 2232: 2228: 2194: 2178: 2174: 2163: 2147: 2143: 2137: 2124: 2111: 2095: 2091: 2080: 2073: 2060: 2059: 2037: 2036: 2033: 2031:Destabilization 1991: 1990: 1989: 1988: 1987: 1984: 1975: 1974: 1973: 1970: 1959: 1950: 1939: 1933: 1930: 1919: 1907: 1896: 1888: 1884: 1850: 1830: 1810: 1790: 1784: 1780: 1755: 1742: 1734: 1733: 1698: 1678: 1672: 1668: 1643: 1630: 1614: 1603: 1602: 1593: 1586: 1579: 1571: 1567: 1563: 1559: 1525: 1505: 1499: 1495: 1479: 1468: 1467: 1443: 1438: 1437: 1418: 1417: 1386: 1373: 1363: 1352: 1337: 1332: 1331: 1309: 1308: 1307:and the volume 1289: 1288: 1245: 1232: 1218: 1217: 1194: 1193: 1152: 1147: 1146: 1140:surface tension 1137: 1133: 1112: 1111: 1092: 1091: 1063: 1050: 1028: 1023: 1022: 960: 959: 945:surface tension 933: 922: 916: 913: 902: 890: 879: 856:Plateau borders 794: 783: 782: 781: 776: 770: 767: 724: 722: 708: 696: 681: 670: 664: 661: 653:help improve it 650: 641: 637: 626: 620: 617: 607: 595: 591: 554: 550: 543: 509:dispersed media 441:medieval German 416:Cleaning sponge 387: 376: 375: 374: 369: 358: 352: 349: 341:help improve it 338: 329: 325: 314: 303: 297: 294: 283: 264: 260: 249: 238: 232: 229: 214: 202: 198: 187: 176: 170: 167: 124: 122: 112: 100: 59: 55: 48: 37: 30: 23: 22: 15: 12: 11: 5: 6753: 6751: 6743: 6742: 6737: 6727: 6726: 6720: 6719: 6717: 6716: 6711: 6706: 6700: 6698: 6694: 6693: 6691: 6690: 6689: 6688: 6676: 6671: 6670: 6669: 6657: 6656: 6655: 6643: 6641:Wilson Bentley 6638: 6636:Joseph Plateau 6633: 6628: 6623: 6622: 6621: 6609: 6604: 6599: 6593: 6591: 6587: 6586: 6584: 6583: 6582: 6581: 6576: 6574:Plateau's laws 6571: 6569:Fluid dynamics 6566: 6556: 6555: 6554: 6549: 6544: 6534: 6533: 6532: 6527: 6522: 6517: 6507: 6501: 6499: 6495: 6494: 6487: 6485: 6483: 6482: 6477: 6472: 6467: 6462: 6461: 6460: 6455: 6450: 6445: 6435: 6430: 6425: 6420: 6415: 6410: 6405: 6399: 6397: 6393: 6392: 6387: 6385: 6384: 6377: 6370: 6362: 6356: 6355: 6339:"Foam Physics" 6334: 6326: 6325:External links 6323: 6319: 6318: 6307: 6296: 6269:978-0199662890 6268: 6250: 6222: 6207: 6179: 6162: 6159: 6157: 6156: 6145: 6125: 6088: 6051: 6024: 6003:(1): 339–346. 5987: 5954: 5907: 5900: 5879: 5845: 5826:(5): 904–910. 5806: 5780: 5769:(2): 203–210. 5753: 5744: 5687: 5648: 5601: 5589: 5582: 5561: 5518: 5499:(2): 303–313. 5483: 5470: 5463: 5443: 5407: 5391: 5346: 5331: 5310: 5284:IUPAC (1997). 5276: 5248: 5220:978-0199662890 5219: 5193: 5164: 5134: 5132: 5129: 5128: 5127: 5122: 5117: 5112: 5107: 5102: 5097: 5092: 5090:Chaotic bubble 5087: 5085:Ballistic foam 5082: 5075: 5072: 5068: 5067: 5063: 5062: 5060: 5057: 5048: 5043: 5034: 5014: 5009: 5001:, avalanches, 4996: 4986: 4984: 4978: 4977: 4974: 4972: 4969: 4964: 4955: 4953: 4948: 4942: 4940:Plateau's laws 4936: 4934: 4928: 4927: 4924: 4922: 4917: 4912: 4910: 4904:Interferometry 4901: 4892: 4886: 4873: 4870: 4864: 4863: 4861: 4859: 4857: 4855: 4853: 4836: 4827: 4825: 4816: 4814: 4808: 4807: 4804: 4801: 4798: 4795: 4792: 4789: 4786: 4783: 4780: 4777: 4771: 4768: 4767: 4764: 4762: 4761: 4754: 4747: 4739: 4732: 4729: 4728: 4727: 4719: 4712: 4710: 4704: 4697: 4695: 4689: 4682: 4680: 4672: 4665: 4663: 4653: 4646: 4642: 4639: 4586: 4585: 4536: 4534: 4527: 4518:Main article: 4515: 4512: 4478:self-skin foam 4470: 4467: 4441: 4440: 4391: 4389: 4382: 4375:Syntactic foam 4373:Main article: 4370: 4369:Syntactic foam 4367: 4283: 4282: 4265: 4264: 4179: 4177: 4170: 4163: 4162: 4117: 4115: 4108: 4103: 4077: 4076: 4074: 4067: 4060:Polymeric foam 4055: 4052: 4044: 4041: 4002: 3999: 3997: 3994: 3976: 3975: 3890: 3888: 3881: 3875: 3872: 3861: 3860: 3843: 3842: 3793: 3791: 3784: 3777: 3776: 3756: 3754: 3747: 3742: 3716: 3715: 3713: 3706: 3700: 3697: 3679: 3678: 3629: 3627: 3620: 3614: 3613:Speed of sound 3611: 3601: 3598: 3581: 3576: 3569: 3565: 3559: 3555: 3549: 3545: 3542: 3539: 3535: 3529: 3524: 3517: 3513: 3507: 3503: 3497: 3492: 3489: 3482: 3478: 3472: 3469: 3466: 3462: 3444: 3441: 3423: 3418: 3411: 3407: 3401: 3397: 3391: 3384: 3380: 3376: 3371: 3366: 3359: 3355: 3349: 3345: 3339: 3313: 3309: 3286: 3282: 3259: 3255: 3232: 3228: 3205: 3201: 3176: 3171: 3164: 3160: 3154: 3150: 3144: 3137: 3133: 3129: 3124: 3119: 3112: 3108: 3102: 3098: 3092: 3058: 3055: 3038: 3035: 3032: 3031: 3011: 3009: 3002: 2996: 2993: 2991: 2988: 2960: 2956: 2952: 2948: 2945: 2944: 2931: 2923: 2919: 2915: 2910: 2903: 2899: 2895: 2889: 2885: 2882: 2879: 2876: 2871: 2867: 2863: 2858: 2854: 2850: 2847: 2844: 2830: 2829: 2816: 2808: 2804: 2800: 2795: 2788: 2784: 2780: 2774: 2770: 2767: 2764: 2759: 2755: 2739: 2735: 2731: 2724: 2712: 2708: 2705: 2704: 2692: 2687: 2683: 2679: 2676: 2671: 2667: 2663: 2660: 2657: 2652: 2648: 2637: 2625: 2620: 2616: 2612: 2609: 2604: 2600: 2596: 2593: 2590: 2585: 2581: 2565: 2542: 2531: 2530: 2516: 2508: 2504: 2500: 2495: 2488: 2484: 2480: 2474: 2470: 2467: 2462: 2458: 2442: 2438: 2434: 2427: 2426: 2414: 2409: 2405: 2401: 2396: 2392: 2388: 2380: 2376: 2372: 2365: 2361: 2357: 2354: 2348: 2345: 2331: 2330: 2318: 2313: 2309: 2305: 2297: 2293: 2289: 2282: 2278: 2274: 2268: 2265: 2238: 2234: 2230: 2226: 2223: 2222: 2209: 2201: 2197: 2193: 2190: 2185: 2181: 2177: 2170: 2166: 2162: 2159: 2154: 2150: 2146: 2140: 2136: 2131: 2127: 2123: 2118: 2114: 2110: 2102: 2098: 2094: 2087: 2083: 2079: 2076: 2070: 2067: 2044: 2032: 2029: 1985: 1978: 1977: 1976: 1971: 1964: 1963: 1962: 1961: 1960: 1958: 1955: 1952: 1951: 1910: 1908: 1901: 1895: 1892: 1886: 1882: 1879: 1878: 1865: 1857: 1853: 1849: 1844: 1837: 1833: 1829: 1824: 1817: 1813: 1809: 1804: 1797: 1793: 1789: 1783: 1779: 1776: 1773: 1770: 1767: 1762: 1758: 1754: 1749: 1745: 1741: 1727: 1726: 1713: 1705: 1701: 1697: 1692: 1685: 1681: 1677: 1671: 1667: 1664: 1661: 1658: 1655: 1650: 1646: 1642: 1637: 1633: 1629: 1626: 1621: 1617: 1613: 1610: 1591: 1584: 1577: 1569: 1565: 1561: 1557: 1554: 1553: 1540: 1532: 1528: 1524: 1519: 1512: 1508: 1504: 1498: 1494: 1491: 1486: 1482: 1478: 1475: 1450: 1446: 1425: 1414: 1413: 1398: 1393: 1389: 1385: 1380: 1376: 1372: 1369: 1366: 1361: 1358: 1355: 1349: 1344: 1340: 1316: 1296: 1285: 1284: 1272: 1269: 1266: 1263: 1260: 1257: 1252: 1248: 1244: 1239: 1235: 1231: 1228: 1225: 1201: 1190: 1189: 1176: 1173: 1170: 1167: 1164: 1159: 1155: 1135: 1131: 1119: 1099: 1088: 1087: 1075: 1070: 1066: 1062: 1057: 1053: 1049: 1046: 1043: 1040: 1035: 1031: 993: 992: 979: 976: 973: 970: 967: 935: 934: 893: 891: 884: 878: 875: 841:Plateau's laws 827:, also called 796: 795: 778: 777: 713:. Please help 699: 697: 690: 683: 682: 644: 642: 635: 628: 627: 598: 596: 589: 584: 558: 557: 555: 548: 542: 539: 423:are two-phase 389: 388: 371: 370: 332: 330: 323: 316: 315: 268:The article's 267: 265: 258: 251: 250: 205: 203: 196: 189: 188: 103: 101: 94: 89: 63: 62: 60: 53: 29:Form of matter 28: 24: 14: 13: 10: 9: 6: 4: 3: 2: 6752: 6741: 6738: 6736: 6733: 6732: 6730: 6715: 6712: 6710: 6707: 6705: 6702: 6701: 6699: 6695: 6687: 6686: 6682: 6681: 6680: 6677: 6675: 6672: 6668: 6667: 6663: 6662: 6661: 6658: 6654: 6653: 6649: 6648: 6647: 6644: 6642: 6639: 6637: 6634: 6632: 6631:Ernst Haeckel 6629: 6627: 6626:Adolf Zeising 6624: 6620: 6619: 6615: 6614: 6613: 6610: 6608: 6605: 6603: 6600: 6598: 6595: 6594: 6592: 6588: 6580: 6577: 6575: 6572: 6570: 6567: 6565: 6562: 6561: 6560: 6557: 6553: 6550: 6548: 6545: 6543: 6540: 6539: 6538: 6535: 6531: 6528: 6526: 6523: 6521: 6518: 6516: 6513: 6512: 6511: 6508: 6506: 6503: 6502: 6500: 6496: 6491: 6481: 6478: 6476: 6473: 6471: 6470:Vortex street 6468: 6466: 6463: 6459: 6456: 6454: 6451: 6449: 6448:Quasicrystals 6446: 6444: 6441: 6440: 6439: 6436: 6434: 6431: 6429: 6426: 6424: 6421: 6419: 6416: 6414: 6411: 6409: 6406: 6404: 6401: 6400: 6398: 6394: 6390: 6383: 6378: 6376: 6371: 6369: 6364: 6363: 6360: 6352: 6348: 6344: 6343:Sixty Symbols 6340: 6335: 6333: 6329: 6328: 6324: 6322: 6316: 6312: 6308: 6305: 6301: 6297: 6292: 6286: 6271: 6265: 6261: 6260: 6255: 6251: 6246: 6240: 6225: 6219: 6215: 6214: 6208: 6203: 6197: 6182: 6176: 6172: 6171: 6165: 6164: 6160: 6152: 6148: 6142: 6138: 6137: 6129: 6126: 6120: 6115: 6111: 6107: 6103: 6099: 6092: 6089: 6083: 6078: 6074: 6070: 6066: 6062: 6055: 6052: 6047: 6043: 6039: 6035: 6028: 6025: 6019: 6014: 6010: 6006: 6002: 5998: 5991: 5988: 5982: 5977: 5973: 5969: 5965: 5958: 5955: 5950: 5946: 5942: 5938: 5934: 5930: 5926: 5922: 5918: 5911: 5908: 5903: 5901:9781316025420 5897: 5893: 5886: 5884: 5880: 5868: 5864: 5860: 5856: 5849: 5846: 5841: 5837: 5833: 5829: 5825: 5821: 5817: 5810: 5807: 5794: 5790: 5784: 5781: 5776: 5772: 5768: 5764: 5757: 5754: 5748: 5745: 5740: 5736: 5731: 5726: 5722: 5718: 5714: 5710: 5706: 5702: 5698: 5691: 5688: 5683: 5679: 5675: 5671: 5667: 5663: 5659: 5652: 5649: 5644: 5640: 5636: 5632: 5628: 5624: 5620: 5616: 5612: 5605: 5602: 5598: 5593: 5590: 5585: 5583:1-57766-425-6 5579: 5575: 5568: 5566: 5562: 5557: 5553: 5549: 5545: 5541: 5537: 5533: 5529: 5522: 5519: 5514: 5510: 5506: 5502: 5498: 5494: 5487: 5484: 5480: 5474: 5471: 5466: 5464:9781119961093 5460: 5456: 5455: 5447: 5444: 5428: 5424: 5417: 5411: 5408: 5404: 5398: 5396: 5392: 5387: 5383: 5379: 5375: 5370: 5365: 5361: 5357: 5350: 5347: 5342: 5335: 5332: 5327: 5321: 5313: 5307: 5303: 5299: 5295: 5291: 5287: 5280: 5277: 5272: 5268: 5264: 5259: 5252: 5249: 5243: 5237: 5222: 5216: 5212: 5211: 5206: 5200: 5198: 5194: 5188: 5182: 5167: 5161: 5157: 5156: 5148: 5146: 5144: 5142: 5140: 5136: 5130: 5126: 5123: 5121: 5118: 5116: 5113: 5111: 5108: 5106: 5103: 5101: 5098: 5096: 5093: 5091: 5088: 5086: 5083: 5081: 5078: 5077: 5073: 5061: 5058: 5056: 5052: 5049: 5047: 5044: 5042: 5038: 5035: 5033: 5029: 5025: 5024:conductimetry 5021: 5018: 5015: 5013: 5010: 5008: 5004: 5000: 4997: 4994: 4990: 4987: 4985: 4983: 4980: 4979: 4975: 4973: 4970: 4968: 4967:Interferences 4965: 4963: 4959: 4956: 4954: 4952: 4949: 4947: 4943: 4941: 4937: 4935: 4933: 4930: 4929: 4925: 4923: 4921: 4918: 4916: 4915:Interferences 4913: 4911: 4909: 4905: 4902: 4900: 4896: 4893: 4890: 4887: 4885: 4881: 4877: 4874: 4872:Frankel's law 4871: 4869: 4866: 4865: 4862: 4860: 4858: 4856: 4854: 4852: 4848: 4844: 4840: 4837: 4835: 4831: 4828: 4826: 4824: 4820: 4817: 4815: 4813: 4810: 4809: 4805: 4803:Applications 4802: 4799: 4796: 4793: 4790: 4787: 4784: 4781: 4778: 4775: 4774: 4769: 4760: 4755: 4753: 4748: 4746: 4741: 4740: 4737: 4730: 4725: 4722: 4716: 4711: 4708: 4701: 4696: 4692: 4686: 4681: 4678: 4675: 4674:Silicone foam 4669: 4664: 4661:(memory) foam 4660: 4656: 4650: 4645: 4640: 4638: 4636: 4635:mass transfer 4632: 4631:contamination 4628: 4624: 4620: 4617: 4613: 4609: 4605: 4601: 4597: 4593: 4582: 4579: 4571: 4561: 4557: 4553: 4547: 4546: 4542: 4537:This section 4535: 4531: 4526: 4525: 4521: 4513: 4511: 4509: 4508: 4503: 4499: 4495: 4491: 4487: 4483: 4479: 4475: 4468: 4466: 4464: 4460: 4456: 4452: 4448: 4437: 4434: 4426: 4416: 4412: 4408: 4402: 4401: 4397: 4392:This section 4390: 4386: 4381: 4380: 4376: 4368: 4366: 4362: 4360: 4356: 4352: 4351:blowing agent 4347: 4345: 4341: 4335: 4333: 4323: 4319: 4317: 4311: 4309: 4300: 4296: 4294: 4290: 4279: 4276: 4261: 4258: 4250: 4247:December 2020 4239: 4236: 4232: 4229: 4225: 4222: 4218: 4215: 4211: 4208: – 4207: 4203: 4202:Find sources: 4196: 4192: 4186: 4185: 4180:This section 4178: 4174: 4169: 4168: 4159: 4156: 4148: 4145:December 2020 4138: 4134: 4130: 4124: 4123: 4118:This section 4116: 4107: 4106: 4101: 4099: 4092: 4091: 4086: 4085: 4080: 4075: 4066: 4065: 4061: 4053: 4051: 4049: 4042: 4040: 4038: 4034: 4029: 4027: 4023: 4019: 4014: 4012: 4008: 4000: 3995: 3993: 3989: 3982: 3972: 3969: 3961: 3950: 3947: 3943: 3940: 3936: 3933: 3929: 3926: 3922: 3919: – 3918: 3914: 3913:Find sources: 3907: 3901: 3900: 3896: 3891:This section 3889: 3885: 3880: 3879: 3873: 3871: 3869: 3857: 3854: 3839: 3836: 3828: 3818: 3814: 3810: 3804: 3803: 3799: 3794:This section 3792: 3788: 3783: 3782: 3773: 3764: 3760: 3757:This section 3755: 3751: 3746: 3745: 3740: 3738: 3731: 3730: 3725: 3724: 3719: 3714: 3705: 3704: 3698: 3696: 3694: 3689: 3685: 3675: 3672: 3664: 3661:December 2013 3654: 3650: 3646: 3640: 3639: 3635: 3630:This section 3628: 3624: 3619: 3618: 3612: 3610: 3607: 3599: 3597: 3593: 3579: 3574: 3567: 3563: 3557: 3553: 3547: 3543: 3540: 3537: 3533: 3527: 3522: 3515: 3511: 3505: 3501: 3495: 3490: 3487: 3480: 3476: 3470: 3467: 3464: 3460: 3449: 3442: 3440: 3436: 3421: 3416: 3409: 3405: 3399: 3395: 3389: 3382: 3378: 3374: 3369: 3364: 3357: 3353: 3347: 3343: 3337: 3327: 3311: 3307: 3284: 3280: 3257: 3253: 3230: 3226: 3203: 3199: 3189: 3174: 3169: 3162: 3158: 3152: 3148: 3142: 3135: 3131: 3127: 3122: 3117: 3110: 3106: 3100: 3096: 3090: 3075: 3071: 3069: 3064: 3056: 3054: 3052: 3048: 3043: 3036: 3028: 3019: 3015: 3012:This section 3010: 3006: 3001: 3000: 2994: 2989: 2987: 2985: 2981: 2977: 2973: 2969: 2964: 2929: 2921: 2917: 2913: 2908: 2901: 2897: 2893: 2887: 2883: 2880: 2877: 2869: 2865: 2861: 2856: 2852: 2845: 2842: 2835: 2834: 2833: 2814: 2806: 2802: 2798: 2793: 2786: 2782: 2778: 2772: 2768: 2765: 2762: 2757: 2753: 2745: 2744: 2743: 2730: 2727: − 2723: 2719: 2690: 2685: 2681: 2677: 2674: 2669: 2665: 2661: 2658: 2655: 2650: 2646: 2638: 2623: 2618: 2614: 2610: 2607: 2602: 2598: 2594: 2591: 2588: 2583: 2579: 2571: 2570: 2569: 2558: 2554: 2540: 2514: 2506: 2502: 2498: 2493: 2486: 2482: 2478: 2472: 2468: 2465: 2460: 2456: 2448: 2447: 2446: 2432: 2407: 2403: 2399: 2394: 2390: 2378: 2374: 2370: 2363: 2359: 2355: 2352: 2346: 2343: 2336: 2335: 2334: 2311: 2307: 2295: 2291: 2287: 2280: 2276: 2272: 2266: 2263: 2256: 2255: 2254: 2250: 2248: 2244: 2207: 2199: 2195: 2191: 2188: 2183: 2179: 2175: 2168: 2164: 2160: 2157: 2152: 2148: 2144: 2138: 2129: 2125: 2121: 2116: 2112: 2100: 2096: 2092: 2085: 2081: 2077: 2074: 2068: 2065: 2058: 2057: 2056: 2042: 2030: 2028: 2026: 2022: 2018: 2014: 2010: 2008: 2004: 2000: 1996: 1982: 1968: 1957:Stabilization 1956: 1948: 1945: 1937: 1927: 1923: 1917: 1916: 1911:This section 1909: 1905: 1900: 1899: 1893: 1891: 1863: 1855: 1851: 1847: 1842: 1835: 1831: 1827: 1822: 1815: 1811: 1807: 1802: 1795: 1791: 1787: 1781: 1777: 1774: 1771: 1768: 1760: 1756: 1752: 1747: 1743: 1732: 1731: 1730: 1711: 1703: 1699: 1695: 1690: 1683: 1679: 1675: 1669: 1665: 1662: 1659: 1656: 1648: 1644: 1640: 1635: 1631: 1624: 1619: 1615: 1611: 1608: 1601: 1600: 1599: 1597: 1590: 1587: − 1583: 1576: 1538: 1530: 1526: 1522: 1517: 1510: 1506: 1502: 1496: 1492: 1489: 1484: 1480: 1476: 1473: 1466: 1465: 1464: 1448: 1444: 1423: 1391: 1387: 1383: 1378: 1374: 1367: 1364: 1359: 1356: 1353: 1347: 1342: 1338: 1330: 1329: 1328: 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