Abstract
This is an introduction to fluid foams for non-specialists. After presenting some applications and modeling of foams in general, we focus on ideal two-dimensional fluid foams at equilibrium. We discuss : the interplay of topology, geometry and forces; the central role of pressure and energy; an analogy with 2D electrostatics; the role of disorder; the minimal perimeter problem.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aref, H., D. Vainchtein (2000): ‘The equation of state of a foam’, Phys. Fluids, 12, pp. 23–28 contains two demonstrations. Two simpler demonstrations were then successively proposed by us, in [15], and by Fortes, M. (2001): ‘The surface energy of finite clusters of soap bubbles’, Phys. Fluids, 13, pp. 3542–3546. Note that it was presented as an already old conjecture in Ross, S. (1969): ‘Bubbles and Foam, Ind. Eng. Chem., 61, p. 48 sqq.
Aste, T., D. Boosé, N. Rivier (1996): ‘From one bubble to the whole froth: A dynamical map’, Phys. Rev. E 53, 6181–6191.
Aubert, J., A. Kraynik, P. Rand (1986): ‘Les mousses aqueuses’, Pour la Science Juillet 1986 pp. 62–71
Berge, B., A. Simon, A. Libchaber (1990): ‘Dynamics of gas bubbles in monolayers’, Phys. Rev. A 41 pp. 6893–6900.
Courty, S. (2001): Solides bidimensionnels à la surface de l’eau: étudemécanique et optique, PhD dissertation, University of Grenoble, unpublished.
(2001): ‘Décapants pour four’, Que Choisir mars 2001, 380, pp. 53–57.
Elias, F., C. Flament, J.-C. Bacri, O. Cardoso, F. Graner (1997): ‘Two-dimensional magnetic froth: Coarsening and topological correlations’, Phys. Rev. E, 56, pp. 3310–3318.
Elias, F., C. Flament, J. A. Glazier, F. Graner, Y. Jiang (1999): ‘Foams out of stable equilibrium: cell elongation and side-swapping’, Phil. Mag. B 79, pp. 729–751.
Emmer, M. (1991): Bolle di saponi: un viaggio tra arte, scienzia a fantasia (La Nuova Italia Editrice, Scandicci, Firenze).
Fortes, M., P. Teixeira (2001): ‘Minimum perimeter partitions of the plane into equal numbers of regions of two different areas’, Eur. Phys. J. E 6, 131–138.
de Gennes, P.-G. (2000): Les mousses, Cours au Collège de France, Paris, unpublished.
Glazier, J.A (1989): Dynamics of Cellular Patterns, Ph.D. dissertation, University of Chicago, unpublished.
Glazier, J.A., D. Weaire (1992): ‘The kinetics of cellular patterns’, J. Phys.: Cond. Matt. 4, pp. 1867–1894.
Graner, F. (2001): ‘La mousse’, La Recherche, 345, pp. 46–49.
Graner F, Y. Jiang, E. Janiaud, C. Flament (2001): ‘Equilibrium states and ground state of two-dimensional fluid foams’. Phys. Rev. E, 63 pp. 011402/1–13
Graustein, W.C. (1931): ‘On the average number of sizes of polygons in a net’, Annals of Math. 32, pp. 149–153. The demonstration is based on Euler theorem, applied here to a non simply-convex foam (e.g. on a torus) [12, 25].
Hales T. C. (2001): ‘The honeycomb conjecture’ Discrete Comput. Geom. 25, pp. 1–25; see also Science News, July 24, 1999; Klarreich E., American Scientist 88, March–April 2000, 152.
Hutchings, M., F. Morgan, M. Ritoré, A. Ros (2000): ‘Proof of the doublebubble conjecture’, Electron. Res. Announc. Amer. Math. Soc., 6 pp. 45–49, www.ugr.es/~ritore/bubble/bubble.htm. See also Morgan, F. (2001): ‘Proof of the double bubble conjecture’ American Mathematical Monthly, 108 (March 2001), pp. 193–205.
Hutzler, S., D. Weaire (1999): Physics of Foams (Oxford University Press, Oxford).
Morgan F. (2000): Geometric Measure Theory: a Beginner’s Guide, revised 3rd ed. (Academic Press, Boston).
Jiang, Y., M. Asipauskas, J.A. Glazier, M. Aubouy, F. Graner (2000): ‘Ab initio derivation of stress and strain in fluid foams’, in [40], pp. 297–304.
Landau, L.D., E.M. Lifschitz (1973): Teoriya Polia (Nauka, Moscow); english translation: The classical theory of fields, fourth revised edition, 2000 (Reed Elsevier, Oxford), chapter 5, p. 95.
von Neumann J. (1952): ‘Discussion’, in: Metal Interfaces, ed. C. Herring (American society for metals, Cleveland Ohio) pp. 108–110, quoted e.g. in [12, 13].
Plateau, J (1873): Statique Expérimentale et Théorique des Liquides Soumis aux Seules Forces Moléculaires (Gauthier-Villars, Paris).
Rivier, N. (1993): ‘Order and disorder in packings and froths’. In: Disorder and granular media, eds. D. Bideau, A. Hansen, (Elsevier Science Publ., Amsterdam), pp. 55–102.
Sadoc J.-F., N. Rivier eds. (1999): Foams and Emulsions, Proceedings of 1997 summer school, Cargèse, France (Nato ASI series E, Kluwer, Dordrecht).
Sandre, O. (1999): unpublished pictures.
Schliecker G., S. Klapp (1999): Europhys. Lett., 48, p. 122.
Seul, M., D. Andelman (1995): ‘Domain Shapes and Patterns: The Phenomenology of Modulated Phases’, Science 267 pp. 476–483.
Smith, C.S (1952): ‘Grain shapes and other metallurgical applications of topology’, in: Metal Interfaces, ed. C. Herring (American society for metals, Cleveland Ohio) pp. 65–108. Smith’s notations E 0, E b correspond respectively to v + and v + + v −, respectively.
Teixeira P., F. Graner, M. Fortes (2002): ‘Mixing and sorting of bidisperse two-dimensional bubbles’, preprint.
Vaz M.F., F. Graner, M. Fortes (2002): ‘Energy of free clusters of bubbles’, preprint.
Vignes-Adler, M., F. Graner (2002): ‘La vie éphémère des mousses’, Pour la Science, 293, pp. 48–55.
Weaire, D. (1995): De la bulle à la mousse’, La Recherche 273 (mars 1995) pp. 246–252.
Weaire, D. ed. (1997): The Kelvin problem (Taylor and Francis, London).
Weaire, D., J. Banhart (1999): Foams and Films, Proceedings of 1999 internationalworkshop on foams and films, Leuven, Belgium (MIT Verlag, Bremen).
Weaire, D., F. Bolton, P. Molho, J.A. Glazier (1991): ‘Investigation of an elementary model for magnetic froth’, J. Phys.: Cond. Matt. 3, pp. 2101–2114.
Weaire, D., S.J. Cox, F. Graner (2002): ‘On the non-uniqueness of foam equilibrium geometry’, Eur. Phys. J. E, to appear.
Weaire, D., N. Rivier (1984): ‘Soap, Cells and Statistics-Random Patterns in Two Dimensions’. Contemp. Phys. 25, pp. 59–99.
Zitha, P., J. Banhart, G. Verbist (2000): Foams, Emulsions and their Applications, Proceeding of the Eurofoam 2000 conference, Delft, Netherlands (MIT Verlag, Bremen).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Graner, F. (2002). Two-Dimensional Fluid Foams at Equilibrium. In: Mecke, K., Stoyan, D. (eds) Morphology of Condensed Matter. Lecture Notes in Physics, vol 600. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45782-8_8
Download citation
DOI: https://doi.org/10.1007/3-540-45782-8_8
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-44203-5
Online ISBN: 978-3-540-45782-4
eBook Packages: Springer Book Archive