Simple shearing flow of dry soap foams with tetrahedrally close-packed structure

Journal of Rheology

Volumn 44, Issue 3, 2000, Pages 453-471

  Reinelt, Douglas A ^a   Kraynik, Andrew M ^b  

^a SOUTHERN METHODIST UNIVERSITY   (United States)

^b SANDIA NATIONAL LABORATORIES   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ELASTOPLASTICITY; FOAMS; INTERFACIAL ENERGY; SHEAR FLOW; STRESSES; SURFACE STRUCTURE; SURFACE TENSION; TOPOLOGY;

DRY SOAP FOAMS; MACROSCOPIC STRESS; PLATEAU LAWS; POLYHEDRAL FOAM CELL; SURFACE EVOLVER; TETRAHEDRALLY CLOSE PACKED STRUCTURE;

RHEOLOGY;

EID: 0033703241     PISSN: 01486055     EISSN: None     Source Type: Journal    
DOI: 10.1122/1.551096     Document Type: Article

References (49)

1. Brakke, K. A., "The surface evolver," Exp. Math. 1, 141-165 (1992).
2. Bolton, F. and D. Weaire, "The effects of Plateau borders in the two-dimensional soap froth. II. General simulation and analysis of rigidity loss transition," Philos. Mag. B 65, 473-487 (1992).
3. Durian, D. J., "Bubble-scale model of foam mechanics: melting, nonlinear behavior, and avalanches," Phys. Rev. E 55, 1739-1751 (1997).
4. Gardiner, B. G., "Rheology and coarsening of aqueous foams," Ph.D. thesis, The University of Newcastle, NSW, Australia, 1999.
5. Gonzalez-Santos, J. G., "A numerical study of simple shearing flow of foams," Ph.D. thesis, Southern Methodist University, Dallas, TX, 1998.
6. Gopal, A. D. and D. J. Durian, "Nonlinear bubble dynamics in a slowly driven foam," Phys. Rev. Lett. 75, 2610-2613 (1995).
7. Gopal, A. D. and D. J. Durian, "Shear-induced "melting" of an aqueous foam," J. Colloid Interface Sci. 213, 169-178 (1999).
8. Herdtle, T., "Numerical studies of foam dynamics." Ph.D. thesis, University of California at San Diego, La Jolla, CA, 1991.
9. Hutzler, S., D. Weaire, and F. Bolton, "The effects of Plateau borders in the two-dimensional soap froth. III. further results," Philos. Mag. B 71, 277-289 (1995).
10. Kelvin, Lord (W. Thompson), "On the division of space with minimum partitional area," Philos. Mag. 24, 503-514 (1887).
11. Kraynik, A. M., "Foam flows," Annu. Rev. Fluid Mech. 20, 325-357 (1988).
12. Kraynik, A. M. and M. G. Hansen, "Foam and emulsion rheology: a quasistatic model for large deformations of spatially-periodic cells," J. Rheol. 30, 409-439 (1986).
13. Kraynik, A. M., M. K. Neilsen, D. A. Reinelt, and W. E. Warren, "Foam micromechanics: structure and rheology of foams, emulsions, and cellular solids," in Foams and Emulsions, edited by J. F. Sadoc and N. Rivier, Proceedings of the school on foams, emulsions, and cellular materials, Cargese, France, May 11-14, 1997 (Kluwer, Boston, 1999a), pp. 259-286.
14. Kraynik, A. M. and D. A. Reinelt, "Elastic-plastic behavior of a Kelvin foam," FORMA 11, 255-270 (1996a).
15. Kraynik, A. M. and D. A. Reinelt, The Kelvin Problem: Foam Structures of Minimal Surface Area, edited by D. Weaire (Taylor and Francis, London, 1996b), pp. 93-108.
16. Kraynik, A. M. and D. A. Reinelt, "Linear elastic behavior of dry soap foams," J. Colloid Interface Sci. 181, 511-520 (1996c).
17. Kraynik, A. M. and D. A. Reinelt, "The microrheology of wet foams." in Proceedings of XIIth International Congress on Rheology, edited by A. Ait-Kadi, J. M. Dealy, D. F. James, and M. C. Williams, Quebec City, Canada, August 18-23, 1996d, pp. 625-626.
18. Kraynik, A. M. and D. A. Reinelt, "Foam microrheology: from honeycombs to random foams," Proceedings of the 15th Annual Meeting of the Polymer Processing Society (on CD-ROM). 's-Hertogenbosch, The Netherlands, May 31-June 4, 1999.
19. Kraynik, A. M., D. A. Reinelt, and M. Loewenberg, "Foam microrheology," Foams and Films, edited by D. Weaire and J. Banhart, Proceedings of the International Workshop of Foams and Films, Leuven, Belgium, March 5-6, 1999b, pp. 97-104.
20. Lacasse, M.-D., G. S. Grest, D. Levine, T. G. Mason, and D. A. Weitz, "Model for the elasticity of compressed emulsions." Phys. Rev. Lett. 76, 3448-3451 (1996a).
21. Lacasse, M.-D., G. S. Grest, and D. Levine, "Deformation of small compressed droplets" Phys. Rev. E 54, 5436-5446 (1996b).
22. Li, X., R. Charles, and C. Pozrikides, "Simple shear flow of suspensions of liquid drops," J. Fluid Mech. 320, 395-416 (1996).
23. Loewenberg, M., "Numerical simulation of concentrated emulsion flows," J. Fluids Eng. 120, 824-832 (1998).
24. Love, A. E. H., A Treatise on the Mathematical Theory of Elasticity (Dover, New York, 1994).
25. Mason, T. G., J. Bibette, and D. A. Weitz, "Elasticity of compressed emulsions," Phys. Rev. Lett. 75, 2051-2054 (1995).
26. Mason, T. G., J. Bibette, and D. A. Weitz, "Yielding and flow of monodisperse emulsions," J. Colloid Interface Sci. 179, 439-448 (1996).
27. Mason, T. G., M.-D. Lacasse, G. S. Grest, D. Levine, J. Bibette, and D. A. Weitz, "Osmotic pressure and viscoelastic shear moduli of concentrated emulsions," Phys. Rev. E 56, 3150-3166 (1997).
28. Matzke, E. B., "The three-dimensional shape of bubbles in foam-an analysis of the role of surface forces in three-dimensional cell shape determination," Am. J. Botany 33, 58-80 (1946).
29. Monnereau, C. and M. Vignes-Adler, "Optical tomography of real three-dimensional foams," J. Colloid Interface Sci. 202, 45-53 (1998a).
30. Monnereau, C. and M. Vignes-Adler, "Dynamics of real 3D foam coarsening," Phys. Rev. Lett. 80, 5228-5231 (1998b).
31. Monnereau-Pittet, C., and M. Vignes-Adler, "Topology of three-dimensional soap foams," in Foams and Films, edited by D. Weaire and J. Banhart, Proceedings of the International Workshop of Foams and Films, Leuven, Belgium, March 5-6, 1999, pp. 79-82.
32. Nye, J. F., Physical Properties of Crystals (Clarendon, Oxford, 1985).
33. Plateau, J. A. F., Statique Experimentale et Theorique des Liquides Soumis aux Seules Forces Moleculaires (Gauthier-Villiard, Paris, 1873).
34. Princen, H. M., "Rheology of foams and highly concentrated emulsions: I. Elastic properties and yield stress of a cylindrical model system," J. Colloid Interface Sci. 91, 160-175 (1983).
35. Princen, H. M., "Rheology of foams and highly concentrated emulsions: II. Experimental study of the yield stress and wall effects for concentrated oil-in-water emulsions," J. Colloid Interface Sci. 105, 150-171 (1985).
36. Princen, H. M. and A. D. Kiss, "Rheology of foams and highly concentrated emulsions: III. Static shear modulus." J. Colloid Interface Sci. 112, 427-437 (1986).
37. Princen, H. M. and A. D. Kiss, "Rheology of foams and highly concentrated emulsions. IV. An experimental study of the shear viscosity and yield stress of concentrated emulsions." J. Colloid Interface Sci. 128, 176-187 (1989).
38. Prud'homme, R. K., and S. A. Khan, Eds., Foams: Theory, Measurements, and Applications, Surfactant Science Series, Vol. 57 (Marcel Dekker, New York, 1995).
39. Reinelt, D. A. and A. M. Kraynik, "Large elastic deformations of three-dimensional foams and highly concentrated emulsions," J. Colloid Interface Sci. 159, 460-470 (1993).
40. Reinelt, D. A. and A. M. Kraynik, "Simple shearing flow of a dry Kelvin soap foam," J. Fluid Mech. 311, 327-343 (1996).
41. Rivier, N., "Kelvin's conjecture on minimal froths and the counter-example of Weaire and Phelan," Philos. Mag. Lett. 69, 297-303 (1994).
42. Saint-Jalmes, A. and D. J. Durian, "Vanishing elasticity for wet foams: equivalence with emulsions and role of polydispersity," J. Rheol. 43, 1411-1422 (1999).
43. Schwarz, H. W., "Rearrangements in polyhedric foam," Recueil 84, 771-781 (1964).
44. Taylor, J. E., "The structure of singularities in soap-bubble-like and soap-film-like minimal surfaces," Ann. Math. 103, 489-539 (1976).
45. Weaire, D. and M. A. Fortes, "Stress and strain in liquid and solid foams," Adv. Phys. 43, 685-738 (1994).
46. Weaire, D. and T-L. Fu. "The mechanical behavior of foams and emulsions," J. Rheol. 32, 271-283 (1988).
47. Weaire, D. and J. P. Kermode, "Computer simulation of a two-dimensional soap froth. II. Analysis of results," Philos. Mag. B 50, 379-395 (1984).
48. Weaire, D. and R. Phelan, "A counter-example to Kelvin's conjecture on minimal surfaces," Philos. Mag. Lett. 69, 107-110 (1994).
49. Zinchenko, A. Z.. M. A. Rother, and R. H. Davis, "A novel boundary-integral algorithm for viscous interaction of deformable drops," Phys. Fluids 9, 1493-1511 (1997).