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

Journal Article · Mon May 01 04:00:00 EDT 2000 · Journal of Rheology

DOI:https://doi.org/10.1122/1.551096· OSTI ID:20216308

Reinelt, Douglas A ^[1]; Kraynik, Andrew M ^[2]

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1. Department of Mathematics, Southern Methodist University, Dallas, Texas 75275-0156 (United States)
2. Engineering Sciences Center, Sandia National Laboratories, Albuquerque, New Mexico 87185-0834 (United States)

The microrheology of dry soap foams subjected to quasistatic, simple shearing flow is analyzed. Two different monodisperse foams with tetrahedrally close-packed (TCP) structure are examined: Weaire-Phelan (A15) and Friauf-Laves (C15). The elastic-plastic response is evaluated by using the Surface Evolver to calculate foam structures that minimize total surface area at each value of strain. The foam geometry and macroscopic stress are piecewise continuous functions of strain. The stress scales as T/V{sup 1/3}, where T is surface tension and V is cell volume. Each discontinuity corresponds to large changes in foam geometry and topology that restore equilibrium to unstable configurations that violate Plateau's laws. The instabilities occur when the length of an edge on a polyhedral foam cell vanishes. The length can tend to zero smoothly or abruptly with strain. The abrupt case occurs when a small increase in strain changes the energy profile in the neighborhood of a foam structure from a local minimum to a saddle point, which can lead to symmetry-breaking bifurcations. In general, the new structure associated with each stable solution branch results from an avalanche of local topology changes called T1 transitions. Each T1 cascade produces different cell neighbors, reduces surface energy, and provides an irreversible, film-level mechanism for plastic yield behavior. Stress-strain curves and average stresses are evaluated by examining foam orientations that admit strain-periodic behavior. For some orientations, the deformation cycle includes Kelvin cells instead of the original TCP structure; but the foam does not remain perfectly ordered. Bifurcations during subsequent T1 cascades lead to disorder and can even cause strain localization. (c) 2000 Society of Rheology.

• OSTI ID: 20216308
• Journal Information: Journal of Rheology, Journal Name: Journal of Rheology Journal Issue: 3 Vol. 44; ISSN JORHD2; ISSN 0148-6055
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BIFURCATION
FOAMS
RHEOLOGY
SHEAR PROPERTIES
SOAPS
STRAINS
STRESS ANALYSIS
SURFACE TENSION
THEORETICAL DATA