skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

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

Abstract

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,more » 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.« less

Authors:
 [1];  [2]
  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)
Publication Date:
OSTI Identifier:
20216308
Resource Type:
Journal Article
Journal Name:
Journal of Rheology
Additional Journal Information:
Journal Volume: 44; Journal Issue: 3; Other Information: PBD: May 2000; Journal ID: ISSN 0148-6055
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; FOAMS; SOAPS; SHEAR PROPERTIES; RHEOLOGY; SURFACE TENSION; STRESS ANALYSIS; BIFURCATION; STRAINS; THEORETICAL DATA

Citation Formats

Reinelt, Douglas A., and Kraynik, Andrew M. Simple shearing flow of dry soap foams with tetrahedrally close-packed structure. United States: N. p., 2000. Web. doi:10.1122/1.551096.
Reinelt, Douglas A., & Kraynik, Andrew M. Simple shearing flow of dry soap foams with tetrahedrally close-packed structure. United States. doi:10.1122/1.551096.
Reinelt, Douglas A., and Kraynik, Andrew M. Mon . "Simple shearing flow of dry soap foams with tetrahedrally close-packed structure". United States. doi:10.1122/1.551096.
@article{osti_20216308,
title = {Simple shearing flow of dry soap foams with tetrahedrally close-packed structure},
author = {Reinelt, Douglas A. and Kraynik, Andrew M.},
abstractNote = {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.},
doi = {10.1122/1.551096},
journal = {Journal of Rheology},
issn = {0148-6055},
number = 3,
volume = 44,
place = {United States},
year = {2000},
month = {5}
}