Tuesday, 12 October 2004 - 10:05 AM

This presentation is part of : Torquato Symposium

Structure and Rheology of Random Foam

Andrew M. Kraynik1, Douglas A. Reinelt2, and Frank Van Swol1. (1) Sandia National Laboratories, Dept 9114 MS0834, Albuquerque, NM 87185-0834, (2) Southern Methodist University, Department of Mathematics, Dallas, TX 75275-0156

The equilibrium microstructure of dry soap foams is calculated with Brakke's Surface Evolver for spatially periodic systems that contain up to 1728 cells. Initial conditions are based on weighted-Voronoi (Laguerre) tessellations of hard spheres that have been jammed together in molecular dynamics simulations. The cell-size distribution, which varies from monodisperse to highly polydisperse, is controlled through the size distribution of spheres. Topological and geometric statistics that characterize the fully relaxed foam structures and individual cells are evaluated. Quantities of interest include: faces per cell F; edges per face n; cell volumes V; and various areas, edge lengths, and shape functions. The simulations are in excellent agreement with the distribution functions and inventory of cell types obtained by Matzke in his seminal experiments on monodisperse foam. The connection between macroscopic rheological behavior and foam structure will also be discussed. Under quasi-static conditions, foams exhibit elastic-plastic behavior; the stress scales as σ/R where σ is surface tension and R is a characteristic length related to cell size. The shear modulus is in excellent agreement with experimental data of Princen and Kiss: increasing polydispersity makes the foam softer. The nonlinear elastic response follows Mooney-Rivlin behavior with N1 > -N2. The elastic limit and other yield phenomena involve intermittent cascades of topological transitions; this cell-neighbor switching is a fundamental mechanism of foam flow.

Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

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