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Scaliing in Three-Dimensional Foams

Published online by Cambridge University Press:  25 February 2011

D.J. Durian ,
D.A. Weitz  and
D.J. Pine
D.J. Durian
Affiliation:
Department of Physics, University of California, Los Angeles, CA 90024 Exxon Research and Engineering Company, Rt. 22 E, Annandale, NJ 08801
D.A. Weitz
Affiliation:
Exxon Research and Engineering Company, Rt. 22 E, Annandale, NJ 08801
D.J. Pine
Affiliation:
Exxon Research and Engineering Company, Rt. 22 E, Annandale, NJ 08801
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Abstract

The coarsening and internal dynamics of a bulk foam are probed noninvasively by exploiting the strong multiple scattering of light that gives foams their familiar white color. By approximating the light propagation as a diffusion process, transmission measurements provide a direct probe of the average bubble size d. A second corroborating measure of d is obtained by analyzing temporal intensity fluctuations of the multiply scattered light within the framework of diffusing-wave spectroscopy. Both sets of measurements show the same behavior: At early times d is approximately a constant (20µm). After about twenty minutes the foam begins to coarsen and scaling behavior is observed such that the growth of d is a power-law in time, tz with z=0.45±0.05. This result is in near accord with the theoretical prediction, z=1/2, for foam in the limiting case of space-filling polyhedral bubbles. In addition, the change in packing conditions during coarsening gives rise to a nonequilibrium dynamical process which also exhibits temporal scaling: Neighboring bubbles undergo sudden structural rearrangements at a rate per unit volume which decays as t−Y with y=2.0±0.2. This value of y cannot be explained by the presence of only a single time-dependent length scale in the foam structure. Since these bubble rearrangement events serve to relax local stress, they must also play a role in the relaxation of externally imposed stress. Therefore, elucidation of their origin and scaling behavior will lead to an increased understanding of the rheology and stability of foams.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 248: Symposium O – Complex Fluids , 1991 , 295
Copyright
Copyright © Materials Research Society 1992

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