Scaliing in Three-Dimensional Foams
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SCALIING
IN THIEE-DUIMENSIONAL
FOAMS
D.J. DURIANe t , D.A. WEITZ%, AND D.J. PINE' "*Departmentof Physics, University of California, Los Angeles, CA 90024 tExxon Research and Engineering Company, Rt. 22 E, Annandale, NJ 08801
ABSTACT 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 (20am). 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. INTRODUCTION Foams are cellular materials which consist of a random dispersion of gas bubbles in a small volume fraction of liquid 1 . They have a wide variety of uses based on their low density, high interfacial surface area, and their unusual rheological properties. In all such applications, however, the useful lifetime of the foam is limited since all foams are unstable and tend to coarsen over time. Scientifically, foams remain of current interest in part because neither the fundamental origin of their unique rheological behavior nor the physical mechanisms which affect their stability are well understood 2 . Experimental study of such questions has traditionally been hampered by lack of direct, noninvasive probes of foam structure and dynamics. Since foams are intrinsically opaque, all attempts to optically image foam structure have previously been restricted to surface bubbles. In this report, we exploit the strong multiple light scattering character of foams to develop quantitative probes of both the structure and internal dynamics of foam. We use these new techniques follow the time evolution of a three dimensional foam which coarsens by diffusion of gas from smaller to larger
Mat. Res. Soc. Symp. Proc. Vol. 248. 01992 Materials Res
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