The coarsening of a three-dimensional foam is studied with multiple light-scattering techniques. Scaling behavior is observed with the average bubble diameter growing in time as t(z) where z = 0.45 /- 0.05. Changes in the packing conditions during coarsening give rise to a dynamical process that also exhibits temporal scaling. Neighboring bubbles undergo sudden structural rearrangement events at a rate per unit volume that decays as t(-y) where y = 2.0 /- 0.2.
The structure and dynamics of three-dimensional foams are probed quantitatively by exploiting the strong multiple scattering of light that gives foams their familiar white color. Approximating the propagation of light as a diffusion process, transmission measurements provide a direct probe of the average bubble size. A model for dynamic light scattering is developed that can be used to interpret temporal fluctuations in the intensity of multiply scattered light. The results identify previously unrecognized internal dynamics of the foam bubbles. These light-scattering techniques are direct, noninvasive probes of bulk foams and therefore should find wide use in the study of their properties.
We show that diffusing-wave spectroscopy can be used as a non-invasive probe of the bulk properties of three-dimensional foams. A new picture accounting for the origin of the temporal fluctuations of multiply scattered light is developed and corroborated with direct observations through a microscope. Our interpretation and measurements yield the growth law for the coarsening of foam bubbles and new insight into their dynamics.