Bubble rearrangement dynamics and light transport in aqueous foams

The general scope of this work investigates two essential, yet surprisingly elusive, properties of aqueous foams. The first concerns how multiply scattered light is transported throughout the foam. The second concerns the dynamics of bubble rearrangement events for coarsening foams.;The absorption of diffuse photons in aqueous foams is measured by adding a dye to the continuous liquid phase. For very wet and for dry foams, the absorption of the diffuse photons equals the absorption length of the liquid divided by the liquid volume fraction, indicating photons propagate by a random walk, sampling each phase in proportion to its volume. Foams of intermediate wetness, by contrast, absorb photons more strongly than expected, indicating photons have a higher probability for being transported in the network. This suggests novel transport effects such as photons that enter a border in a state that only allows internal reflection for the border length. We further investigate light transport in foams by considering a two-dimensional model foam with scattering described by geometric optics and the Fresnel equations. Here we develop theoretical results for bulk transport quantities, such as the scattering length, in terms of the basic microscopic structural elements of the foam. Results are compared with a computer simulation. Essential to this work is determining key quantities, such as the scattering length, for each phase separately. The transport quantity for the foam is then constructed from the phase dependant parts using probability weights. The probability weights represent the probability that a diffuse photon scatters at network and disperse incidence, and are determined simply in terms of the index of refraction for the liquid and gas.;Study of bubble rearrangement dynamics for coarsening foams proceeds in two steps. First, simultaneous measurement of second and three-time temporal intensity correlations are performed to test the validity of Diffusing-Wave Spectroscopy (DWS). We find that the electric field is Gaussian, and hence DWS is valid, for typical experimental geometries equivalent to illumination and detection with a plane wave, both for backscattering and transmission through an optically-thick slab. However, we find that the Gaussian character breaks down for point-in/point-out backscattering geometries in which the illumination spot size is small. This is due to the intermittent nature of scattering site dynamics arising from bubble rearrangements. Second, we use the novel dynamic light scattering technique Speckle-Visibility Spectroscopy (SVS), which is not limited by the Gaussian assumption required in DWS. This technique gives the time-trace for the average scattering site speed within a prescribed volume of the sample.;Results are analyzed in terms of distributions of event times, event speeds, and event displacements. The distribution of rest times between successive events is also measured; comparison with DWS results shows that the spatial structure of a typical event consists of a core of only a few bubbles which undergo topology change, plus a surrounding halo of bubbles which shift by an amount that decays to one wavelength at four to five bubbles away.