Dynamics and coarsening in three-dimensional foams

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 scattexd 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. The kinetics of phase separation and coarsening are phenomena of long standing interest [l]. Soap froths are common and fascinating examples, thought to be useful models of grain growth [a]. Recent experiments have focused on two-dimensional systems, where the structure and coarsening are readily observable [3-61. By contrast, because of the problem of visualizing an opaque system, no analogous experiments have been performed on three-dimensional foams. Nevertheless, such foams are of great scientific interest and have many industrial and commercial applications [7]. In this paper, we present a novel interpretation of the origin of temporal fluctuations of multiply scattered light in foams and obtain new information about the structure, dynamics, and time evolution of three-dimensional foams. For convenient and highly reproducible foam samples, we used a commercially available brand of shaving cream. Gillette Foamy Regular [8] consists mainly of an aqueous solution of mixed ionic surfactants (stearic acid and triethanolamine) which is supersaturated with hydrocarbon gases (isobutane, propane, and butane). When these contents are released, the gases come out of solution, surfactants adsorb to bubble interfaces, and a foam is produced. By weighing known volumes of foam, we find that the first 10-50 g of Foamy expelled from a new can have a constant density of (7.77k0.08) x lo-’ g ~ m ~ , corresponding roughly to 0.92 volume fraction of bubbles. Foam samples were always taken from this range. To estimate the behaviour of Foamy, we first viewed a portion from below with an optical microscope. The foam consisted of a collection of nearly-spherical bubbles of about 20 p m average initial diameter. While the polydispersity was considerable, no very large bubbles were observed. This permitted the average size of surface bubbles to be followed by eye to within about 15% as shown by the full circles in figure 1. As the foam aged, the coarsening process was directly observed: small bubbles shrank and disappeared while large bubbles grew larger. In addition, a different type of 0953-8984/90/SA0433+04$03.50 @ 1990 IOP Publishing Ltd SA433