The dynamics of two-dimensional foams.

This dissertation describes research on the structure and dynamics of two-dimensional foams. New experimental results are presented and new algorithms developed to study foam dynamics with particular emphasis on foams that evolve with significant rupture. In the introduction, basic principles and statistical properties of two-dimensional coarsening cellular patterns are reviewed. Theoretical and computational models which have been developed are also discussed. In Chapter 2, experimental results are presented for the relaxation of a two dimensional soap foam in which wall breakage is initiated through gentle warming of the foam cell. Significantly different phenomenology from the relaxation of non-breaking foams is observed. At a critical "break time," which depends on the temperature ramping rate and initial conditions, a large scale mechanical cascade of wall rupture sets in leading to a rapid disintegration of the foam. In Chapter 3, an efficient new algorithm for simulating the evolution of two-dimensional dry soap foams is presented. Our physically based model for the evolution is based on a combination of mass transfer, vertex movement, and edge relaxation. The stochastic nature of topological transitions due to numerical error has been carefully examined. In Chapter 4, simulations of breaking foams by this new algorithm are presented. The separation of vertex and edge movements permits a study of foam evolution that includes wall rupture. This evolution exhibits a sensitive dependence on both the type of breaking "rule" chosen as well as the initial conditions. The topological evolution is characterized in terms of certain "evolution exponents," and we show simulation results that agree with theoretical considerations. In Chapter 5, normal grain growth in anisotropic polycrystals is simulated using a new algorithm developed from the one used to simulate normal foams. The simulation results, without breakage, show a decrease in growth exponents which is due to the reduction in the mean surface energy during evolution. However, including breakage of low angle tilt grain boundaries substantially increases the growth exponents. These simulations highlight the fact that competition between anisotropic effects and boundary breakage can lead to a wide range of possible growth exponents