BUBBLE-SCALE MODEL OF FOAM MECHANICS - MELTING, NONLINEAR BEHAVIOR, AND AVALANCHES

By focusing on entire gas bubbles, rather than soap films or vertices, a microscopic model was recently developed for the macroscopic deform ation and flow of foam in which dimensionality, energy storage, and di ssipation mechanisms, polydispersity, and the gas-liquid ratio all can be varied easily [D. J. Durian, Phys. Rev. Lett. 75, 4780 (1995)]. He re, a more complete account of the model is presented, along with resu lts for linear rheological properties as a function of the latter two important physical parameters; It is shown that the elastic character vanishes with increasing liquid content in a manner that is consistent with rigidity percolation and that is almost independent of polydispe rsity. As the melting transition is approached, the bubble motion beco mes increasingly nonaffine and the relaxation time scale appears to di verge. Results are also presented for nonlinear behavior at large appl ied stress, and for the sudden avalanchelike rearrangements of bubbles from one tightly packed configuration to another at small applied str ain rates. The distribution of released energy is a power law for smal l events, but exhibits an exponential cutoff independent of system siz e. This is in accord with multiple light scattering experiments, but n ot with other simulations predicting self-organized criticality.