DIFFUSION THROUGH FOAMS AND FRACTAL-LIKE CELLULAR SOLIDS

The diffusion of gases through foams with nonuniform cell sizes is described using fractal models. These models corresponds to the limit of extreme nonuniformity, since essentially all cell sizes are present in fractal-like foams. The calculated diffusion currents in the fractal models are anomalous, and a diffusion current entering a fractal surface, J(t), can exhibit a power-law time dependence [J(t) almost-equal-to t -alpha]. The exponent alpha depends on the structure of the model. In the simplest one-dimensional case, alpha is determined by the fractal dimension. For the three-dimensional fractal models, alpha is related to an additional parameter that compares the resistances of large and small cells to the current flow. Qualitatively, we show that diffusion in foams with a large variety of cell sizes can be anomalously large or anomalously small, and the unusual currents depend as much on the distribution of cell-wall thicknesses as they depend on cell-wall sizes.