Bubble walls are very thin their thickness strongly depends on the intensity of mutual repulsion between surfactant-loaded gas-liquid interfaces and only weakly on foam wetness ( ϕ=liquid volume/total volume) below a critical wetness at which the foam transforms into a bubbly liquid. Foams consist of gas bubbles surrounded by a continuous liquid phase. Liquid foams include soap froths and food and industrial foams, as well as many liquid-phase pollutants. All simulations eventually reach a self-similar growth regime, with the distribution functions time independent and the number of bubbles decreasing with time as a power law whose exponent depends on the wetness.
The simulations begin with 2 × 10 5 bubbles for ϕ = 0.00 and 1.25 × 10 5 bubbles for ϕ = 0.05 and 0.20, allowing us to track the distribution functions for bubble size, topology and growth rate over two and a half decades of volume change. We represent the liquid phase as an ensemble of many small fluid particles, which allows us to monitor liquid flow in the region between bubbles. Using a Cellular Potts model, we simulate these mechanisms during the evolution of three-dimensional foams with wetnesses of ϕ = 0.00, 0.05 and 0.20. Analyzing the combined effects of these mechanisms requires examining a volume with enough bubbles to provide appropriate statistics throughout coarsening. During coarsening, bubbles also move relative to each other, changing bubble topology and shape, while liquid moves within the regions separating the bubbles.
As the number of bubbles in a given volume decreases in time, the average bubble size increases: i.e.
The smaller the bubble, the faster it shrinks. Large bubbles grow at the expenses of smaller ones. In wet liquid foams, slow diffusion of gas through bubble walls changes bubble pressure, volume and wall curvature.
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