Abstract
The equation of state of a dry foam with ideal gas in the bubbles, proposed by Ross, is proved. This equation suggests that a foam with a free boundary will expand to a maximum volume if the external pressure is lowered at constant temperature. The same foam enclosed in a container, on the other hand, can be expanded further but, as the volume is increased, will eventually become unstable. We speculate that this instability leads to a “bubble differentiation” transition of the kind observed by Herdtle in numerical simulations of two-dimensional foam with ideal gas in the bubbles. In the simulations the foam separated into two “phases,” one with a large number of small bubbles, another with a small number of very large bubbles.
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