Power-law distribution of pressure fluctuations in multiphase flow

Bubbling fluidized beds are granular systems, in which a deep layer of particles is set in motion by a vertical gas stream, with the excess gas rising as bubbles through the bed. We show that pressure fluctuations in such a system have non-Gaussian statistics. The probability density function has a power-law drop-off and is very well represented by a Tsallis distribution. Its shape is explained through the folding of the Gaussian distribution of pressure fluctuations produced by a monodisperse set of bubbles, onto the actual distribution of bubble sizes in the bed, assuming that bubbles coalesce via a Smoluchowski-type aggregation process. Therefore, the Tsallis statistics arise as a result of bubble polydispersity, rather than system nonextensivity.