A bubble number density constitutive equation

A statistical formulation is used to describe gas-liquid two-phase flows. It is shown that this kind of flow cannot be considered a dilute system as is currently done. A correction factor, the pair correlation function, is introduced to account for ''dense effects''. Integrating the transport equation of the bubble volume distribution function over all possible volumes, a number density transport equation is obtained, which explicitly accounts for bubble breakup and coalescence phenomena. A complete model is constructed in conjuction with the mass and momentum conservation equations. Its predictions were compared with experimental results on bubble columns. Excellent agreement was found. The theoretical model was able to predict the void fraction axial distributions, which showed strong variations. ((orig.))