ABSTRACT The classical mathematical treatment of two-phase flows is based on the average of the conservation equations for each phase. In the passage to the infinitesimal limit, the concomitant loss of detail is seldom recovered in terms of numerical simplicity; one intractable problem having been translated imperfectly into another, almost as intractable as the first. A complementary approach to the modelling of this systems is the statistical population balance, which is based on the generalized Boltzmann transport equation of a bubble distribution function. The approach is a powerful tool to describe non-equilibrium features, such as flow development and flow pattern transitions. Successful results have been achieved in the modeling of bubbly-slug flow pattern transitions and void fraction development along tubes. Also, a novel model of boiling crisis was derived following this type of analysis. This article presents a perspective review of the advances reached in the application of bubble population balances, as well as a discussion of present trends towards the completion of a general technique.
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