Disperse multiphase flows

The majority of the equipment used in the chemical process industry employs multiphase flow. Bubble columns, fluidized beds, flame reactors, and equipment for liquid–liquid extraction, for solid drying, and size enlargement or reduction are common examples. In order to efficiently design, optimize, and scale up industrial systems, computational tools for simulating multiphase flows are very important. Polydisperse multiphase flows are also common in other areas, such as fuel sprays in auto and aircraft engines, brown-out conditions in aerospace vehicles and particulate flows occurring in the environment. Although at first glance the multifarious industrial and environmental multiphase flows appear to be very different from each other, they have a very important common element: it is possible to identify a continuous phase and a disperse phase (usually with a distribution of characteristic “particle sizes”).

Historically the development of the theoretical framework and of computational models for disperse multiphase flows has focused on two different aspects: (i) the evolution of the disperse phase (e.g. breakage and coalescence of bubbles or droplets, particle–particle collisions, etc.) and (ii) multiphase fluid dynamics. The first class of models is mainly concerned with the description of the disperse phase, and is based on the solution of the spatially homogeneous population balance equation (PBE). A PBE is a continuity statement written in terms of a number density function (NDF), which will be described in detail in Chapter 2.