Coalescence space model

A generalization of these population balance methods to reactions with arbitrary RTD was given by Rattan and Adler [126]. They expanded the phase space of the distribution functions to include the life expectation as well as concentration of the individual fluid elements i/ (C, A, 0- The population balance then reduces to all of the previous developments for the various special cases of segregated or micromixed flow, the perfect macromixing coalescence-redispersion model, and can be solved as continuous functions or by discrete Monte Carlo techniques. Goto and Matsubara [127] have combined the coalescence and two-environment models into a general, but very complex, approach that incorporates much of the earlier work. 

Recent SAXS work by Wu [56] has demonstrated that the ionic domains in Nafion membranes are most probably spherical and exhibit a size distribution and spacing that does not vary much with equivalent weight (EW). The latter work suggested that strings of smaller spherical aggregates could be sufficiently close to coalesce upon swelling with water uptake by the membrane, and thus could provide percolation pathways for ionic transport. This picture could replace the nanoscale (1.2 nm-wide) channels suggested in earlier models for Nafion to explain transport phenomena. 

In [624] measurements were carried out in a single model scale. These showed that the sorption characteristics for the coalescing material system water/air can be satisfactorily represented in the space ... 

Of particular interest is the case of a heterogeneous mixture with small volume content of the disperse phase W 1. In this case we can assume that the disperse phase exerts a weak influence on the continuous phase. Then fields of velocity, pressure, temperature and other parameters of the continuous phase could be determined by using one-velodty model, and then, for given distributions of parameters, one can determine the behavior of disperse phase. If the disperse phase represents a discrete system of inclusions (solid particles, drops, bubbles, macromolecules), it can be characterized by a distribution n V, t, P) of inclusions over volumes V at a point of space P. Inclusions can exchange mass (due to evaporation, condensation, fusion etc.) with the continuous phase, and also interact between themselves, - they can collide, coagulate, coalesce, break, form the inclusions of various size and shape. In addition, a phase can nucleate in conditions of mixture super-saturation and then increase in size due to a phase transition. The... 

The Bailes and Larkai model incorporates a number of assumptions such as the use of a monodispersion and uniform interdroplet spacing. However, developing a model incorporating a typical droplet distribution with random droplet spacing would be significantly more complicated. No attempt is made, either, to incorporate file effects of flow velocity or regime, and the experimental results do not indicate whether tests were carried out in laminar or turbulent flow (though laminar flow can be deduced). These parameters would also have had an effect on droplet collision frequency, and therefore the rate of coalescence. 

There are several versions of diis column. The earliest model was introduced around 1946 and h was the first to enjoy wide commercial qiplication. h provides altematir compartments to aid dispersion with impellers and coalescence with a wire mesh (about 97% void space). Cavity and mass tiansfer data have been developed for columns with diameters from 25 to 300 mm and in three different liquid-liquid systems. The r rted column capacity depends on the system properties but varies from about 14.000 to 24,(XX)L/h (or 350-600 gal/h - fi. The Mutphtee-siage efficiency for a 12 in. diameter column can be correlated as... 

Section 12-2 deals with liquid-liquid dispersion, while in Section 12-3 we discuss coalescence. Section 12-4 gives an introduction to the methods used for population balance models, along with references for further reading. In Section 12-5 we describe more concentrated dispersed phase systems, including phase inversion. Section 12-6 deals with other considerations, such as suspension, mass transfer, and other complexities. Section 12-7 with equipment used in liquid-liquid operations. Section 12-8 with scale-up, and Section 12-9 provides industrial examples. Nomenclature and references then follow. Although every attempt has been made to make this a stand-alone chapter, space limitations occasionally make it necessary to refer to other chapters in the book. 

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