Model network of zones

Scientists of the Institute of Science and Technology of UMIST (Manchester, UK) and collaborating laboratories have developed a network-of-zones model (Mann et al, 1981 Mann and Knysh, 1984 Mann and El-Hamouz, 1992, 1995 Mann et al, 1995 Nienow et al, 1992 Togatorop et al, 1994 and Wang and Mann, 1990, 1992). According to this model a reaction volume is represented by an assembly of backmixed zones, each of equal volume. The liquid... 

FIGURE 1.7 Network of zones model for stirred reactors 2 x 10 x 10 network. Flow through different zones was specified using experimental measurements (from Mann and Mavros, 1982). 

Brucato, A. Rizzuti, L. In The Application of the Network-of-Zones Model to Solid-Liquid Suspensions, Proceedings 6th European Conference on Mixing, Pavia, Italy, 1988 273-280. 

Brucato, A. Magelli, F. Nocentini, M. Rizzuti, L. An application of the network-of-zones model to solids suspension in multiple impeller mixers. Trans. Instn. Chem. Engrs. 1990, 69, Part A, 43-52. 

A different numerical strategy to simulate multiphase mixing was introduced by Mann and Mann and Hackett. The idea of the method, called the network-of-zone, is to subdivide the flow domain in a set of small cells assumed to be mixed perfectly. The cells are allowed to exchange momentum and mass with their neighboring cells by convective and diffusive fluxes. Brucato and Rizzuti and Brucato et al. applied this idea to the modeling of solid-liquid mixing. An unsteady mass balance for the particles was derived to estimate the solid distribution in the vessel, namely ... 

The logical extension of this approach is to divide the crystallizer into many compartments. This is known as the network of zones approach and has been used suceessfully by Mann (1993). Here, the exchange flows between compartments are not modeled but applied separately, either from a knowledge of the overall flow pattern achieved from experimental measurements or from a CFD flow model. Additionally, rules are applied which describe the turbulent transport of particles and species between zones. 

The inherent problem of all compartment models is the poor spatial resolution. By significantly increasing the number of compartments (up to 40000 zones) the network-of-zone (NOZ) models could overcome this problem [23-25]. However, the problem of identification and physical interpretation of the model parameters remains unchanged. The macromixing effects are reflected in the choice... 

Another reaction mechanism, which is conveniently mentioned under this heading, is due to Hill [479] who suggested that ions (atoms or molecules) frorh the product may move through the dislocation network of the reactant and activate potential nuclei, particularly in the vicinity of the reaction interface. Thus a reaction zone, within which potential nucleusforming sites are activated, is developed in front of an advancing interface. With appropriate assumptions, this reaction model provides an alternative explanation of the exponential rate law, eqn. (8), which in Sect. 3.2 was discussed with reference to chain reactions. 

Single-crystal work by Walmer (37) (on a fully-ordered crystal) showed a maximum of the coercive force in the 111 direction and minima in the 110 and 100 directions, the 100 minimum being the lower of the two (Figure 10). Work by Brissonneau and coworkers (8) on the distribution of platelets in completely-ordered PtCo has led to a model shown in Figure 11, wherein each zone shown in the figure contains a fully-developed network of (110) platelets oriented in two of the three possible orthogonal directions. 

The semi-specific, visualization uses additional information about certain concepts, instances and their relationships to achieve a more conclusive presentation. As an example, the ordered composition hierarchy (tree) in Fig. 4.10 displays the composition and realization hierarchy of an extruder. All information necessary for this presentation is stored as meta-level annotations of the appropriate concepts Extruder, Functional Zone and Screw Element), and their respective relations. Thus, the same presentation can be easily applied to any other model fragment that conforms to the same or a similar structure. Another possible application is to present a flowsheet as a network of devices and streams, by using a different kind of annotations. 

Clarke,B.L., 1974. Stability analysis of a model reaction network using graph theory. J.Chem.Phys. 60,1493-1501. Constales, D., Yablonsky, G.S., Marin, G.B., Gleaves, J.T., 2001. Multi-zone TAP-reactors theory and application I. 

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