Particulate flow model description

Chapter 4 contains a summary of the basic theory of granular flow. These concepts have been adopted describing particulate flows in fluidized bed reactors. The theory was primarily used for dense bed reactors, but modified closures of this type have been employed for more dilute flows as well. Compared to the continuum theory presented in the third chapter, the granular theory is considered more complex. The main purpose of introducing this theory, in the context of reactor modeling, is to improve the description of the particle (e.g., catalyst) transport and distribution in the reactor system. 

The available continuum models for dispersed multi-phase flows thus follow one of two asymptotic approaches. The dilute phase approach is formulated based on the continuum mechanical principles in terms of the local conservation equations for each of the phases. A macroscopic model is then obtained by averaging the local equations based on an appropriate averaging procedure. In the dense phase approach, on the other hand, a kinetic theory description is adopted for the dispersed particulate phase (granular material), whereas an averaged continuum model formulation is adopted for the interstitial phase. 

For die first case study, the particulate filled nanopolymers is studied. An investigation on viscometric flow for particulate filled nanopolymers is presented as the second case study in this chapter. Application of synthetic or natural inorganic fillers is reviewed as the third case study. The next two case studies are devoted to description of a multiscale micromechanical model and plication of cement materials reinforcement with nanoparticles. 

The results observed in this ehapter emphasize that the microcomposites rheology description models do not give adequate treatment of melt viscosity for particulate-filled nanocomposites. The correct description of the nanocomposites rheological properties can be obtained within the frameworks of viscous liquid flow fractal models. It is significant, that such an approach differs principally from the used ones to describe microcomposites. So, nanofiller particles aggregation reduces both melt viscosity and elastic modulus of nanocomposites in the solid-phase state. For microcomposites, melt viscosity enhancement is accompanied by elastic modulus increase. 

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