Particle phase, discrete consideration

Discrete particle modeling (DPM) is an advanced computational technique for particulate systems (in this case, fluidized beds) that has already been presented in Chapter 7 of Volume 3, Modem Drying TechnoU. DPM combines continuous (Eulerian) CFD for the gas phase with a discrete (Lagrangian) consideration of the particle phase by means of a discrete element method (DEM), and is therefore often also denoted as DEM-CFD. Its appHcation enables the resolution of not only interactions between the gas and the particle phase, but also of particle-particle and particle-wall interactions, in the sense of a four-way coupling (compare also with Chapter 5 in Volume 1, Modem Drying Technology). 

The FD region at the top is characterized by the dominance of the fluid over the movement of particles, as already shown in Fig. 11. When the fluid-dominated FD regime is first formed, the clusters of fast fluidization are disintegrated to form an essentially one-phase structure in which the particles are, however, not completely discretely suspended, that is, at a much higher concentration as compared to the ef computed for the broth before Upt. This is shown by the fluctuating voidage considerably above zero, as can be seen in the upper right-hand side of Fig. 11. 

In this approach, the finite volume methods discussed in the previous chapter can be applied to simulate the continuous fluid (in a Eulerian framework). Various algorithms for treating pressure-velocity coupling, and the discussion on other numerical issues like discretization schemes are applicable. The usual interpolation practices (discussed in the previous chapter) can be used. When solving equations of motion for a continuous fluid in the presence of the dispersed phase, the major differences will be (1) consideration of phase volume fraction in calculation of convective and diffusive terms, and (2) calculation of additional source terms due to the presence of dispersed phase particles. For the calculation of phase volume fraction and additional source terms due to dispersed phase particles, it is necessary to calculate trajectories of the dispersed phase particles, in addition to solving the equations of motion of the continuous phase. 

The methods are very complicated and require a large number of discrete items of information to describe a particle shape reasonably well they actually produce the signature of the particle, particularly if the coefficients are coupled with their respective phase angle. Meloy found that, in spite of a considerable scatter of data points, the log-log plot of coefficient amplitudes yields a straight line. He named this the law of morphological coefficients and defined the concept of random particles whereby, by definition and under certain assumptions, a random particle has a straight line as its signature. 

In general, high impact polystyrenes are multiphase systems consisting of a continuous rigid polystyrene phase and discrete rubber particles 0.5-lOjU in diameter. The incorporated rubber particles are crosslinked and contain grafted polystyrene, and their inner structure is determined by the manufacturing process and can vary considerably. The principle polystyrene structures have been described in detail (I, 2). 

Study of the morphological features of EEC indicate precipitation in the course of the epoxy resin cm"e of particles of the discrete phase of the rubber, the dispersion of which in the epoxy polymer matrix has a considerable effect on the mechanical properties of the latter. If the rubber particles are large enough, they can be detected by optical microscopy, but the most important results are obtained by electron microscopy. 

Inhomogeneous or multiphase reaction systems are characterised by the presence of macroscopic (in relation to the molecular level) inhomogeneities. Numerical calculations of the hydrodynamics of such flows are extremely complicated. There are two opposite approaches to their characterisation [63, 64] the Euler approach, with consideration of the interfacial interaction (interpenetrating continuums model) and the Lagrange approach, of integration by discrete particle trajectories (droplets, bubbles, and so on). The presence of a substantial amount of discrete particles in real systems makes the Lagrange approach inapplicable to study motion in multicomponent systems. Under the Euler approach, a two-phase flow is described... 

Many factors influence not only how the polymer phase separates but also the size of the discrete domains and whether a bimodal particle distribution occurs. These are the basic chemistry and molecular weight of the epoxy resins present (this will significantly affect solubility parameters), the polymer loading and the rate and temperature of cure. The latter will affect the rate of change of solubility parameter and the matrix viscosity profile, both of which are important considerations. 

A continuous second phase in polycrystalline ceramics, such as a continuous pore phase or fibers in a composite may undergo capillary-induced shape changes leading to breakup and the formation of discrete pores or particles. Since the physical distribution of secondary phases has important consequences for the properties of ceramics, the morphological stability of continuous phases in ceramics is of considerable interest. An analysis by Rayleigh (1) permits a qualitative understanding of many of these phenomena. 

To achieve concentrations above 50% it is necessary that at least a portion of the polymer be present in agglomerates of greater than colloidal size. In a latex, the polymer is present in the form of globules existing as a discrete phase in an aqueous matrix. Natural and synthetic rubbers, vinyl resins, and acrylics are the most important of the adhesive latexes. The polymer is not limited in molecular weight since the viscosity does not depend on what is contained within the discrete particles. The viscosity of the latex depends primarily on solids content and the composition of the aqueous phase. Latexes are commonly available in concentrations of 35 to 55% but it is possible, in some cases, to go considerably higher before reaching an excessive consistency. 

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