Multiphase dynamic behavior

The two extreme hypotheses on mixing produce lumped models for the fluid dynamic behavior, whereas real reactors show complex mixing patterns and thus gradients of composition and temperature. It is worthwhile to stress that the fluid dynamic behavior of real reactors strongly depends on their physical dimensions. Moreover, in ideal reactors the chemical reactions are supposed to occur in a single phase (gaseous or liquid), whereas real reactors are often multiphase systems. Two simple examples are the gas-liquid reactors, used to oxidize a reactant dissolved in a liquid solvent and the fermenters, where reactions take place within a solid biomass dispersed in a liquid phase. Real batch reactors are briefly discussed in Chap. 7, in the context of suggestions for future research work. 

Non-Debye dielectric relaxation in porous systems is another example of the dynamic behavior of complex systems on the mesoscale. The dielectric properties of various complex multiphase systems (borosilicate porous glasses [153-156], sol-gel glasses [157,158], zeolites [159], and porous silicon [160,161]) were studied and analyzed recently in terms of cooperative dynamics. The dielectric response in porous systems will be considered here in detail using two quite different types of materials, namely, porous glasses and porous silicon. 

Over the years, dynamic testing has become the preferred method of testing the rheological behavior of the multiphase systems. For example, Nishi et al. [1981] carried out careful studies on the dynamic behavior of PS/PVME. The specimens were cast at temperatures either below or above the lower critical solution temperature, LCST = 95°C. While those prepared at T < LCST (single-phase system) showed superposition of dynamic data onto a master curve, the ones that were cast at T > LCST did not. 

Instrumentation is an important issue in fluidization engineering, particularly because of the multiphase, dynamic, and nonlinear nature of fluidized beds. In commercial plants, instrumentation should be conducted basically for process control, but detection of unusual behavior and prevention of unwanted losses are important as well. For bench and pilot plants instrumentation should be different compared to that for commercial plants, since maximum information output should be aimed at for safe design and scale-up. 

A number of methods exist to simulate dispersed multiphase flows. When choosing a particular simulation method, it is important to consider first the relevant length scales. The most obvious length scales are, from large to small, the dimensions of the confinement (equipment dimensions), the dimensions of the discrete elements (particles, bubbles, or droplets), and the mean free path of the molecules in the continuous fluid phase. The molecular mean free path ranges firom less than a nanometer in a liquid to the order of 100 nm in a gas at ambient pressure. Discrete molecular effects such as Brownian forces and molecular slip conditions are therefore very important in nanofluidic and small microfluidic devices (Hadjiconstantinou, 2006). They are also very important for the dynamic behavior of nano (structured) particles in gas flows and colloidal particles suspended in a liquid. In these... 

Energy and natural resources processing. NSF should sustain its support of basic research in complex behavior in multiphase systems, catalysis, separations, dynamics of solids transport and handling, and new scale-up and design methodologies. 

The analysis of a multiphase flow system is complex, in part because of the difficulties in assessing the dynamic responses of each phase and the interactions between the phases. In some special cases, the gas-solid mixture can be treated as a single pseudo-homogeneous phase in which general thermodynamic properties of a gas-solid mixture can be defined. This treatment provides an estimate for the bulk behavior of the gas-solid flow. The following treatment is based on the work of Rudinger (1980). 

In the present study, the effects of composition, molecular weight, and heat treatment on the relaxation behavior of styrene—butadiene-styrene (SBS) block polymers are investigated. There is evidence (e.g., 6,7,8) that these types of multicomponent multiphase systems exhibit unusual phenomena in their dynamic mechanical behavior and in other physical properties. These are apparently related to the presence of the so-called interphase mixing region between the elastomeric and glassy domains. Similar evidence has been obtained by gas diffusion and sorption studies on the copolymer samples used in this investigation (9). 

DYNAMICS OF DISTRIBUTION The natural aqueous system is a complex multiphase system which contains dissolved chemicals as well as suspended solids. The metals present in such a system are likely to distribute themselves between the various components of the solid phase and the liquid phase. Such a distribution may attain (a) a true equilibrium or (b) follow a steady state condition. If an element in a system has attained a true equilibrium, the ratio of element concentrations in two phases (solid/liquid), in principle, must remain unchanged at any given temperature. The mathematical relation of metal concentrations in these two phases is governed by the Nernst distribution law (41) commonly called the partition coefficient (1 ) and is defined as = s) /a(l) where a(s) is the activity of metal ions associated with the solid phase and a( ) is the activity of metal ions associated with the liquid phase (dissolved). This behavior of element is a direct consequence of the dynamics of ionic distribution in a multiphase system. For dilute solution, which generally obeys Raoult s law (41) activity (a) of a metal ion can be substituted by its concentration, (c) moles L l or moles Kg i. This ratio (Kd) serves as a comparison for relative affinity of metal ions for various components-exchangeable, carbonate, oxide, organic-of the solid phase. Chemical potential which is a function of several variables controls the numerical values of Kd (41). 

Dynamic birefringence techniques have been developed by Stein et al. (66), Read (54), Yamada and Hayashi (85) and Hopkins (25). By this technique the stress, strain and birefringence are measured simultaneously while the applied strain varies. By making such measurements as a function of frequency and temperature one can in principle separate the time dependencies of orientation of molecular response in a multiphase system as well as correlate the optical behavior with the mechanical spectrum. This technique can be correlated for example with the dynamic X-ray technique allowing separation of the amorphous and crystalline behavior. 

Dynamic mechanical characteristics, mostly in the form of the temperature response of shear or Young s modulus and mechanical loss, have been used with considerable success for the analysis of multiphase polymer systems. In many cases, however, the results were evaluated rather qualitatively. One purpose of this report is to demonstrate that it is possible to get quantitative information on phase volumes and phase structure by using existing theories of elastic moduli of composite materials. Furthermore, some special anomalies of the dynamic mechanical behavior of two-phase systems having a rubbery phase dispersed within a rigid matrix are discussed these anomalies arise from the energy distribution and from mechanical interactions between the phases. 

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