Hydrodynamics flow structure

Figure 2.6. Experimental assembly scheme for investigation of hydrodynamic flows structure in tubular turbulent apparatus. 1 - tubular turbulent apparatus, 2 - water line, 3, 4 - rotameters of central (Wi) and side (wz) flows, 5 - block of indicator introduction, 6 - spectrophotometer.

In Bridgman growth [155], a boat or vessel filled with the melt is slowly cooled from one side, so that the crystal forms from that side. In Czochralski growth [156,157] a cylindrical crystal sits on the surface of the melt and is slowly pulled upward. In both cases the hydrodynamical flow of the melt is an important factor in the chemical composition and fine structure of the resulting crystal. 

This section focuses on steady and unsteady hydrodynamic modes that emerge as the rotational speed of the inner cylinder (expressed by Ta) and pressure-driven axial flow rate (scaled by Re) are varied, while the outer cylinder is kept fixed. These modes constitute primary, secondary and higher order bifurcations, which break the symmetry of the base helical Couette-Poiseuille (CP) flow and represent drastic changes in flow structure. Figure 4.4.2 presents a map of observed hydrodynamic modes in the (Ta, Re) space, and marks the domain where all of the hydrodynamic modes that interest us appear. We will return to this figure shortly. 

Reactors which generate vortex flows (VFs) are common in both planktonic cellular and biofilm reactor applications due to the mixing provided by the VF. The generation of Taylor vortices in Couette cells has been studied by MRM to characterize the dynamics of hydrodynamic instabilities [56], The presence of the coherent flow structures renders the mass transfer coefficient approaches of limited utility, as in the biofilm capillary reactor, due to the inability to incorporate microscale details of the advection field into the mass transfer coefficient model. 

DNAs are soluble only in aqueous solutions and their fibrous crystals can be prepared by slow evaporation from the aqueous solution. Duplex structures in the fibers have been studied by X-ray diffraction [2,3] and sohd state NMR [4-6]. Orientation of DNA strands by using hydrodynamic flow gradients in the dilute aqueous solution [7,8] and lyotropic liquid crystal... 

On the basis of the observations in the macroscale, the flow of a fast fluidized bed can be represented by the core-annulus flow structure in the radial direction, and coexistence of a bottom dense region and a top dilute region in the axial direction. Particle clusters are an indication of the heterogeneity in the mesoscale. A complete characterization of the hydrodynamics of a CFB requires the determination of the voidage and velocity profiles. There are a number of mathematical models accounting for the macro- or mesoaspects of the flow pattern in a CFB that are available. In the following, basic features of several types of models are discussed. 

Gosch, M., Blom, H., Holm, J., Heino, T., Rigler, R., Hydrodynamic flow profiling in microchannel structures by single molecule fluorescence correlation spectroscopy. Anal. Chem. 2000, 72, 3260-3265. 

Gas-liquid bubble columns and gas-liquid-solid slurry bubble columns are widely used in the chemical and petrochemical industries for processes such as methanol synthesis, coal liquefaction, Fischer-Tropsch synthesis and separation methods such as solvent extraction and particle/gas flotation. The hydrodynamic behavior of gas-liquid bubble columns and gas-liquid-solid slurry bubble columns are of great importance for the design and scale-up of reactors. Although the hydrodynamics of the bubble and slurry bubble columns has been a subject of intensive research through experiments and computations, the flow structure quantification of complex multi-phase flows are still not well understood, especially in the three-dimensional region. In bubble and slurry bubble columns, the presence of gas bubbles plays an important role to induce appreciable liquid/solids mixing as well as mass transfer. The flows within these systems are divided into two... 

Finally, a challenging problem is to discuss the influence of hydrodynamic flow fields on the phase behavior of polymer blends. This is of fundamental interest and of technological importance as well since stresses and corresponding deformations are encountered during processing of blends. Extension of studies to blend systems under external flow is necessary for the better understanding of structure formation in polymer blends outside equilibrium. 

Furthermore, investigations on mass transfer across the interface will be continued in order to determine the mass transfer coefficient for drops exposed to the hydrodynamic flow and to be able to state the influence of surfactants on the interfacial tension under high pressure. For those systems implying solid particles their geometrical structure will need to be characterized with the aim of describing diffusion mechanisms. 

In many structured products, water management includes several mass transport mechanisms such as hydrodynamic flow, capillary flow and molecular self-diffusion depending on the length scale. Hydrodynamic flow is active in large and open structures and it is driven by external forces such as gravity or by differences in the chemical potential, that is, differences in concentrations at different locations in the structure. Capillary flow also depends on surface tension and occurs in channels and pores on shorter length scales than in hydrodynamic flow. A capillary gel structure will hold water, and external pressures equivalent to the capillary pressure will be needed to remove the water. 

Theologos and Markatos (1992) used the PHOENICS program to model the flow and heat transfer in fluidized catalytic cracking (FCC) riser-type reactors. They did not account for collisional particle-particle and particle-wall interactions and therefore it seems unlikely that this type of simulation will produce the correct flow structure in the riser reactor. Nevertheless it is one of the first attempts to integrate multiphase hydrodynamics and heat transfer. 

The measurements by Harley, Pfahler, and Urbanek not only provide a solid basis for modeling fluid flows in small ducts but also raise a question about the nature of that flow at elevated temperatures. The lower-temperature data justify the use of hydrodynamic theory in simple ducts. Whether this will hold in more complex flow structures needs further study. For gas flow in ducts where the Knudsen number is 0.05 or greater, slip flow is observed. Urbanek s data suggest that there may be increased wall interactions as the temperature approaches the boiling point. A more definitive study is needed to clarify this point. 

The hydrodynamic study at a mesoscopic scale requires the understanding of instantaneous local solids flow structure. The time-variant flow behavior is complex. Analyses of the instantaneous flow structure require recognizing the following factors. 

A notable feature of the spiral structures is the lack of a heavy core as seen in spiral galaxies, such as M51, shown in Plate 5.1. A reasonable explanation of this and of the uniform alignment and chirality of the spirals is that they originate in turbulent flow firom a central point, and therefore seen oriented in the same radial projection. In hydrodynamics such structures are known as vortices or eddies. Each of the eddies generated by the turbulent expansion is the potential nucleus of a new galaxy. 

It is possible to determine the ideal ablation factor by using the results of numerical solution of equations (13.73) and (13.74). It depends on three dimensionless parameters h, which describes the relation between electric and hydrodynamic forces acting on the drop Re, which characterizes the flow structure and d, which includes the mesh electrode parameters. The dependences Ki on these three parameters are shown in Fig. 13.23. 

Rather different picture is observed under formation of hydrodynamic flows (coolant) structure in annular canals of tubular turbulent apparatus (Fig. 4.24). Flows structures in annular canals of cylindrical and divergent-convergent apparatus (Bo = 80) practically coincide up to volumetric flow of liquid flows Wa = 110 cmVsec. At Wa> 110 cmVsec in divergent-convergent apparatus reduction of criterion Bo is observed that is determined by the rise of longitudinal mixing rate (Fig. 4.25) and in cylindrical canal the rise of criterion Bo is observed (Fig. 4.24). 

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