Taylor dispersion mechanism

The latter mechanism assumed is the well-known Taylor dispersion (T9, TIO, Til), which has been studied extensively (All, G6, L9, T14, S2). High-speed motion pictures taken by Towell et al. (T23) in a 40-cm bubble column (R3) have shown the presence of turbulent eddies, on a scale roughly equal to the column diameter, with systematic large-scale circulation patterns superimposed. Their pictures showed that liquid near the wall flowed downward, while liquid near the center of the column flowed upward, consistent with the flow theory developed earlier and with the Taylor dispersion mechanism. 

For recirculation flow the Taylor dispersion mechanism was introduced by Shyu and Miyauchi (S13). Equation (4-12) is a revised result for it. For this flow regime, Ohki and Inoue (02) developed an expansion model with parameters adjusted to the data available, and also introduced the Taylor dispersion mechanism for the low-gas-velocity region of uniform bubble flow. 

G. Taylor, Dispersion of a viscous fluid on the wall of a tube, J. Fluid Mechanics 70 161 (1961). S. Irandoust, B. Andersson, E. Bengtsson, and M. Siverstrdm, Scaling up of a monolithic catalyst reactor with two-phase flow, Ind. Eng. Chem. Res. 28 1489 (1989). 

The influence of longitudinal dispersion on the extent of a first-order catalytic reaction has been studied by Kobayashi and Arai (K14), Furusaki (F13), van Swaay and Zuiderweg (V8), and others. They use the one-dimensional two-phase diffusion model, and show that longitudinal dispersion of the emulsion has little effect when the reaction rate is low. Based on the circulation flow model (Fig. 2) Miyauchi and Morooka (M29) have shown that the mechanism of longitudinal dispersion in a fluidized catalyst bed is a kind of Taylor dispersion (G6, T9). The influence of the emulsion-phase recirculation on the extent of reaction disappears when the term tp defined by Eq. (7-18) (see Section VII) is greater than about 10. For large-diameter beds, where p does not satisfy this restriction, their general treatment includes the contribution of Taylor dispersion for both the reactant gas and the emulsion (M29). 

Note (1) For Taylor dispersion, there is an effective diffusion coefficient which increases proportionally with square of the velocity of the flow. The spot spreads much faster in the direction of the flow than if molecular diffusion is the only mechanism responsible. 

Dispersion can also result from the Taylor-Aris mechanism discussed in detail in Section 4.4. This important mechanism involves a coupling between axial flow, which broadens the front, and radial diffusion, which tends to sharpen it. This effect is a major reason why breakthrough curves blur. 

Although the dominant mixing mechanism of an immiscible liquid polymeric system appears to be stretching the dispersed phase into filament and then form droplets by filament breakup, individual small droplet may also break up at Ca 3> Ca. A detailed review of this mechanism is given by Janssen (34). The deformation of a spherical liquid droplet in a homogeneous flow held of another liquid was studied in the classic work of G. I. Taylor (35), who showed that for simple shear flow, a case in which interfacial tension dominates, the drop would deform into a spheroid with its major axis at an angle of 45° to the how, whereas for the viscosity-dominated case, it would deform into a spheroid with its major axis approaching the direction of how (36). Taylor expressed the deformation D as follows... 

Theoretical aspects of emulsion formation in porous media were addressed by Raghavan and Marsden (51-53). They considered the stability of immiscible liquids in porous media under the action of viscous and surface forces and concluded that interfacial tension and viscosity ratio of the immiscible liquids played a dominant role in the emulsification of these liquids in porous media. A mechanism was proposed whereby the disruption of the bulk interface between the two liquids led to the initial formation of the dispersed phase. The analysis is based on the classical Raleigh-Taylor and Kelvin-Helmholz instabilities. 

The axial dispersion coefficient E r given by the Taylor mechanism for the above case is given by the procedure of Tichacek et al. (T14) for turbulent pipe flow. Integrating Eq. (4-5) twice with respect to r, one has... 

Two approximations are introduced, for simplicity, to perform the integration of Eq. (4-9) for the Taylor mechanism dispersion coefficient Ezr-First, the term included in the second integral of Eq. (4-9) is eliminated from the integral by taking an effective mean value Vn, (= dvt), with d being a mean of a. Second, the local liquid holdup is eliminated from the multiple integral by using the mean liquid holdup Cl. with a correction factor/of order unity (/al). 

The non-ideality of catalyst surfaces has ever been one the major difficulties in understanding the detailed mechanisms of contact catalysis. The Advances in Catalysis were opened in 1948 by an article of Taylor on the heterogeneity of catalyst surfaces for chemisorption [4] that the matter was not easy to model is understood by observing that 41 years later the role of particle size on the catalytic activity of supported metals was the subject of of another review in the same series [5] moreover, the family of solids of catalytic interest has since Taylor s review been increased by the availability of new techniques for the preparation of highly dispersed solids, like crystalline zeolites and amorphous aerogels. 

He et al. [46] demonstrated that short pulses of electrostatic potential applied along the axis of formation of water droplets in oil can generate a Taylor cone and formation of droplets via an electro-hydrod5miic mechanism [50]. These droplets are typically poly disperse (3-25 pm) and it is difficult to produce individual droplets. Weitz et al. [51] demonstrated control over volumes and frequencies of formation of droplets with the use of electric field. 

Tha transport mechanisms of molecular diffusion and mass carried by eddy motion are again assumed edditive although the contribution of the molecular diffusivity term is quite small except in the region nenr a wall where eddy motion is limited. The eddy diffusivity is directly applicable to problems snch as the dispersion of particles or species (pollutants) from a souree into a homogeneously turbulent air stream in which there is little shear stress. The theories developed by Taylor.36 which have been confirmed by a number of experimental investigations, can describe these phenomena. Of more interest in chemical engineering applications is mass transfer from a turbolent fluid to a surface or an interface. In this instance, turbulent motion may he damped oni as the interface is approached aed the contributions of both molecolar and eddy diffusion processes must he considered. To accomplish this. 9ome description of the velocity profile as the interface is approached must be available. 

In the rotary annular contactor [D2, L2, T2] shown schematically in Fig. 4.27 [T2], the organic and aqueous phases flow countercurrently by gravity in the annular space between a rotating itmer cylinder and a stationary outer cylinder. Taylor-instability vortices generated in the annulus promote dispersion and interfacial area. This is one of the simplest of the mechanically a tated contactors, and it has been developed for possible application to fuel reprocessing. In laboratory extractions of uranium from nitric add with TBP in kerosene, Davis [D2] obtained values as low as 7.5 cm for the column hei t equivalent to a theoretical stage. The rotor speed varied from 1200 to 2000 r/min, with annular widths of 0,1 to 0.35 cm and a stator diameter of 2.2 cm. The residence time per theoretical stage was 10 s or less. 

The way we have presented the one-dimensional dispersion model so far has been as a modification of the plug-flow model. Hence, u is treated as uniform across the tubular cross section. In fact, the general form of the model can be applied in numerous instances where this is not so. In such situations the dispersion coefficient D becomes a more complicated parameter describing the net effect of a number of different phenomena. This is nicely illustrated by the early work of Taylor [G.I. Taylor, Proc. Roy. Soc. (London), A219, 186 (1953) A223, 446 (1954) A224, 473 (1954)], a classical essay in fluid mechanics, on the combined contributions of the velocity profile and molecular diffusion to the residence-time distribution for laminar flow in a tube. 

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