Axial dispersion intensity

Fluid mixing in particulate fluidization In particulate fluidization, the values of Pep are much higher than the corresponding ones for packed beds (2 -10 times) for the same value of Rep, covering the range 0.004 -0.06 for 0.4 < Rep < 100, and thus axial dispersion is more intense (Gunn, 1968). 

Axial dispersion can affect measurements of decay and growth rates of transients of interest. In Figure 5 is sketched the concentration of a transient, initially formed as a square wave by a light pulse of uniform intensity from — L < x < L and zero elsewhere. As shown in Figure 6, at later times the profile becomes smoothed by diffusion. As the purge flow pushes reactive species past the pinhole at x = 0, the spatial dependence of the concentration becomes a time-varying concentration that will contribute to any time variation caused by kinetics. 

Equation 10.115 has a considerable fundamental and practical importance. It combines parameters of fimdamentally different origins, the plate number at infinite dilution, N, which characterizes the intensity of axial dispersion taking place in the column and two parameters of thermod5mamic origin, the retention factor at infinite dilution, ICg, related to the initial slope of the isotherm, and the loading factor, proportional to the sample size and related to the saturation capacity of the isotherm. Accordingly, Eq. 10.115 indicates the extent to which the self-sharpening effect on the band profile due to the nonlinear thermodynamics is balanced by the dispersive effect of axial and eddy diffusion and of the mass transfer resistances. 

The function of these reactors is to increase the intensity of radial mixingy by which the parabolic velocity profile in the axial direction, formed when the sample zone is injected into a laminar flow of carrier stream, is reduced. Thus, (a) the reagent becomes more readily mixed with the sample, and (b) the axial dispersion of the sample zone is reduced. 

Axial dispersion of heat In the case of strong exothermic or endothermic reactions, axial temperature profiles will occur even in intensively cooled reactors, and axial (longitudinal) dispersion smoothens these profiles. This dispersion can be described by an effective axial thermal conductivity Xax that combines heat conduction via the gas and solid phase. 

The hypothesis [9.4], under whieh we have just recovered the RTD law for a tubular reactor with axial dispersion, can be restated in the form of a bounding of the turbulence intensity between two values comparing the dimensions of the reactor to the integral scale of turbulence ... 

The above formulas are provided as theoretical guidance for the use of the dispersion model. For evaluation of actual coefficients the reader can consult the numerous experimental studies and correlations for tubes, packed and fluidized beds presented by Wen and Fan (58). One should remember that theory only justifies the use of the axial dispersion model at large Peclet nuu ers (Pe >> 1) and at small intensities of dispersion, i.e. D /uL < 0.15. Therefore, attempts in the literature to apply the dispersion model to small deviations from stirred tank behavior, i.e. for large intensities of dispersion, D /uL > 1, such as in describing liquid backmixing in bubble columns, should be considered with caution. Better physical models of the flow patterns are necessary for such situations and the dispersion model should be avoided. 

In the bubble column the velocity profile of recirculating liquid is shown in Fig. 27, where the momentum of the mixed gas and liquid phases diffuses radially, controlled by the turbulent kinematic viscosity Pf When I/l = 0 (essentially no liquid feed), there is still an intense recirculation flow inside the column. If a tracer solution is introduced at a given cross section of the column, the solution diffuses radially with the radial diffusion coefficient Er and axially with the axial diffusion coefficient E. At the same time the tracer solution is transported axially Iby the recirculating liquid flow. Thus, the tracer material disperses axially by virtue of both the axial diffusivity and the combined effect of radial diffusion and the radial velocity profile. 

Figure 3.8. Dispersion in coiled tubes according to Speberg s model [3.13]. (a) Equivelocity profiles in axial direction, showing the deformation of the parabolic profile by centrifugal forces, (b) Equivelocity profiles in radial direction showing the intense radial mass transfer rate close to the wall (De = 100 for other details see text).

The mixer causes a tangential, a radial and an axial flow. The mixing and dispersive effect are very intensive at the moment that the product passes the mixing head. High shearing forces that are required for dispersing, result from the narrow slits of the stator, the friction among the particles in the fluid and from the reduced space between rotor and stator. 

When operated in a batchwise mode, the induced turbulent field should be intensive enough to ensure the mixing of the complete sample volume, since only a small zone beneath the sonotrode tip actively contributes to the dispersion process. Alternatively, there are flow cells for continuous operation, in which the suspension flows axially onto the sonotrode tip and where the dispersion zone is usually defined by the cell geometry (Fig. 5.4). As a result of the high power consumption and, thus, energy dissipation, the samples should be cooled during ultrasonication. 

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