Dispersion straight tubes

Figure 5 Schematic diagrams of reactors used in FIA in order of increasing dispersion (a) single bed string reactor, (b) knitted tube, (c) coiled tube, (d) straight tube, and (e) external mixing chamber with stirring.

The traditional parabolic model with Danckwerts boundary conditions is also used in the literature to describe dispersion effects in packed beds (and porous media). However, unlike the case of capillaries and straight tubes, the flow field in packed beds is more complex and is three-dimensional. However, for many cases of interest, the average velocity in the transverse directions is zero. In such cases, dispersion in the flow direction can be described by the... 

Agarwal and Jayaraman Spectral method with finite difference method 100 < Aoe Asc < Iff For the range of A e Asc from Iffff to Iff the axial dispersion in a circular curved tube is markedly less than that in a straight tube... 

For ARe < 300, axial dispersion in helical coils was found to be of the same order as that in straight tube, and for equal power consumption helical coils facilitate less axial dispersion than do straight tubes... 

For increasing values of the axial dispersion in the helical coils decreases as compared with that in straight tube... 

Fig. 7 Comparison of various axial dispersion correlations (k = Dc/Dg, ratio of dispersion in coiled tube to the straight tube).

Using the method of moments, Aris (1956) was able to generalize Eq. [25] for a straight tube with an aperture of arbitrary cross-section. His expression for the dimensionless dispersion coefficient is ... 

In this context, Griffiths reported in 1911 the interactions of an aqueous plug with a chemically inert carrier stream flowing through a narrow, straight tube [53]. He carried out the first experimental work demonstrating the essence of the dispersion process and concluded (without a mathematical treatment) that "a tracer injected into a water stream spreads out in a symmetrical manner about a plane in the cross section that moves with the mean flow velocity" [54], He also pointed out the establishment of a fully developed laminar flow regime. 

In a straight tube of uniform diameter (Fig. 2.SA), the parabolic profile (Fig. 3.4) formed by laminar flow remains undisturbed up to a flow velocity not normally reached in a typical FIA system, and since the radial diffusion occurring in the time frame oif an FIA experiment is not sufficient to offset the axial dispersion initially formed during sample injection, an asymmetrical peak is recorded (Figs. 2.4a and 2.10a). 

Figure 2.10. Dispersion of a dye, injected as a sample zone (Sy = 25 jiL) into A, straight tube By coiled tube C, knitted tube and D, a SBSR reactor. The reactor volumes (Vr = 160 iL) and pumping rates (Q = 0.75 mL/min) were identical in all experiments. The same piece of Microline tubing (L = 80 cm, 0.5 mm inside diameter) was used in experiments Ay By and C. (The injected dye was bromthymol blue, carrier stream 0.1 M borax and wavelength 620 nm, cf. Chapter 6.) The SBSR reactor was made of 0.86 mm inside diameter tube filled with 0.6-mm glass beads. Note that the isodispersion points on the peaks were recorded with microreactors made of identical length and diameter, but different geometry.

The computer simulations of chemical kinetics in a straight tube reactor [1065] were based on an equation combining diffusion, convection, and reaction terms. The sample dispersion without chemical reactions gave very similar results to that of Vanderslice [1061], yet the value of that paper is that it expanded the study to computation of FIA response curves for fast and slower chemical reactions. The numerically evaluated equation was similar to that of Vanderslice [1061], however with inclusion of a term for reaction rate. Two model systems were chosen and spectro-photometrically monitored in a FIA system with appropriately con-... 

It is significant that the preceding conclusions of Reijn et al., obtained for SBSR reactor, are in agreement with the results that Wada et al. [1065] obtained with a straight tube reactor, thus confirming the important conclusion that chemical reactions do not alter the dispersio of the analyte in the reactor. Therefore, the experimental values (D, t, T, and ct ), obtained with a nonreacting tracer alone, are well suited for the description of dispersion in any FIA system in the presence or absence of chemical reaction. 

Axial dispersion in packed beds, and Taylor dispersion of a tracer in a capillary tube, are described by the same form of the mass transfer equation. The Taylor dispersion problem, which was formulated in the early 1950s, corresponds to unsteady-state one-dimensional convection and two-dimensional diffusion of a tracer in a straight tube with circular cross section in the laminar flow regime. The microscopic form of the generalized mass transfer equation without chemical reaction is... 

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