Curved tube, flow through

The CL emission of Scheme 3 catalyzed by HRP can be applied to the quantitative analysis of catecholamines, such as dopamine (68), epinephrine (132), L-DOPA (30), norepinephrine (133), deoxyepinephrine (134) isoproterenol (135) and dihydroxybenzy-lamine (136), in a F1A system, after undergoing the oxidation shown for dopamine (68) in equation 20. The mechanism of this process is not totally clear however, the CL yields of equation 20 depend upon the pH of the system (pH 9 is convenient and is achieved by adjusting the concentration of imidazole), the temperature (60 °C is adequate) and the structure of the analyte (a calibration curve is needed for each one). Taking 68 as reference (100%) the CL yields after 30 min incubation (achieved by controlling the flow through a long capillary tube) are as shown in equation 42350-351. 

Data acquired by many investigators have shown a close analogy between the rates of heat and mass transfer, not only in the case of packed beds but also in other cases, such as flow through and outside tubes, and flow along flat plates. In such cases, plots of the /-factors for heat and mass transfer against the Reynolds number produce almost identical curves. Consider, for example, the case of turbulent flow through tubes. Since... 

Table 1 lists the characteristics of the measured RTD for five different conditions. The first one is shown in Figure 2. The evolution of this curve can be explained by equation (1), although the peaks are not ideal Dirac pulses, because the flow inside the reactor (i.e. the reactor tube (c) and the recirculation pipe (d) in Figure 1) is not of the ideal plug flow type. Therefore, the tracer pulse broadens and eventually spreads throughout the reactor. Nevertheless, the distance between two peaks is a reasonably accurate estimate of the circulation time r/(R+1) in the reactor, and from this the flow through the reactor can be calculated. The recycle ratio R is calculated from the mean residence time r and the circulation time r/(R+l). 

The opportunity to measure the dilute polymer solution viscosity in GPC came with the continuous capillary-type viscometers (single capillary or differential multicapillary detectors) coupled to the traditional chromatographic system before or after a concentration detector in series (see the entry Viscometric Detection in GPC-SEC). Because liquid continuously flows through the capillary tube, the detected pressure drop across the capillary provides the measure for the fluid viscosity according to the Poiseuille s equation for laminar flow of incompressible liquids [1], Most commercial on-line viscometers provide either relative or specific viscosities measured continuously across the entire polymer peak. These measurements produce a viscometry elution profile (chromatogram). Combined with a concentration-detector chromatogram (the concentration versus retention volume elution curve), this profile allows one to calculate the instantaneous intrinsic viscosity [17] of a polymer solution at each data point i (time slice) of a polymer distribution. Thus, if the differential refractometer is used as a concentration detector, then for each sample slice i. 

Our main concern here is to present the mass transfer enhancement in several rate-controlled separation processes and how they are affected by the flow instabilities. These processes include membrane processes of reverse osmosis, ultra/microfiltration, gas permeation, and chromatography. In the following section, the different types of flow instabilities are classified and discussed. The axial dispersion in curved tubes is also discussed to understand the dispersion in the biological systems and radial mass transport in the chromatographic columns. Several experimental and theoretical studies have been reported on dispersion of solute in curved and coiled tubes under various laminar Newtonian and non-Newtonian flow conditions. The prior literature on dispersion in the laminar flow of Newtonian and non-Newtonian fluids through... 

Figure 4-5. The streamlines for the secondary flow of a fluid that is moving through a slightly curved tube. Contour values are plotted in incre- Inside ments of 0.2222.

Figure 4-6. Contours of constant axial velocity for pressure-driven flow through a slightly curved tube. Values are plotted in increments of 0.3819.

In Chap. 4 we explored the consequences of a weak departure from strict adherence to the conditions for unidirectional flow namely, the effect of slight curvature in flow through a circular tube. For that case, the centripetal acceleration associated with the curved path of the primary flow was shown to produce a weak secondary motion in the plane orthogonal to the tube axis. In this chapter we consider another class of deviations from unidirectional flow that occur when the boundaries are slightly nonparallel. 

The laminar flow data of Figure 3.39 have a higher slope (0.52 than predicted by theory (0.33)-probably because of "secondary flow effects". The data were taken in a spiral flow thin channel device. Whenever fluid passes through a curved tube or channel, centrifugal forces tend to throw fluid outward from the center of the channel. It then recirculates inward along the walls of the channel (see Figure 3.40). It is well known that coiled tube heat exchangers possesses superior heat transfer characteristics because of secondary flow effects. 

Fig. 17.15 shows how the friction factor increased with time in a "sample" finned tube heat exchanger exposed to an air flowing through laden with calcium carbonate particles the apparatus shown in Fig. 17.14. It may be regarded as a typical curve obtained in the laboratory apparatus. During the experiments water at temperature in the range 10 - 90°C was passed through the tubes. The equipment allowed thermal performance and pressure drop to be measured. From Fig. 17.15 it can be seen that the friction factor rises asymptotically to a level 50%...

Dean vortices are the secondary flows that occur in the cross section of a curved channel or helically coiled tubes. Figure 10.6 shows the secondary flow developed in a helically coiled tube. When fluid flows through the helically curved tube, the faster elements of the fluid in the center of the tube tend to be moved outward by centrifugal force, while the slower elements of the fluid are forced inward to maintain mass balance, resulting in counterrotating vortices in the... 

I-V curves for these artificial ion channels were obtained by mounting the membrane sample between the two halves of a U-tube conductivity cell. Each half-cell was filled with 5 mL of a 10 mM pH = 7 phosphate buffer that was also 100 mM in KCl. A Ag/AgCl reference electrode was inserted into each half-cell solution, and a Keithley Instruments 6487 picoammeter/voltage source was used to apply the desired transmembrane potential and measure the resulting ionic current flowing through the gold nanotube. 

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