Profile mixed flow

The time-to-distance transfonnation requires fast mixing and a known flow profile, ideally a turbulent flow with a well-defined homogeneous composition perpendicular to the direction of flow ( plug-flow ), as indicated by tire shaded area in figure B2.5.1. More complicated profiles may require numerical transfomiations. 

When a sample is injected into the carrier stream it has the rectangular flow profile (of width w) shown in Figure 13.17a. As the sample is carried through the mixing and reaction zone, the width of the flow profile increases as the sample disperses into the carrier stream. Dispersion results from two processes convection due to the flow of the carrier stream and diffusion due to a concentration gradient between the sample and the carrier stream. Convection of the sample occurs by laminar flow, in which the linear velocity of the sample at the tube s walls is zero, while the sample at the center of the tube moves with a linear velocity twice that of the carrier stream. The result is the parabolic flow profile shown in Figure 13.7b. Convection is the primary means of dispersion in the first 100 ms following the sample s injection. 

Viscous forces within the fluid will always prevent a completely unhindered discharge, but in extrusion practice an additional die head resistance is used to generate backflow and mixing, so that a more uniform product is obtained. The flow profile along the channel is then of some intermediate form, such as that shown in Figure 8.18c. 

Figure 5.4a compares the profiles for a mixed-flow and plug-flow reactor between the same inlet and outlet concentrations, from which it can be concluded that the mixed-flow reactor requires a larger volume. The rate of reaction in a mixed-flow reactor is uniformly low as the reactant is instantly diluted by the product that has already been formed. In a plug-flow or ideal-batch reactor,... 

Example 14.1 Consider again the chlorination reaction in Example 7.3. This was examined as a continuous process. Now assume it is carried out in batch or semibatch mode. The same reactor model will be used as in Example 7.3. The liquid feed of butanoic acid is 13.3 kmol. The butanoic acid and chlorine addition rates and the temperature profile need to be optimized simultaneously through the batch, and the batch time optimized. The reaction takes place isobarically at 10 bar. The upper and lower temperature bounds are 50°C and 150°C respectively. Assume the reactor vessel to be perfectly mixed and assume that the batch operation can be modeled as a series of mixed-flow reactors. The objective is to maximize the fractional yield of a-monochlorobutanoic acid with respect to butanoic acid. Specialized software is required to perform the calculations, in this case using simulated annealing3. 

The first distinction to be drawn, as far as heat transfer is concerned, is between the plug-flow and mixed-flow reactor. In the plug-flow reactor shown in Figure 20.1, the heat transfer can take place over a range of temperatures. The shape of the profile depends on the following. 

Level (3) global e.g., reactor model some key parameters reactor volume, mixing/flow, residence time distribution, temperature profile, reactor type... 

Figure 6.3 Concentration profile through an iV-stage mixed flow reactor system compared with single flow reactors.

For exothermic reactions we illustrate this procedure in Fig. 9.4 for three paths path AB for plug flow with an arbitrary temperature profile, path CD for noniso-thermal plug flow with 50% recycle, and point E for mixed flow. Note that for mixed flow the operating line reduces to a single point. 

Example 2-6 Consider the situation where the reactants at constant density are fed continuously into a pipe of length L instead of a tank of volume V as in the batch reactor. The reactants react as they flow down the tube with a speed u, and we assume that they flow as a plug without mixing or developing the laminar flow profile. Show that the conversion of the reactants is exactly the same in these very different reactor configurations. 

Figure 8-7 Effect of radial mixing on flow profile and p(t).

NMR imaging techniques were applied to the measurements of velocity field in opaque systems such as tomato juice and paper pulp suspensions [58-60]. In both cases, the particle concentrations are sufficiently high that widely applied techniques such as hot film and laser Doppler anemometry could not be used. The velocity profile for a 6 % tomato juice slurry clearly showed a power-law behavior [58, 59]. Row NMR images for a 0.5 % wood pulp suspension provided direct visual of three basic types of shear flow plug flow, mixed flow and turbulent flow as mean flow rate was increased. Detailed analysis of flow NMR image is able to reveal the complex interaction between the microstructure of suspensions and the flow [60]. 

For the small microchannel dimensions involved (Figure 7), conductive heat transfer plays an important role, augmenting the heat transfer coefficients by a factor of 5 or more to values in the vicinity of 700 W/m2K. This phenomenon is also responsible for good transverse mixing, counteracting the negative effects of laminar-flow profiles. 

Axial mixing correlates directly with the residence time distribution in an extruder. The width of the residence time distribution is determined by the flow profiles in the screw... 

Any experiment suffers to some extent from the influence of various uncontrolled factors, such as mass- and heat-transfer regimes in different parts of the reaction system, irregularity of temperature fields and flow profiles, dead spaces, poor mixing, and independent flow of reactants, wall chemistry and its variation with time, etc. Another problem is a correlation between signals received from different sensors and real values of measured physical parameters. There is a voluminous literature on this subject here we just mention the pitfalls related to the measurements of surface and gas temperatures in the course of reaction involving very active radical species. 

Figure 7.6 Serpentine mixer used for the generation of eluent gradients with LC EOF pumps. (A) Inlet of serpentine mixer displaying two distinct fluid flows (B) non-uniform fluorescent intensity profile along the channel cross-section (C) outlet of serpentine mixer displaying the fully mixed flows (D) equalized fluorescent intensity profile along the channel cross-section.

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