Mixing and reaction

Two chambers of equal volume, each containing gas species A and B, are compressed into a single chamber. As a result, the average density of chamber 2 increases due to the compression. The mixture concentration in chamber 1 differs to that in chamber 2. That is, the concentration vector in chamber 1, Cj is different from 3. Since density is longer constant, it is not possible to express the mixture concentration in chamber 2 as a linear combination of concentration vectors Cj and 3. Instead, the mass of components A and B are conserved, and hence a mass balance may be performed. 

Similar to the discussion in Chapter 2, a component mass balance for A gives 

A similar procedure may be carried out with component B, giving 

The system of equations may be combined into mass fraction vectors 

These can be written more compactly in vector notation as follows  

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There are many potential advantages to kinetic methods of analysis, perhaps the most important of which is the ability to use chemical reactions that are slow to reach equilibrium. In this chapter we examine three techniques that rely on measurements made while the analytical system is under kinetic rather than thermodynamic control chemical kinetic techniques, in which the rate of a chemical reaction is measured radiochemical techniques, in which a radioactive element s rate of nuclear decay is measured and flow injection analysis, in which the analyte is injected into a continuously flowing carrier stream, where its mixing and reaction with reagents in the stream are controlled by the kinetic processes of convection and diffusion. 

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. 

Two examples of dual-channel manifolds for use In flow Injection analysis where R1 and R2 are reagent reservoirs P Is the pump S Is the sample I Is the Injector B Is a bypass loop W Is waste C Is the mixing and reaction coll and D Is the detector. 

Fluidization. Particles suspended in a gas stream behave like a Hquid. They can be mixed by turbulent motion in a duidized bed. This mixer is used for mixing and drying, or mixing and reaction. 

Lee, Y.-M. and Lee, L.J., 1987. Effect of mixing and reaction on a fast step growth polymerization. International Polymer Processing, 1, 144-152. 

Sulzer Chemtech (2006) Mixing and Reaction Technology, Sulzer Chemtech, Winterthur. 

A detailed characterization of micro mixing and reaction performance (combined mixing and heat transfer) for various small-scale compact heat exchanger chemical reactors has been reported [27]. The superior performance, i.e. the process intensification, of these devices is evidenced and the devices themselves are benchmarked to each other. 

Table 5.4-24 summarises the various characteristic time constants for reaction and mixing. Instantaneous (very rapid), fast (rapid) and slow (very slow) reactions have been classified based on characteristic time constants (time scales) for mixing and reaction. Denoting the mixing time scale by xm (t99, to, xms, xds, or x ,) reactions can be classified as follows from the viewpoint of competition with individual stages of mixing tm xf => instantaneous TM XR => fast TM XR => slow... 

Losey MW, Jackman RJ, Firebaugh SL, Schmidt MA, Jensen KF (2002) Design and fabrication of microfluidic devices for multiphase mixing and reaction. J Microelectromech Syst 11 709-717... 

Thus, the final product mixture will depend on the relative importance of mixing and reaction in determining (T )i(f). Finally, note that since the second environment was necessary to describe the ignition source, this simple description of ignition and extinction would not be possible with a one-environment model (e.g., the conditional moment closure). 

This is rarely done in practice. For example, all commonly used models ignore possible effects of chemical reactions on the scalar-mixing process. Compare this with the flamelet model, where mixing and reactions are tightly coupled. 

Note that the empirical PDF in (7.2) depends explicitly on the number of notional particles IV/. However, it also depends implicitly on the number of grid cells (M) through the particle transport algorithm described below. The statistical error associated with estimation of the mean composition (< />) using (7.4) will scale as ,2)/N/)1/2. In zones of the flow where the variance (e//2) is small (e.g., in streams with pure fluid (e/> 2) = 0), Ni can be small However, in zones where mixing and reactions are important, Ni = 100-500 is typically required to obtain particle-number-independent estimates. 

Yellow 96 Dye was produced by the mixing and reaction of two chemicals, orf/zo-nitrochlorobenzene (o-NCB) and 2-ethylhexylamine (2-EHA). The dye was used to tint petroleum fuel products. 

Pope, S. B. 1991. Mapping closures for turbulent mixing and reaction. Theoretical Computational Fluid Dynamics 2 255-70. 

Frankel, S.H., C.K. Madnia, P. A. McMurtry, and P. Givi. 1993. Binary scalar mixing and reaction in homogeneous turbulence Some linear eddy model results. 

There is one significant, but frequently overlooked implicit assumption w hen discussing mixing and reaction. The assumption is that only one solution to the diffusion-reaction equation exists. This does not have to be the case. Already in 1952, the mathematician Turning predicted the existence of exotic solutions in 3D space [45]. These give rise to... 

Oscilloscopic observations were made to estimate the mixing and reaction times. Tests with dyes showed that the mixing time was well within the 33-msec, chopping time of the spectrophotometer. Brief observations during the approximately 8-msec, view of the sample beam permitted each cycle allowed an estimate of 15 to 20 msec, for the mixing time. Similar observations with ferrous mercapto-acetate solutions injected into oxygen-containing buffers showed no differences from the tests with dyes. Apparently the oxidation is completed within a few milliseconds or less. 

This was developed at the Chemical Engineering Department of Valladolid University, Spain (see Fig. 9.4-8). In this type of reactor the temperature and pressure effects are isolated. This is achieved by using a cooled wall vessel, which is maintained near 400 C, and a reaction chamber where the reactants are mixed and reaction takes place. This reaction chamber is made of a special material to withstand the oxidizing effect of the reactants at a maximum temperature of 800 °C and a pressure of 25 MPa. It is enclosed in the main vessel, which is pressurized with the feed-stream before entering the reaction chamber, so that it works at about 400 °C and does not suffer from the oxidizing atmosphere. It is made of relatively thin stainless steel [15]. 

The rates of the reactions are not usually limiting for in vitro reactions, whereas slow reactions can cause serious mixing and reaction-volume problems in post-column procedures. This effect is not very serious in TLC. 

For the case study, it is not difficult to obtain that = 4.6 x 104 PEI/h, i.e. / is a constant. Therefore, when the feed condition of a reaction process is fixed, back-mixing and reaction temperature affect Igen and 7out in the same way. Since j> = voCc.outMc x 10-3, it is not difficult to find that, when the feed condition and Q out are specified, back-mixing and reaction temperature influence 7out and pei in the same way, too. 

Figure 19 The influence of mixing and reaction rates on reactor behavior.

For a slow reaction, the mixing rates are all much faster than the inherent kinetics in this case the mixing and reaction processes are decoupled. For a motionless-mixer system, there must be sufficient residence time downstream of the mixer for the reaction to go to completion. For long reaction times, a stirred tank can be used to give the required residence time. The process then becomes ... 

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