Mixing problems

Although the right-hand sides of Eqs. (8.27) and (8.28) are the same, the former applies to the mixture (subscript mix), while the latter applies to the mixing process (subscript m). The fact that these are identical emphasizes that in Eq. (8.27) we have calculated only that part of the total entropy of the mixture which arises from the mixing process itself. This is called the configurational entropy and is our only concern in mixing problems. The possibility that this mixing may involve other entropy effects—such as an entropy of solvation-is postponed until Sec. 8.12. 

The muller is useful for mixing problems requiring certain types of aggregate breakdown, fricdional anchorage of particles to one another, and densification of the final mix. Materials which are excessively fluid or sticky should be avoided. The muller mixer is generally used for batch operations (Fig. 19-9g), although Fig. 19-9/j shows a continuous muller. 

Some mycehal fermentations exhibit early sporulation, breakup of mycehum, and low yields if the shear is excessive. A tip speed or 250 to 500 cm/s (8 to 16 ft/s) is considered permissible. Mixing time has been proposed as a scale-up consideration, but httle can be done to improve it in a large fermenter because gigantic motors would be required to get rapid mixing. Culturing cells from plants or animals is beset by mixing problems because these cell are easily damaged by shear. 

Bakker, A., Fasano, J., and Leung, D. E., Pinpoint mixing problems with lasers and simulation software, Chem. Eng., pp. 94-100, January 1994. 

Sund, E. B., and Lien, K. (1996). An opdmal control fcmnulation of the reacdon-mixing problem. AIChE Annu. Meet, Chicago. 

Alternative microcrystallizer configurations are being developed that seek to avoid the mixing problems asociated with conventional agitated vessels and offer the potential of consistent precipitation of high quality crystal products. 

The oxidation methods described previously are heterogeneous in nature since they involve chemical reactions between substances located partly in an organic phase and partly in an aqueous phase. Such reactions are usually slow, suffer from mixing problems, and often result in inhomogeneous reaction mixtures. On the other hand, using polar, aprotic solvents to achieve homogeneous solutions increases both cost and procedural difficulties. Recently, a technique that is commonly referred to as phase-transfer catalysis has come into prominence. This technique provides a powerful alternative to the usual methods for conducting these kinds of reactions. 

Special baffles. For certain mixing problems, v arious baffling arrangements have been found to be advantageous (see Reference [30]). 

The use of ultra-fine AP to increase the burning rates of double-base propints has been described previously. This technology has also been used with hydrocarbon binders, but dispersion and high viscosity have presented mixing problems. Fine AP can be conveniently dispersed by slurrying first with a surfactant and an organic liq such as 1,1,2-trichloro-1,2,2-trifluoroethane or normal hexane in a process described by Alley (Ref 58a). Sodium sulfonate... 

At the outset it is useful to consider some common examples of problems encountered in industrial mixing operations, since this will not only reveal the ubiquitous nature of the process, but will also provide an appreciation of some of the associated difficulties. Several attempts have been made to classify mixing problems and, for example, REAVELL(1) used as a criterion for mixing of powders, the flowability of the final product. HARNBY et at.(2) base their classification on the phases present that is liquid-liquid, liquid-solid and so on. This is probably the most useful description of mixing as it allows the adoption of a unified approach to the problems encountered in a range of industries. This approach is now followed here. 

The mixing problems considered so far have related to batch systems in which two materials are mixed together and uniformity is maintained by continued operation of the... 

An example of a low conversion reactor would be a conventionally agitated kettle with large turbine agitators and jacket cooling. The utility of this type of reactor can be extended to intermediate conversions by the use of anchor or helical agitators to partially overcome heat transfer and mixing problems at higher viscosities. 

The symbol x is used here and in following pages in a somewhat different sense than in earlier portions of the book, where it represents the number of structural units. The segment employed in mixing problems often is conveniently defined as that portion of a polymer molecule requiring the same space as a molecule of solvent it is unrelated to the size of the structural unit, which is of no interest here. The present x, like the previous one, defines the size of a polymer species, however. 

Realistic mixing problems are inherently difficult owing to the complexity of the flow fields, to the fact that the fluids themselves are Theologically complex, and to the coupling of length scales. For this very reason, mixing problems have been attacked traditionally on a case-by-case basis. Modeling becomes intractable if one wants to incorporate all details at once. Nevertheless it appears important to focus on common features and to take a broad view. 

Example 5.7B What would be the PID controller settings for the dye mixing problem if we use IMC-based tuning relations ... 

X Example 5.7C How do the different controller settings affect the system time response in the dye mixing problem ... 

Commercial CFD software has become a reliable tool for carrying out simulations for laminar flows and based on RANS for turbulent flows. Practising engineers gradually have become convinced about the usefulness of RANS-based simulations. This review, however, emphasizes that CFD now has much more to offer. For practicing engineers confronted with mixing problems, it is... 

Thus, the CFD simulation need to only treat the turbulent mixing problem for the mixture fraction. Once (or its statistics) are known, the acid and base concentrations can be found from Eqs. (49) and (50), respectively. 

The modem condition of PT allows three basic groups of problems a problem of bonds, a problem of sites, and a mixed problem to be solved [8], Briefly we shall consider these groups. 

In variants of the mixed problem of percolation, the situations are considered when availability of sites and bonds is correlated and the ranges of distribution of sites and bonds on the sizes overlap. This variant of a problem is considered, for example, in Refs. [120,121],... 

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