Mixed theory

Curl, R.L., 1963. Dispersed phase mixing-theory and effects in simple reactors. American Institution of Chemical Engineers Journal, 9, 175. 

Uhl, V.W. and Gray, J.B., 1986. Mixing Theory and practice (3 vols). New York Academic Press. 

The orbital mixing theory was developed by Inagaki and Fukui [1] to predict the direction of nonequivalent orbital extension of plane-asymmetric olefins and to understand the n facial selectivity. The orbital mixing rules were successfully apphed to understand diverse chemical phenomena [2] and to design n facial selective Diels-Alder reactions [28-34], The applications to the n facial selectivities of Diels-Alder reactions are reviewed by Ishida and Inagaki elesewhere in this volume. Ohwada [26, 27, 35, 36] proposed that the orbital phase relation between the reaction sites and the groups in their environment could control the n facial selectivities and review the orbital phase environments and the selectivities elsewhere in this volume. Here, we review applications of the orbital mixing rules to the n facial selectivities of reactions other than the Diels-Alder reactions. 

For the general case of interacting fluid elements, (1.9) and (1.10) no longer hold. Indeed, the correspondence between the RTD function and the composition PDF breaks down because the species concentrations inside each fluid element can no longer be uniquely parameterized in terms of the fluid element s age. Thus, for the general case of complex chemistry in non-ideal reactors, a mixing theory based on the composition PDF will be more powerful than one based on RTD theory. 

As discussed in Chapter 3, classical scalar-mixing theory yields a mean scalar dissipation rate of... 

As discussed in Chapter 3, at very high Reynolds numbers, turbulent mixing theory predicts that the scalar dissipation rate will be independent of Re and Sc. Thus, most molecular models ignore all dependencies on these parameters, even at moderate Reynolds numbers. In general, the inclusion of dependencies on Re, Sc, or Da is difficult and, most likely, will have to be done on a case-by-case basis. 

Among the purposes of this paper is to report the results of calorimetric measurements of the heats of micellar mixing in some nonideal surfactant systems. Here, attention is focused on interactions of alkyl ethoxylate nonionics with alkyl sulfate and alkyl ethoxylate sulfate surfactants. The use of calorimetry as an alternative technique for the determination of the cmc s of mixed surfactant systems is also demonstrated. Besides providing a direct measurement of the effect of the surfactant structure on the heats of micellar mixing, calorimetric results can also be compared with nonideal mixing theory. This allows the appropriateness of the regular solution approximation used in models of mixed micellization to be assessed. 

The Life of an Element of Fluid. Let us estimate how long a fluid element retains its identity. First, all large elements are broken into smaller elements by stretching or folding (laminar behavior) or by turbulence generated by baffles, stirrers, etc., and mixing theory estimates the time needed for this breakup. 

The random mixing theory and mixing processes have been extensively explored (2). Randomization requires equally sized and weighted particles, with little or no surface effects, showing no cohesion or interparticle interaction, to achieve the best results it cannot be applied to all practical mixing situations, especially where cohesive or interacting particles are mixed. 

Uhl VW, Von Essen JA. Scale-up of equipment for agitating liquids. In Uhl VW, Gray JB, eds. Mixing Theory and Practice, Vol. III. New York Academic Press, 1986 200. 

Calderbank P H (1967) Mass Transfer in Mixing, Theory and Practice. In Uni V W and Gray J B (eds.), Academic Press New York, London. 

Making use of the random mixing theory, the canonical ensemble partition function becomes... 

This chapter is on mixing principles, their respective devices and their characterization and is intended to give the reader an idea of how well they already function. This chapter is not really on mixing theory and physics of micro mixers. 

Fig. 7.17 Unmixed polyethylene superconcentrate (50% carbon black) in a mixture of superconcentrate and unfilled polyethylene as a function of viscosity ratio. [Reprinted by permission from V. W. Uhl and J. B. Gray, Mixing Theory and Practice, Vol. II, Academic Press, New York, 1967.]...

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