Role of Mixing

All aspects of mixing in chemical reactors are based on the theory of residence time distribution first enunciated by Danckwerts (1953). Therefore, we begin our discussion of mixing with a brief description of this theory. 

When a steady stream of fluid flows through a vessel, different elements of the fluid spend different amounts of time within it. This distribution of residence times is denoted by a curve which represents, at any given time, the amount of fluid with ages between t and t- -dt flowing out in the exit stream. When normalized with respect to the total flow (i.e., expressed as fraction of the total flow), this distribution, known as the residence time distribution (RTD), satisfies the condition 

The two important characteristics of any distribution are the spread, which is characterized by its mean (fin our case), and the shape, which is characterized by its standard deviation a. The mathematical tool most commonly used to determine these parameters is the analysis of moments, which is fully described in several books, for example, Nauman and Buflham (1983), Nauman (1987), and Levenspiel (1972, 1993). The expression for f is 

The distribution function is usually derived from different types of experimentally determined curves of concentration (usually of a tracer in an inert stream) versus time. These curves represent responses to different signals introduced at the upstream end of the reactor. Two common signals, pulse and step, are 

This represents the fraction of molecules leaving the reactor that had a residence time of t or less. 

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Correlations of nucleation rates with crystallizer variables have been developed for a variety of systems. Although the correlations are empirical, a mechanistic hypothesis regarding nucleation can be helpful in selecting operating variables for inclusion in the model. Two examples are (/) the effect of slurry circulation rate on nucleation has been used to develop a correlation for nucleation rate based on the tip speed of the impeller (16) and (2) the scaleup of nucleation kinetics for sodium chloride crystalliza tion provided an analysis of the role of mixing and mixer characteristics in contact nucleation (17). Pubhshed kinetic correlations have been reviewed through about 1979 (18). In a later section on population balances, simple power-law expressions are used to correlate nucleation rate data and describe the effect of nucleation on crystal size distribution. 

The role of mixing in heterogeneous reactions is obvious. In multiphase processes mixing imposed by a stirrer or an external pump is necessary to increase the interface through which reactants pass to meet their partner in the other phase and/or to intensify mass transfer between phases. Mixing can also play a significant role in the case of homogeneous reactions. Chemical reactions occur at the molecular level. Reactant molecules introduced into a reactor encounter the environment in the vicinity of the inlet. The composition of the mixture there is obviously... 

Vedamuthu, E. R., Sandine, W. E. and Elliker, P. R. 1966. Flavor and texture in Cheddar cheese. I. Role of mixed strain lactic starter cultures. J. Dairy Sci. 49, 144-150. 

The Tuscany Magmatic Province consists of an association of calc-alkaline to lamproitic mafic to intermediate magmas and silicic intrusive and effusive rocks. Silicic melts have been formed by crustal melting, with an important role of mixing with mantle-derived magmas. Mafic melts are of mantle origin but resemble closely some upper crustal rocks, such as metapelites, in terms of incompatible trace elements and radiogenic isotope... 

Chau, A. Mackay, D., A Study of Oil Dispersion The role of Mixing and Weathering, Manuscript Report EE-104, Environment Canada Ottawa, ON, 1988, 46 pp. 

T.A. Popov, andB.J. Blaauboer, Biotransformation of pesticides. The role of mixed function oxidase system in pesticide toxicity, in Toxicology of Pesticides in Animals, ed., T.S.S. Dikshith, CRC Press, Boca Raton, FL, 41, 1991. 

Importance of mixing in flow reactors having biochemical reactions has been studied in the past (1.-4). The results of these studies, are however, not applicable to fermentation systems operated in batch or semi-batch manner and very few publications have addressed themselves to such systems (2 ). On the other hand, fermentations are most commonly carried out in batch or semi-batch systems in which the role of mixing towards performances at different scales of operations is not well understood. Possible reasons for this lack of interest have been a presumption of perfect mixing in non-flowing reactors and the... 

Evaluate the role of mixing of reactants. Is a premixed feed better ... 

Role of Mixed-Function Oxidases in Insect Growth and Development... 

Role of Mixed-function Oxidases in Steroidogenic Reactions... 

Chabot N. L. and Drake M. J. (1999) CrystaUization of magmatic iron meteorites the role of mixing in the molten core. Meteorit. Planet. Sci. 34, 235—246. 

The role of mixed media (water and water-miscible organic solvents) in colour reactions which are useful in spectrophotometric methods has also been discussed [81]. 

Morad, S., Marfil, R., Al-Aasm, l.S. Gomez-Gras, D. (1992) The role of mixing-zone dolomitization in sandstone cementation evidence from the Triassic Bunt-... 

The role of mixing of molecular states can be particularly important for excitonic bands with a small Davydov splitting in crystals with unit cells containing several molecules. 

In order to exemplify of the formulas (3.126) and (3.127) we consider crystals of anthracene type with two molecules per unit cell. In such crystals one usually considers a mixing of the first excited state (1) with the second excited state (2). Since the oscillator strength of the first excited state is much smaller than those of the second excited state, the role of mixing is more relevant for the lower electronic transition (for details, see Section 3.10 of this chapter). 

The role of mixing has been studied in systems with more complex reaction schemes or considering more complex fluid-dynamical properties, and in the context of chemical engineering or microfluidic applications (for reviews on microfluidics see e.g. Squires (2005) or Ottino and Wiggins (2004)). Muzzio and Liu (1996) studied bi-molecular and so-called competitive-consecutive reactions with multiple timescales in chaotic flows. Reduced models that predict the global behavior of the competitive-consecutive reaction scheme were introduced by Cox (2004) and by Vikhansky and Cox (2006), and a method for statistical description of reactive flows based on a con-... 

For an early report on the role of mixed aggregates see Seebach D, Amstutz R, Dunitz JD (1981) HelvChim Acta 64 2622... 

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