Micromixing definition

In Fig. 7, the mixture fractions in each environment and l2 are shown. By definition of the inlet conditions, in the inlet tubes — 0 and 2 = 1. The variations away from the inlet values represent the effect of micromixing. For example, if we set y — 0 in Eqs. (36) and (37) to eliminate micromixing, then and 2 would remain at their inlet values at all points in the reactor. Note that the spatial distributions of 1 and %2 are antisymmetric with respect to the vertical axis (as would be expected from the initial conditions.) In the outlet tube, and 2 are very near the perfectly micromixed value of 1/2. Finally, by comparing Fig. 6 and Fig. 7, we can observe that macromixing occurs slightly faster than micromixing in this reactor (i.e.,pn are closer to their outlet values than are .)... 

The micromixing time has an exact definition in terms of the rate of decay of concentration fluctuations. The mixture fraction is defined in Chapter 5. 

In the statistical theory of fluid mixing presented in Chapter 3, well macromixed corresponds to the condition that the scalar means () are independent of position, and well micromixed corresponds to the condition that the scalar variances are null. An equivalent definition can be developed from the residence time distribution discussed below. 

By definition, averaging (1.16) with respect to the operator ( ) (definedbelow in (1.18)) causes the micromixing term to drop out 22... 

The importance of including mesomixing in the definition of tm has been demonstrated using jet-mixer scale-up experiments by Baldyga et al. (1995). In these experiments, the micromixing rate was found to scale as... 

The specification of G and M(n) depends on the definition of the micromixing model. However, the conservation of probability requires that the sum of the probabilities be unity. Thus, from (5.342), we find... 

As done below for two examples, expressions can also be derived for the scalar variance starting from the model equations. For the homogeneous flow under consideration, micromixing controls the variance decay rate, and thus y can be chosen to agree with a particular model for the scalar dissipation rate. For inhomogeneous flows, the definitions of G and M(n) must be modified to avoid spurious dissipation (Fox 1998). We will discuss the extension of the model to inhomogeneous flows after looking at two simple examples. 

The time it takes a molecule to pass through a reactor is called its residence time 6. Two properties of 6 are important the time elapsed since the molecule entered the reactor (its age) and the remaining time it will spend in the reactor (its residual lifetime). We are concerned mainly with the sum of these times, which is 6, but it is important to note that micromixing can occur only between molecules that have the same residual lifetime molecules cannot mix at some point in the reactor and then unmix at a later point in order to have different residual lifetimes. A convenient definition of residence-time distribution function is the fraction J ) of the effluent stream that has a residence time less than 0. None of the fluid can have passed through the reactor in zero time, so / = 0 at 0 = 0. Similarly, none of the fluid can remain in the reactor indefinitely, so that Japproaches 1 as 0 approaches infinity. A plot of J 6) vs 0 has the characteristics shown in Fig. 6-2a. 

The characteristic dimensionless numbers such as Reynolds number (Re) and Peclet number (Pe) are very suitable for discussing the operating conditions for micromixers. From the definitions in Equations (7.1) and (7.2), the relation... 

Most of the research on reactive extrusion is performed in twin screw extruders, although a single-screw co-kneader has definite advantages if micromixing plays an important role. Franz (24) gave an overview of applications of reactive extrusion with a Busskneader in a paper discussing the polycondensation reaction of silanoles to produce silicon oils. Aeppli (25)... 

Micromixing is concerned with all the processes whereby parts of a fluid initially unmixed come into contact and mix on a molecular scale. However, this definition has to be specified. Let p(C) be the local concentration distribution of a given component in an imperfect mixture. The average concentration is... 

Mass Transfer Performance tests were designed to test for micromixing or for mass transfer performance and thus, to facilitate definition of the cell design specifications. Limited reaction data had been recorded for the 2-proposal reaction over alumina. 

---