Micromixing partial

Micromixing between these two extremes (partial segregation) is possible, but not considered here. A model for (1) is the segregated-flow model (SFM) and for (2) is the maximum-mixedness model (MMM) (Zwietering, 1959). We use these in reactor models in Chapter 20. 

Another Lagrangian-based description of micromixing is provided by multienvironment models. In these models, the well macromixed reactor is broken up into sub-grid-scale environments with uniform concentrations. A four-environment model is shown in Fig. 5.16. In this model, environment 1 contains unmixed fluid from feed stream 1 environments 2 and 3 contain partially mixed fluid and environment 4 contains unmixed fluid from feed stream 2. The user must specify the relative volume of each environment (possibly as a function of age), and the exchange rates between environments. While some qualitative arguments have been put forward to fit these parameters based on fluid dynamics and/or flow visualization, one has little confidence in the general applicability of these rules when applied to scale up or scale down, or to complex reactor geometries. 

As shown in Fig. 5.20, such regions normally occur only near the inlet zones where micromixing is poor. Further downstream, interaction between flamelets will become significant, and the assumptions on which the flamelet model is based will no longer apply.117 Reactors with recirculation zones are also problematic for flamelet models. For these reactors, partially reacted fluid is brought back to mix with the feed streams so that the simple non-premixed flow model no longer applies. 

The micromixing state in an agitated vessel is connected with coalescence of bubbles. Coalescence occurs mainly in the stirrer zone, where the recirculated gas bubbles partially mix with fresh gas in the cavities. It also occurs to a lesser extent in the highly turbulent stream leaving the stirrer, but it is virtually absent in other parts of the vessel because the low kinetic energy of the bubbles cannot stretch out the liquid film between a pair of bubbles to reach the coalescence thickness. 

Only multiple, complex reactions are appropriate, which can be described by more than one reaction equation and more than one reaction rate constant. The progress of these reactions is given by the conversion X of the reactant being consumed, which is present at a sub-stoichiometric concentration, and the yield Yp of the desired product, from which the selectivity Sp = Yp/X and the product distribution Z s P/R can be determined (f - undesired by-product). The product distribution for an extremely fast and complex reaction will depend upon the micromixing, and consequently serves to characterize the interactions between mixing and reaction in partially segregated mixtures. 

Deviations from ideal flow can be classified in two types. In one type of deviation elements of fluid may move through the reactor at different velocities, causing channeling and dead spots. For such behavior to occur, the elements of fluid must not completely mix locally, but remain at least partially segregated as they move through the reactor. The other deviation refers to the extent of the local or micromixing. For exam.ple, there may be some mixing or diffusion in the direction of flow in a tubular reactor. 

Numerical simulations of styrene free-radical polymerization in micro-flow systems have been reported. The simulations were carried out for three model devices, namely, an interdigital multilamination micromixer, a Superfocus interdigital micromixer, and a simple T-junction. The simulation method used allows the simultaneous solving of partial differential equations resulting from the hydrodynamics, and thermal and mass transfer (convection, diffusion and chemical reaction). 

The new process is realized by direct contacting of hydrogen and oxygen (without inert gas) using a micromixer, in the presence of a heterogeneous catalyst in a trickle-bed mode [12]. The key to high selectivity is to have a noble metal catalyst in a partially oxidized state. Otherwise, either only water is formed or no reaction is achieved. 

These test reactions exhibit several suitable features, for example, known kinetics, partial segregation at molecular scale, a product distribution characterizing the degree of micromixing, simple chemical analysis, and many degrees of freedom for the experimentahst. During the experiments, the product distribution is determined by GC analysis of either the residual ester or of the ethanol formed. 

The application of solid catalysts in microreactors has been studied for different processes. Automated laboratory systems were applied for catalyst screenings [53,54]. Ag/Al and Ag/Al203 were applied in microflow-through reactors for the partial oxidation of ethylene [55]. For catalytic applications, a microflow-through arrangement with a static micromixer was used to prepare Au/Ag nanoparticles [56]. Microfluid segments are also of interest for catalytic reactions in microreactors [57]. 

In the case of incomplete micromixing, we have to take into account partial derivatives in spatial direction for our model, so that we get the following mathematical problem ... 

Models for partial micromixing Since the introduction of the parameter J, defined by Equation 3.35, to describe the degree of segregation (Danckwerts, 1953 Zwietering, 1959), there has been an explosion of models to describe the degree of segregation (i.e., of partial micromixing)... 

The competition between reaction and diffusion can be represented by the lEM-model. t is identified with a diffusion time t = yL /33 (see Sec. 3.2 above) where different diffusivities 3j and hence different micromixing times t- may be used for each species. This simple lumped parameter model gives results comparable to those of more sophisticated distributed models, at least for reaction systems which are not too "stiff". An interesting property is revealed by numerical simulations. The simplest way to represent partial segregation in a fluid is to consider that it consists of a mixture of macrofluid (fraction 3) and microfluid (fraction 1-3). It turns out that the ratio (1 - 3)/3 is always close to that of two characteristic times [28 QlSj. In the case of erosive mixing of two reactants in a CSTR (erosion controls mixing and the product of erosion is a microfluid), one finds... 

Figure 2.11 Schematic representation of fluid-fluid microstructured reactors (a micromixer settler b cyclone mixer c interdigital mixer d microchannel with partial overlap e microchannel with membrane or metal contactor f microchannels...

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