Time scale, micro-mixing

Micro reactors show, under certain conditions, low axial flow dispersion reactions with unstable intermediates can be carried out in a fast, stepwise manner on millisecond time-scales. Today s micro mixers mix on a millisecond scale and below [40]. Hence in micro reactors reactions can be carried out in the manner of a quench-flow analysis, used for determination of fast kinetics [93]. 

If a mixer is to be used for reactive processes, it should be designed such that the longest mixing time scale (whether micro-, meso-, or macromixing) is significantly shorter than the characteristic time scale of the desired chemical reaction. As mentioned in Section 3, any of the time scales can be rate determining. 

P 28] A 3-D solid model of the cross-shaped micro mixer is meshed to a sufficiently fine scale with brick elements of 2 pm for the simulations [71]. Simulation results were intended at very short time scales, e.g. in intervals of 50 ps, to verify the mixing patterns at the initial state after application of pressure. The numerical values of the mass fraction are taken to give quantitative measures of the mixing efficiency. The pre-processor fluidics solver and post-processor of ConventorWare were used for the simulations. The software FLUENT 5 was used for verification of these results, since the former software is so far not a widely established tool for fluid dynamic simulation. 

The majority of the research on the photochemistry of porphyrins linked to other moieties has been in the area of photoinduced electron transfer, and the systems studied are all in some sense mimics of the photosynthetic process described above. The simplest way to prepare a system in which porphyrin excited states can act as electron donors or acceptors is to mix a porphyrin with an electron acceptor or donor in a suitable solvent. Experiments of this type have been done for years, and a good deal about porphyrin photophysics and photochemistry has been learned from them. Although these systems are easy to construct, they have serious problems for the study of photoinduced electron transfer. In solution, donor-acceptor separation and relative orientation cannot be controlled. As indicated above, electron transfer is a sensitive function of these variables. In addition, because electron transfer requires electronic orbital overlap, the donor and acceptor must collide in order for transfer to occur. As this happens via diffusion, electron transfer rates and yields are often affected or controlled by diffusion. As mentioned above, porphyrin excited singlet states typically have lifetimes of a few nanoseconds. Therefore, efficient photoinduced electron transfer must occur on a time scale shorter that this. This is difficult or impossible to achieve via diffusion. Thus, photoinduced electron transfer between freely diffusing partners is confined mainly to electron transfer from excited triplet states, which have the required long lifetimes (on the micro to the millisecond time scale). 

Empirical constant in wall function, also used as a reciprocal of a characteristic micro-mixing time scale... 

As regards scale-up it must therefore be noted that mixing efficiency in small devices is more favorable than in large ones. This must also be taken into account in baffled tanks, although here fx.y.z/w is constant, but the circulation and macromixing times are longer This relationship wiU be considered further in connection with micro-mixing and chemical reactions (see [462] and Section 1.4.6.4). 

Considering the agglomerate size to be on the order of the Kolmogoroff scale (or some other appropriate length scale), the micro-mixing time for molecular diffusion is given by... 

For gases, 5c 1, for hquids. Sc 1. This implies that in turbulent flow of liquids, the species concentration field contains smaller scale structures than the velocity field. Similar to the decay time of the turbulent eddies in the velocity field, Tu, (12.2-1), the decay time of the eddies in the species concentration field, the previously introduced micro-mixing time, xy, can be modeled in terms of the correlation of the species mass fraction fluctuations, the so-called scalar (co-) variance, (K F), and its dissipation rate, the so-called scalar dissipation rate, sy. 

The description is based on the previously defined single-particle (Lagrangian) or one-point (Eulerian) joint velocity-composition (micro-)PDF, /(r,yr). As mentioned in Section 12.4.1, in the one-point description no information on the local velocity and scalar (species concentrations, temperature,. ..) gradients and on the frequency or length scale of the fluctuations is included and the related terms require closure models. The scalar dissipation rate model has to relate the micro-mixing time to the turbulence field (see (12.2-3)), either directly or via a transport equation for the turbulence dissipation rate e. A major advantage is that the reaction rate is a point value and its behavior and mean are described exactly by a one-point PDF, even for arbitrarily complex and nonlinear reaction kinetics. 

Paul and Treybal [1971], They found that "Power per unit volume is... incapable of correlating the widely different local conditions within a stirred vessel." Instead, a criterion involving both the intrinsic reaction rate constants and a micro-time scale to account for micro-mixing effects (see Sections 12.2 and 12.3) was developed. 

In Chapter 7 the effects of transport phenomena on the scale of the reactor are considered. We call these macro flow effects. These can be described in terms of macro-mixing. For continuous reactors macro>mixing causes residence time distribution. Combined with micro-mixing this will lead to backmixing. When two or more phases are present in the reactor, the way these are each introduced into and removed from the reactor are quite essential for the performance of the reactor. These various effects are considered in this chapter in order to arrive at an integral reactor model. As in Chapter 3, only isothermal reactor models are considered so far. 

In all these cases, the mechanical agitating device serves two purposes at the same time it creates an overall circulation, which results in macro-mixings and it creates eddies or small scale circulations, causing shear or elongational flow which combined with molecular diffusion results in micro-mixing. 

---