Macro-flow

The key attribute of flows in micro devices is their laminar character, which stands in contrast to the mostly turbulent flows in macroscopic process equipment. Owing to this feature, micro flows are a priori much more accessible to a model description than macro flows and can be described by first-principle approaches without any further assumptions. In contrast, for the simulation of turbulent flows usually a number of semi-heuristic models are applied, and in many situations it is not clear which description is most adequate for the problem under investigation. As a result, it stands to reason to assume that a rational design of micro reactors... 

The term numerical diffusion describes the effect of artificial diffusive fluxes which are induced by discretization errors. This effect becomes visible when the transport of quantities with small diffusivities [with the exact meaning of small yet to be specified in Eq. (42)] is considered. In macroscopic systems such small diffusivities are rarely found, at least when being looked at from a phenomenological point of view. The reason for the reduced importance of numerical diffusion in many macroscopic systems lies in the turbulent nature of most macro flows. The turbulent velocity fluctuations induce an effective diffusivity of comparatively large magnitude which includes transport effects due to turbulent eddies [1]. The effective diffusivity often dominates the numerical diffusivity. In contrast, micro flows are often laminar, and especially for liquid flows numerical diffusion can become the major effect limiting the accuracy of the model predictions. 

Surface-enhanced resonance Raman scattering (SERRS) has also been achieved using silver colloid aggregates produced in situ in the chip. This method was used to detect an azo dye, 5-(2,-methyl-3,5,-dinitrophenylazo)quinolin-8-ol, which is a derivative of the explosive, TNT. With this method, it was possible to detect 10 iL of 10 9 M dye (or 10 fmol). This represented a 20-fold increase in sensitivity over that achieved using a macro flow cell [739]. 

The study of evaporating rivulet flow shows that macroscopic flow and heat transfer may be considerably changed itself by microscopic heat transfer, the example is establishing of thermal apparent contact angle in case of rivulet evaporation. Extremely high evaporation rate in thin film area changes the slope of interface as far as macro flow curvature and wave patterns. NOMENCLATURE... 

Figure 8. Ambient pressure glass (macro) flow cell. (Photograph courtesy of Spectra-Tech, Inc.)...

Spectral methods have been a promising tool for simulating micro- and nanoflows as weU as macro-flows because they have excellent properties of high spatial accuracy and rapid convergence. Therefore, they can capture a broad range of dynamically significant scales of motion very effectively. 

In vulcanized rubber the molecular chains are cross linked by chemical bonds which inhibit macro-flow. That is why vulcanized stocks are more perfectly elastic than raw rubber (cf. the models having piston and spring in series.) The chemical cross links, randomly distributed over the mass of rubber, act as permanent junction points. A netlike structure is obviously present in vulcanized rubber. 

The factors inhibiting macro-flow in vulcanised rubber are the chemical cross links due to vulcanisation (and probably also molecular entanglements), considerably assisted by the phenomenon of crystallisation. In unvulcanised raw rubber macro-flow may occur to a certain extend. In cellulose crystalline junction points of a high degree of stability are responsible for the exclusion of macro-flow. In rubber the chains are very flexible and consist of a large number of statistical chain sections in cellulose the chains are stiffer and consist of a small number of chain elements. In the former case the intermolecular forces are weak, in the latter case they are strong. 

One could also address micro flow using Darcy s law for flow within the fiber bundles but characterized by a different permeability as will be shown later, but to rigorously describe the flow within fiber bundles, one must also account for surface tension and couple this flow with the macro flow in between the fiber bundles. More details can be found in the references that model the microvoid formation in the fiber bundles by adding a sink term to the equation of mass conservation. 

An experimentally measured RTD of a steady state flow reactor reflects the spatial characteristics of the macro-flow and -mixing in the reactor, including eventual effects of micro-flow and -mixing phenomena on the macro-flow and -mixing. Hence, inspection of experimental RTD can be used to infer certain properties of the flow pattern. Local information on the macro- or micro-flow and mixing behavior inside the reactor can, however, not be revealed, due to the length scale over which RTD are defined (see (12.6.1-2)) and measurements are... 

Finally we have the reactor models, which in addition take into account the macro flow effects in the reactor. In principle, even research models have to include these macro flow aspects as they act on the scale of the laboratory reactor, small though this may be. In the large scale reactor models, however, the effects of macro flow are usually more pronounced. 

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. 

To go from volume element models to reactor models the macro flow patterns in the reactor need to be considered. For stirred tank reactors this can be quite simple, in those cases where volume elements in the stirred tank can be described in terms of average conditions. This is not so when macro mixing or residence time distribution are scale dependent, see Chapter 7. When the reactor is tubular, with two countercurrent or parallel flows, the volume element models have to be combined with reactor flow models, including axial mixing. Also this is treated in Chapter 7, for various cases. 

Even for the most preliminary design of a chemical reactor, a number of effects have to be taken into account. The most essential characteristic of reactor design is the combination of the volume element model, of which aspects have been discussed in sections 4, 5 and 6, with effects of macro flow, discussed in Chapter 7. In the case of tubular reactors, or columns, an integration is needed over a length coordinate. This will also be discussed briefly in Chapter 7. 

In Chapter 3 we considered chemical reactors with ideal macro flow patterns where the reactor behaviour was independent of scale. In Chapters 4, 5 and 6 an overview was given of various physical phenomena on the intermediate scale, some of which interact with chemical reactions. Several of these phenomena are scale dependent. To arrive at integral reactor models, we have to consider macro-flow effects, i.e. the effects of transport phenomena on the scale of the reactor dimensions. These are as a rule strongly scale dependent. 

In most batch reactors macro flow effects are of little consequence, though there are a few important exceptions. In semi-batch reactors the macro-flow effects may be particularly relevant in view of the selectivity of the process. 

For describing macro-flow effects in continuous reactors the concepts of residence time distribution, backmixing and axial dispersion or axial mixing are used. 

Mass balances including volume element models and macro-flow effects have to be integrated to arrive at integral reactor models. 

There are two common approaches. The first approaeh is to combine porous media theory with more generalized flow models such as Stokes flow to take into accoimt micro-geometrie effects. This approach is referred to as micro-modeling. Another approach is to use porous media theory and apply it to the entire mould, macro-flow. Micro-flow models can take into account complex geometry regions of a mould, while macro-flow models can consider larger, more complex moulds [15],... 

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