Flow Phenomena on the Micro Scale

In this section we present said discuss a few numerical results for the two problems considered, transient flow said hmsient convection in microchannels, which were respectively handled by the full and the partial integral hmsformation approaches. The aim is to demonshate file convergence behavior within each strategy and to illushate some physical aspects on file fiansient phenomena at the micro-scale. Although the developed solutions sae readily applicable to dififerent physical situations of eifiier hquid or gas flow, we here concentrate om illustiation of results on typical ex ples of lamina gas slip flow. 

Before proceeding with the discussion on microelectronics-related topics, it is useful to remind ourselves that micro-fluidics (introduced in Chapter 3) is an important subject that allows us to appreciate flow phenomena at the micro- and nano-scale. It is of growing importance in intensified unit operations where characteristic lengths may be well below 1 mm, for example. The paragraph below, from a quote by US commentators on the impact that micro-fluidics might have on the process industries, sets the scene. 

Transport phenomena on the microscale have gained particular importance due to an increasing demand for more efficient and sustainable processes. Especially the bridge between nano- and micro technologies requires a deep understanding of multiscale coherences. Advances in microfluidic and nanofluidic technologies have been paralleled by advances in methods for direct optical measurement of transport phenomena on these scales. A variety of methods for microscale flow visualization have appeared and evolved since the late 1990s. These methods and their applications to date are reviewed here in detail, and in the context of the fundamental phenomena that they exploit and the fundamental phenomena that they are applied to measure. 

The structure of the closure laws used for the shear stresses in two-fluid models bears crucial consequences on the capability of two-fluid models to predict the stability characteristics of the presumed flow configuration. Quasi-steady closure laws for the interfacial shear stresses, which are widely used in stability analyses of the stratified flow configuration, are insufficient for capturing the physical phenomena involved during the evolution of waves over a liquid interface sheared by a turbulent gas phase. Modification of the interfacial shear stress model to include a dynamic term is essential for rendering a closure law which is capable of bridging the gap between the micro-scale phenomena at the vicinity of the phases interface and the macro-averaged representation of the flow. 

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... 

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. 

Apart from obvious features such as laminarity, there are speculations that flows in micro channels exhibit a behavior deviating from predictions of macroscopic continuum theory. In the case of gas flows, these deviations, manifesting themselves as, e.g., velocity slip at solid surfaces, are comparatively well understood (for an overview, see [130]). However, for liquid flows on a length scale above 1 pm, there is no clear theoretical foundation for deviations from continuum behavior. Nevertheless, various unexpected phenomena such as friction factors deviating from the continuum prediction [131-133] have been reported. A more detailed discussion of this still unsettled matter is given in Section 2.2. At any rate, one has to be careful here since it may be that measurements in small systems lack precision, essentially because of the incompatibility of analysis in a confined space and with large measuring equipment... 

Here follows a section outlining the heat and mass transport phenomena of the thermochemical conversion on both the micro- and the macro-scale of the fuel bed. Knowledge about the heat and mass transport phenomena on micro-scale is very important to be able to understand and model, for example, the mass flow of conversion gas. 

The ratio of the rms velocity fluctuation to the average velocity in the impeller zone is about 50 percent with many open impellers. If the rms velocity fluctuation is divided by the average velocity in the rest of the vessel, however, the ratio is on the order of 5 percent. This is also the level of rms velocity fluctuation to the mean velocity in pipeline flow. There are phenomena in micro-scale mixing that can occur in mixing tanks that do not occur in pipeline reactors. Whether this is good or bad depends upon the process requirements. 

---