Concentration macroscale

In turbulence theory, this is also known as the concentration macroscale, which plays an important role in the interpretation of micromixing phenomena. 

Let c(x) = C - C be the deviation from the mean at point x and c(x,r) be the same quantity at distance r from this point. The size of segregated regions mav be characterized by the concentration macroscale... 

Traditional macroscale NIR spectroscopy requires a calibration set, made of the same chemical components as the target sample, but with varying concentrations that are chosen to span the range of concentrations possible in the sample. A concentration matrix is made from the known concentrations of each component. The PLS algorithm is used to create a model that best describes the mathematical relationship between the reference sample data and the concentration matrix. The model is applied to the unknown data from the target sample to estimate the concentration of sample components. This is called concentration mode PLS . 

Measurements of macromixing by, for example, a motionless mixer are based on the coefficient of variation (CoV), which is a statistical measure of radial homogeneity at the macroscale. It is defined as the standard deviation of concentration measurements made at the exit of a mixer divided by the mean concentration ... 

The hydrodynamics of a circulating fluidized bed can be analyzed from both the macroscopic and mesoscopic points of view. The nonuniformity of the solids concentration in the radial and axial directions represents macroscopic behavior. The existence of solid clusters characterizes mesoscopic behavior (see 10.5). The hydrodynamic behavior in a macroscale is discussed in the following. 

Fig. 2a shows an actual example of a polarogram run on a microscale (oxidation of anisole in acetic acid/sodium acetate) and on a macroscale (oxidation of durene in acetonitrile/sodium perchlorate). In the latter case the substrate concentration is too high for the plateau value to be reached. 

In their pioneering work, Jensen et al. demonstrated that photochemical transformation can be carried out in a microfabricated reactor [37]. The photomicroreactor had a single serpentine-shaped microchannel (having a width of 500 pm and a depth of 250 or 500 pm, and etched on a silicon chip) covered by a transparent window (Pyrex or quartz) (Scheme 4.25). A miniature UV light source and an online UV analysis probe were integrated to the device. Jensen et al. studied the radical photopinacolization of benzophenone in isopropanol. Substantial conversion of benzophenone was observed for a 0.5 M benzophenone solution in this microflow system. Such a high concentration of benzophenone would present a challenge in macroscale reactors. This microreaction device provided an opportunity for fast process optimization by online analysis of the reaction mixture. 

The differences in concentration between the micro- and macroscale experiments also affect the separation of the waves. The waves of irreversibly reduced compounds cover a greater potential range at higher concentrations than at lower concentrations. A reduction which in the microscale experiments gives two separate reduction waves may be difficult to carry out as a selective reaction. The best way to get a partial reduction in such a case is to use a potential at the foot of the composite wave. 

The difference between the products obtained when PhAsO(OH)2 is reduced under polarographic and macroscale conditions, respectively, has been explained by the differences in the relative concentrations of the different species . Under polarographic conditions the concentration of PhAs(OH)2 is so low that polymerization (reaction 20) does not take place, and PhAs(OH)2 reacts preferentially with PhAsH2 (reaction 18). Precipitation of PhAsH2 is also of minor importance under polarographic conditions due to the lower concentrations. 

The process of formulating mesoscale models from the microscale equations is widely used in transport phenomena (Ferziger Kaper, 1972). For example, heat transfer between the disperse phase and the fluid depends on the Nusselt number, and mass transfer depends on the Sherwood number. Correlations for how the Nusselt and Sherwood numbers depend on the mesoscale variables and the moments of the NDF (e.g. mean particle temperature and mean particle concentration) are available in the literature. As microscale simulations become more and more sophisticated, modified correlations that are based on the microscale results will become more and more common (Beetstra et al, 2007 Holloway et al, 2010 Tenneti et al, 2010). Note that, because the kinetic equation requires mesoscale models that are valid locally in phase space (i.e. for a particular set of mesoscale variables) as opposed to averaged correlations found from macroscale variables, direct numerical simulation of the microscale model is perhaps the only way to obtain the data necessary in order for such models to be thoroughly validated. For example, a macroscale model will depend on the average drag, which is denoted by... 

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