Middleton scale

The design methods de.scribed above rely on correlations of the overall reactor average quantities obtained from experimental tanks of different scales. The most important deficiency of these methods is that local effects are not taken into consideration, while these might be responsible for the overall reactor performance. Accordingly, if none of the above scale-up criteria is found satisfactory (see e.g. data of Middleton et ai, 1986) a more fundamental approach must be applied, although not necessarily as complex as the one presented in Section 5.4.S.2. Such an approach was presented by Paul et al. (1971) who found that the yield of the desired intermediate in a system of consecutive reactions (iodination of L-tjrosine) correlates reasonably with fluctuations of the velocity, So, these fluctuations could be chosen as a criterion for scale-up of the reactor. The average value for u in the upper part of the tank was evaluated from ... 

Early field surveys depended on identification of a syndrome of responses that included symptoms on both native and cultivated plant species. Middleton and Paulus directed the first large-scale survey to determine the extent and severity of photochemical-oxidant effects in California on crops of agronomic importance. Th delineated four categories of crops (field, flower, fruit, and vegetable) and one of weeds. This was the most extensive survey of oxidant effects until the late 1960 s. The information was later used as a basis for subjective estimates of economic losses. This type of visual assessment of foliar injury has been attempted in many states and has been purposefully developed in some for use in economic estimates of damage to vegetation. 

Liquids with equal solubility parameters are miscible, there is no heat of mixing. With increasing difference of <5, two phases coexist, which become miscible at elevated temperature, at the critical consolute temperature Tc. Tc increases with the difference of the <5 s and with the mean molar volume of the two liquids. Another polarity scale was recently introduced by Middleton and co-workers13 based on the bathochromic shift of UV-visible 2max. The obtained spectral polarity index ranks the solvents at one end of the scale is the nonpolar perfluorohexane and at the opposite the highly polar and acidic l,l,2,3,3.3-hexafluoropropan-2-ol. The latter is much more polar than its hydrocarbon analog. 

Hajak G, Cluydts R, Declerck A, Estvill SE, Middleton A, Sonka K, Unden M (2002) Continuous versus non-nightly use of zolpidem in chronic insomnia results of a large-scale, double-blind, randomized, outpatient study. Int Clin Psychopharmacol 17 9-17... 

The gradient elution scheme is a scaled-up procedure originally described by Middleton (10) that has been extended to handle highly refractive materials such as coal liquids. This separation technique uses Alcoa F-20 alumina activated to a 5.5 wt % moisture level as the stationary phase. Details of this separation procedure are given elsewhere (2). This method separates SRC into 13 fractions and these fractions are listed in Table II along with some key chemical and physical descriptions of the cuts. The structural types indicated in Table II for Fractions 1-6 have been assigned based upon model compound studies and low resolution mass spectrometry (MS) (2), whereas the chemical types indicated for Fractions 7-13 are based upon IR observations and additional model compound studies. Recoveries in these separations are normally greater than 90%. 

This box-model approach has been used for comparison with urban dispersion experiments by Middleton, 1998 [431], This has proved satisfactory on neighbourhood scale (> 1 km from source). 

The multiplying constant for concave-blade disk turbines is 0.058 instead of 0.025. This constant has a weak dependence (to the power of about 0.2) on the scale of the equipment. This inequality defines two regions delimited by a vertical line in the Fr vs. Flo flow map, for a given value of the D/T ratio. Nienow, Wisdom, and Middleton developed a relationship to predict the agitation speed of a flat-blade disk turbine at which gas recirculation occurs for a given gas rate. This expression... 

Nienow, A.W. Wisdom, D.J. Middleton, J.C. The effect of scale and geometry on flooding, recirculation and power in gassed stirred vessels. 

Smith, J.M. Middleton van t Riet, K. Scale up of agitated gas-liquid reactors for mass transfer. Proceedings of the 2nd European Conference Mixing BHRA Cambridge, 1977 F4-51-F4-66. 

Middleton J.C., Scale-up of Agitated Gas-Liquid Reactors for Mass Transfer, 2nd European Conf, on Mixing, Paper F4-51/66, Cambridge (1977)... 

Worldwide use of activated silica sols, new modifications involving use of NajSiF, plus silicate, and new applications in sewage treatment have been summarized by Middleton (196). Large-scale use in coagulating solids from water in Chicago has been described by Vaughn (197). 

Although the impacts of human activity upon the natural environment are well documented, the spatial and quantitative dimensions of change are less well understood. Several publications, such as the World Atlas of Desertification (Middleton Thomas, 1997), do an excellent job of illustrating change during the relatively recent past, but few document the extensive change that has taken place on the scale of centuries or millennia. Fewer publications still assess the functional implications and consequences of the changes that have taken place in the Earth System. In some... 

It is evident that having made a choice of scale-up relationship, other factors will be affected in different ways there is often no way to scale up aU the significant factors together, so priorities have to be chosen. An example of this is given in Middleton (1997), to which reference should be made for full details. A summary is given here. 

If the time scale of a chemical reaction is short compared to the time scale of mass transfer, the mass transfer slows the chemical reaction but can also cause the concentration in the liquid-side mass transfer film to be decreased, resulting in an increased driving force and an enhanced mass transfer rate. Levenspiel (1999) and Middleton (1992) present diagrams for the interface concentration profiles likely to happen at the various reaction rates relative to the mass transfer rate. Those are shown in Table 13-10 along with estimates of the ranges of variables for the various regimes [similar to those of Doraiswamy and Sharma (1984)] and important variables for design and scale-up. 

Figure 13-32 shows the results of Middleton et al. (1986) plotted as yield versus power per unit volume, which would be consistent with micromixing control. It is clear that the results for the two reactor sizes do not coincide on such a plot. This work shows that constant power per unit volume (which corresponds to micromixing rate control) is inadequate for scale-up under mesomixing conditions. Yields for the large vessel were considerably lower than for the small vessel at equal power per unit volume. 

Figure 13-33 Yield versus N for Middleton et al. (1986) data shown in Fignre 13-32. The results are close to mesomixing control, as shown by the closer agreement between small and large scale results when scaling is based on N.

---