Static mixing Calculations

Rupture disk, 455 Safety relief valves, 454, 467, 481 Specifications, centrifugal pumps, 209 Spray nozzle particle size, 225 Standards and Codes, 31, 32, 33 Static electricity, 536 Static mixing, 332 Applications, 336 Calculations, 337, 338 Materials of construction, 337 Principles of operation, 335 Type of equipment 334-338... 

Table 1.5 Measures for mixing efficiency calculated from mass contour plots yielded by CFD simulation - benchmarking cross-shaped mixers with and without static mixing elements (SME) [71].

Calculate static mixing process parameters The pertinent process parameters, along with the process information, help establish how difficult the mixing is for the process, as discussed below. 

Figure 5.11 Gibbs free energy of mixing in binary join Mg2Si04-Ca2Si04 dXT = 600 °C and P = bar, calculated with a static interionic potential approach. Reprinted from G. Ottonello, Geochimica et Cosmochimica Acta, 3119-3135, copyright 1987, with kind permission from Elsevier Science Ltd., The Boulevard, Langford Lane, Kidlington 0X5 1GB, UK.

Let us now consider some actual numerical data for specific mixed biopolymer systems. Table 5.1 shows a set of examples comparing the values of the cross second virial coefficients obtained experimentally by static laser light scattering with those calculated theoretically on the basis of various simple excluded volume models using equations (5.32) to (5.35). For the purposes of this comparison, the experimental data were obtained under conditions of relatively high ionic strength (/ > 0.1 mol dm- ), i.e., under conditions where the contribution of the electrostatic term (A if1) is expected to be relatively insignificant. 

Calibration of FAGE1 from a static reactor (a Teflon film bag that collapses as sample is withdrawn) has been reported (78). In static decay, HO reacts with a tracer T that has a loss that can be measured by an independent technique T necessarily has no sinks other than HO reaction (see Table I) and no sources within the reactor. From equation 17, the instantaneous HO concentration is calculated from the instantaneous slope of a plot of ln[T] versus time. The presence of other reagents may be necessary to ensure sufficient HO however, the mechanisms by which HO is generated and lost are of no concern, because the loss of the tracer by reaction with whatever HO is present is what is observed. Turbulent transport must keep the reactor s contents well mixed so that the analytically measured HO concentration is representative of the volume-averaged HO concentration reflected by the tracer consumption. If the HO concentration is constant, the random error in [HO] calculated from the tracer decay slope can be obtained from the slope uncertainty of a least squares fit. Systematic error would arise from uncertainties in the rate constant for the T + HO reaction, but several tracers may be employed concurrently. In general, HO may be nonconstant in the reactor, so its concentration variation must be separated from noise associated with the [T] measurement, which must therefore be determined separately. 

The values of the standard electrode potentials of copper (Cu+ + e- -> Cu, 0.522 V) and zinc (Zn2+ + 2e - Zn, —0.76 V) make it appear unlikely that the metals could be codeposited as the alloy brass. However, if, for example, solutions which are 0.025 M in [Zn(CN)4]2 and 0.05 M in [Cu(CN)3]2 are mixed, simple calculation can show that the static electrode potentials of the two ions have values which approach each other more closely and codeposition becomes much more probable. This can be understood with the help of equation (5) and the knowledge that the dissociation constants of [Zn(CN)4]2 (1.3 x 10-17) and [Cu(CN)3]- (5.6 x 10-28) will greatly modify the activity term. 

For liquid-liquid mixtures, the calculations of mixing time and power (or Newton) number outlined above are valid for unbaffled vessels only as long as the vortex created by the stirrer does not reach the stirrer head. Otherwise, gas entrainment occurs and the physical properties of the system change. The depth of the liquid-gas interface at the vessel axis with respect to static liquid surface level, HL, can be related to the Froude and Galileo numbers. Some of the reported relationships are summarized in Table XIV. The value of H, at which the vortex reaches the upper impeller blades level can be expressed as... 

As observed in other systems, the obvious difficulty in elucidating reaction mechanisms based on static structural snapshots subsequently initiated structural-dynamic theoretical studies of metalloproteinases. The active site chemistry of zinc-dependent enzymes has been studied using a variety of theoretical approaches. For example, mixed quantum mechaiucal/molecular calculations and classical molecular dynamic simulations have been employed, especially studies using density functional methods on redox-active metal centers (42). 

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