Mixing longitudinal

Plug-flow with some longitudinal mixing... 

The plug flow reactor has a flat velocity profile and no longitudinal mixing. These idealizations imply that all fluid elements leaving the reactor have the same age (T). The F(t) function for this system must then be... 

Finally, we should also mention that assisted spin recoupling is by no means restricted to 1H, 13C, and 15N spin species but may also be used to facilitate H and 2H to low- spin transfers. This may be exploited in extensively deuterated samples using rf fields on JH and 2H which are matched to a rotary resonance condition to facilitate spin-diffusion between 13C spins in a longitudinal mixing process. This was recently demonstrated by van Rossum and coworkers in terms of the doublenucleus enhanced recoupling (DONER) experiment [143]. 

But it should be borne in mind that this longitudinal mixing, as can be shown by the kinetic theory of gases, plays no important role at reactor lengths of at least several centimeters and at linear flow rates of at least some centimeters per minute. These conditions will certainly be fulfilled in most of the usual laboratory work, using flow rates of many cubic centimeters per minute and tube cross sections not exceeding a few square centimeters. 

Vertical Mixing by Turbulence Lateral Mixing by Turbulence Longitudinal Mixing by Dispersion... 

Note that this list does not include longitudinal mixing by turbulence. In fact, its influence is masked by longitudinal dispersion. Dispersion, an inevitable byproduct of advective transport, is commonly much larger than turbulent diffusion along the direction of flow. 

In the laboratory batch ozonation is easy to apply, whereas multi-stage continuous-flow systems are difficult to handle (Method 1). However, mainly due to large liquid flow rates the inverse situation is valid for many full-scale applications. Often three oxidation reactors in series are found in waste water ozonation (cf. Table A 3-3). The advantage of a multi-stage CFSTR system - or even a batch system - lies in their faster reaction rates compared to a single CSTR due to the reduced axial/longitudinal mixing. 

Notes on the diffusion-type model for longitudinal mixing in flow (Levenspiel, Smith and Van der Laan). Chem Eng. Sci 10, 266-267 (1959). 

Levenspiel, O., "Longitudinal Mixing of Fluids Flowing in Circular Pipes,"Ind. Eng. Chem. 50 (1958) 343 - 346. 

Rod V. Calculating mass transfer with longitudinal mixing. Br Chem Eng 1966 6 483 188. 

While the minimum residence time is significant for dispersive mixing, the residence time distribution in the extruder influences distributive mixing as a measure for longitudinal mixing performance [20]. The average residence time depends only on screw pitch and screw speed in partially-filled screw sections, and only on throughput in fully-filled screw sections. 

The decrease of the column performance is partially caused by longitudinal mixing and insufficient wetting of the packing due to detachment of the liquid film as shown by Blaha [5]. Another disadvantage of columns is the low gas capacity required to avoid flooding because of the low interfacial tension and the low density differences between the phases. 

To this degree of precision, the critical value of SD for any reactor is independent of its mechanism of longitudinal mixing. 

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