Characteristic mixing time analysis

The mixing mechanism in this laminar flow system must be diffusion because the mixing must occur normal to the laminar flow streamlines. Laminar flow prevails in systems with these small dimensions. Thus, the characteristic mixing time is the characteristic diffusion time, defined for two colaminar streams mixing in a cylindrical channel as  

The design constraint listed earlier requires that 4 tp, or R fD. (The basis for the choice of the factor of 4 is arbitrary but is supported by simulations described later.) Thus, to achieve the desired minimum residence time, the channel diameter must be less than 0.21 mm (0.0085 inch). This value is more limiting than the value of 0.5 mm imposed by the heat transfer analysis. 

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As shown in Fig. 13.4, the difference in the overall conversion is the consequence of a lower conversion rate at the reactor inlet, as expected. Although the characteristic mixing time corresponds to a distance of 0.24 m, the reaction rate (slope of the conversion profile) of the unmixed feed case approaches that of the premixed feed case by 0.1 m, or 10% of the total reactor volume. Furthermore, the predicted conversion for the immixed and premixed feeds is 25.1% and 25.7%, respectively. This corresponds to a relative difference of 2%, an acceptable level of error that will only decrease as the reactor residence time increases. This analysis validates the reactor design criterion that the characteristic mixing time based on... 

Processing Mixing Time Data. Data collected by the conductivity, thermocouple, or pH techniques must be processed to obtain a characteristic mixing time for the system under investigation. The analysis is described below in terms of conductivity readings, but is equally applicable to the other data types. 

The parameter which takes into account the heat and mass transfer, for the analysis of different chemical processes, is the relationship between the characteristic chemical reaction time ( hem) the heat or mass transfer first of all, the mixing time ... 

The application of residence time distribution theory is an established method for identifying process system fluid flow and mixing characteristics. Tracer data analysis via this theory can give valuable insight into a system s hydrodynamic characteristics. It has been applied to understand and improve industrial reactor performance. Two applications are discussed. 

The direct whole-cell method of Holland et al. was extremely rapid, even in comparison to Lubman s MALDI analysis of fractions collected after bacterial sonnication. With the whole-cell approach bacteria were simply sampled from colonies on an agar plate, mixed with the matrix, air-dried, and introduced in batches into the mass spectrometer for analysis. In all of the spectra obtained in these and later experiments, each bacterial strain showed a few characteristic high-mass ions that were attributed to bacterial proteins. Studies demonstrating the whole cell methodology for strain-level differentiation were reported independently by Claydon et al. at almost the same time.18 Shortly thereafter a third study on whole-cell MALDI included bacteria from pathogenic and nonpathogenic strains appeared.19... 

In this barrel, air is expected to come naturally. Temperature and leachate volume were measured twice a week. Once a week, waste was taken out to mix with air and then put back into the barrel. At the same time, sample was taken to measure water content. Stabilization step ended when waste body stopped generating water, varied from 18 to 51 days, due to waste input characteristic and environmental temperature. After this time, raw RDF was collected and stored for further analysis. Stabilization time of El > E3 and R1 > R3 was compared with that of other study (Table 8). 

From the slope of the straight line, the effective mixing cell volume was calculated to be 30.1 cm, with a 50% relaxation time of about 0.08 s. Similar mixing characteristics were observed following a step decrease (i.e., CO + N ), giving an effective mixing cell volume of 31.8 cm and a 50% relaxation time of 0.09 s. Since these response times of the reactor are not much faster than the time scale of the adsorption process (a halfscale relaxation time of about 0.2 s), the transients of the reactor cell were included in our analysis. For our simulations, the mixing cell volume was taken to be 31 cm. ... 

Numerical studies of combustion control in simple combustors with flame holders have been made. The criterion of flame stabilization, based on the unambiguously defined characteristic residence and reaction times, is suggested and validated against numerous computational examples. The results of calculations were compared with available experimental findings. A good qualitative and reasonable quantitative agreement between the predictions and observations were attained. Futher studies are planned to include mixing between fuel jets with oxidizer and to extend the analysis to transonic and supersonic flow conditions. 

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