Cycle time distribution

Mann, U., and Crosby, Cycle Time Distribution in Continuous Systems, Chem. Eng. Sci., 28 623 (1973)... 

In general, different sized particles may have different cycle time distributions and different mass deposition distributions in the spray zone. One approach would be to use small discrete size distribution increments and then to apply Eq. (12) to each size fraction. Inherent in this approach is the assumption that each particle size fraction acts independently. This assumption may not be valid, especially if different particles take different circulation paths within the bed. From the population balance approach, Randolf and Larson (1988) have suggested the use of an effective growth diffusivity coefficient to account for random fluctuations in growth rate. Thus Eq. (6) would be modified to give ... 

FIGURE 17.14 Example Document Cycle Time Distributions. 

In the following we present a method, which relates v t) and Des t) to the time dependent cycle time distribution density w t, t), which governs the dynamics of the system. 

Thus, recycle reactors represent an advantageous device for experimental verification of mixing models, as emphasized here. Recycle reactors can be operated in either batch or continuous mode for this purpose, and they also exhibit the property of short cycle time distribution (CTD), which is very favorable compared with the CTD of normal stirred tanks. 

Mann U, Crosby EJ. Cycle time distribution in continuous systems. Chem Eng Sci 28 623-627, 1973. 

The reason is truncation of dynamics in low-resolution modes in a 14-bit-detector each pixel in low-resolution mode can contain 0 to 16382 counts. With the next photon an arithmetic overflow will occur and the pixel is saturated. In high-resolution mode the same area of the detector is represented by 4 pixels, and if the intensity is evenly distributed it takes 4 times longer before the pixels will be saturated. If the high resolution is not required and the cycle time is 30 s or longer, it is good practice to store away the big files on a spacious USB hard-disk and afterwards to bin the data. 

The effects of liquid fuel pulsation without air forcing were visualized at four instances of time (images not included). At time 0, a high concentration of fuel became visible at the nozzle exit. At time 7t/2, the fuel droplets became evenly dispersed through the quarter cycle. Times tt and 37t/2 showed similar droplet distributions, homogeneous throughout the flow. 

More detailed modeling exposes some weaknesses, for example, the need to use coarse monolithic catalyst structure to achieve reasonable reheat periods without excessive pressure drops. The cycle time of approximately 4 minutes is somewhat short for practical purposes. The cold spot formation in the reaction phase (Figure 14) and the resultant inability of the reaction to distribute itself over the catalyst to utilize the stored heat optimally is probably a modeling artefact caused by too low literature values for the activation energy, possibly reflecting an incorrectly interpreted film transport limitation. 

In the wall thickness fluctuations up to 5 % may occur. As a result of the uneven temperature in the molten polymer during rotation, and also by the not always exactly reproducible rate of cooling, deviations in the dimensions of the finished product may amount to 5 %. Requirements are, that the materials can be molten completely, that the melt is sufficiently low-viscous, and that the molten polymer does not degrade too rapidly. Besides plasticised PVC, HDPE and LDPE are often used, as well as copolymers of PE such as EVA (ethylene - vinyl acetate copolymerj.Because the shear stresses in this process are extremely low, a narrow molar mass distribution is to be recommended, as discussed in 5.4. Cycle times vary between 3 and 40 minutes, dependent on the wall thickness. Cycle times can be reduced considerably by using machines with multiple moulds, since the cycle time... 

Split synthesis enables the rapid generation of large numbers of related compounds (a library ) on a solid support. The procedure entails three steps that can be repeated many times. First, the resin is divided into equal portions (step 1). Each resin portion is then subjected separately to different reactions (step 2). The modified resin portions are combined and mixed (step 3) and are ready for the next cycle of the synthesis (Figure B.ll.l). Successive cycles of distributing, reacting, and mixing of the beads lead to a combinatorial increase of the diversity of products - for example four cycles with 15 different reactions per cycle lead to 154 = 50625 different com-... 

Fig. 10.5. Distribution of exponentially growing cells around the cell cycle. Cells in an exponentially growing population are theoretically distributed round the cell cycle as shown by the solid line. However, as the cell cycle time varies amongst the cells the dotted line more closely resembles the observed distribution. Cells which have just divided have an age of zero while those in the next mitosis have age T. The positions of Gl, S and G2 are shown for a typical cell. (Reproduced from Cleaver, 1967, with kind permission of the author.)...

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