Size distribution vs. time

Equation (21-139) reflects the evolution of granule size distribution for a particular volume element. When integrating this equation over the entire vessel, one is able to predict the granule-size distribution vs. time and position within the granulator. Lastly, it is important to understand the complexities of scaling rate processes on a local level to overall growth rate of the granulator. If such considerations are not... 

As shown in Fig. 8, the airflow vs. bowl capacity for two types of dryers from the same vendor approach linearity as the size of the dryer increases. A similar result is observed for the ratio of the heating vs. bowl capacity for the same dryers, as shown in Fig. 9. Therefore, for a product with constant composition (moisture content) and characteristics (particle size distribution), the time required to dry two different size batches to the same resultant moisture content should be the same if the same inlet temperature was used, and machines with equivalent air flow and heating vs. bowl capacity were used. However, at small scale, differences in the airflow and heating vs. bowl capacity parameters... 

The observed behavior was confirmed by scanning electron microscopy (SEM) analysis of the particle size distribution vs. polymerization time, as illustrated in Figure 12.6. The utilization of... 

Experiments were conducted varying the residence time, air flowrate, and oil concentration over the same ranges used to study overall system performance. The oil concentrations and drop-size distributions were measured at the entrance and exit of each stage. Table 2 shows typical results. Most of the drop removal for the large drops and production of the small drops occurred in the first stage. The third notation cell had the lowest rates of drop production and aggregation and the largest drops which were least influenced by these effects. Thus, this portion of the data was analyzed to determine the order of the kinetic process for drop removal by air bubbles. A typical plot of the oil removal rate vs. the outlet oil concentration is shown in Fig. 4 the oil removal process is first-order with respect to the concentration of oil drops. 

Slight Cold Droplet size distribution data vs. time... 

Taylor and Harmon (72) designed an instrument for measuring drop-size distribution of water sprays that combined the drop-freezing technique and Stokes law of separation. The drops were frozen quickly in hexane, cooled to —20° C. with dry ice, and collected on a shutter. They were then allowed to fall, approximately according to Stokes law, onto a scale pan. The weight on the pan vs. time relationship was then used to compute the drop-size distribution. 

A large number of heterogeneous catalysts have been tested under screening conditions (reaction parameters 60 °C, linoleic acid ethyl ester at an LHSV of 30 L/h, and a fixed carbon dioxide and hydrogen flow) to identify a suitable fixed-bed catalyst. We investigated a number of catalyst parameters such as palladium and platinum as precious metal (both in the form of supported metal and as immobilized metal complex catalysts), precious-metal content, precious-metal distribution (egg shell vs. uniform distribution), catalyst particle size, and different supports (activated carbon, alumina, Deloxan , silica, and titania). We found that Deloxan-supported precious-metal catalysts are at least two times more active than traditional supported precious-metal fixed-bed catalysts at a comparable particle size and precious-metal content. Experimental results are shown in Table 14.1 for supported palladium catalysts. The Deloxan-supported catalysts also led to superior linoleate selectivity and a lower cis/trans isomerization rate was found. The explanation for the superior behavior of Deloxan-supported precious-metal catalysts can be found in their unique chemical and physical properties—for example, high pore volume and specific surface area in combination with a meso- and macro-pore-size distribution, which is especially attractive for catalytic reactions (Wieland and Panster, 1995). The majority of our work has therefore focused on Deloxan-supported precious-metal catalysts. 

Figure 8. (A) Flow rate vs. time during filtration of shallow and deep water at a station in Warm Core Gulf Stream Ring 82-H. (B) Flow-rate decay constant vs. total particulate matter dry-weight concentration for all samples deeper than 100 m. The linear fit to the data is pg/L = 53k + 7.6 with a correlation coefficient of 0.914 and s(y) = 4/jLg/L. Scatter in the data is attributed to additional factors such as size distribution or chemical differences among samples. (C) Filtration performance of theMULVFS in different environments.

Figure 15.10a and b show the product distribution vs. reaction time for Pd particles of 2.1 and 6.1 nm mean size, respectively. Particle size effects on rate and selectivity are described in [57] here we focus on the particle size dependence of the initial activity (reaction time 60 min). Eigure 15.10c displays the initial turnover frequency as a function of mean Pd particle diameter. For this plot, the total number of Pd surface atoms was used for rate normahzation, yielding a pronounced particle size dependence, indicating that larger Pd particles are more active than smaller ones, in agreement with earlier reports ([58] and references therein). 

The pore size distribution of the catalyst matrix is important for the catalytic performance. The optimal matrix pore size distribution will depend on a balance of mesopores and macropores depending on feedstock quality and reactor conditions (e.g. conventional vs. short contact time riser operation). SAM-technology catalysts (SPECTRA, RESIDCAT, ULTIMA) exhibit different pore size distributions that are matched to various types of feedstock and unit conditions. Figure 5 exhibits typical pore size distribution of SPECTRA-944, SPECTRA-444 and ULTIMA-444 catalysts. Since the only differentiating characteristic of these three catalysts is the matrix formulation, the pore size distribution variation is characteristic of the different matrix design ... 

The most important, factors affecting the design of a fluid-solid noncatalytic reactor are the flow patterns of solid and fluid in the vessel. As noted in Sec. 14-1, the simplest case is where the composition of the fluid phase is uniform. Then the conversiori-vs-time relationship for single particles, such as Eq. (14-19), can be employed, along with the residence-time and particle-size distributions of the solid phase, to evaluate the average conversion. This problem is considered in the next section. When the fluid phase does not have a uniform composition the design is more complex. However, quantitative treatment is possible when the flow patterns of both solid and fluid phases are well defined. These kinds of reactors are discussed in Sec. 14-6. 

High-Performance TLC (HPTLC). HPTLC materials have a smaller average particle size (5 vs 20 pm) and a narrower particle size distribution when compared with conventional materials. Actually, the development of the chromatogram is faster and the time for analysis shorter. However, HPTLC materials are preferable for more complex separations their use for determinations of the radiochemical purity in nuclear medicine is limited. 

Table 1 presents the main XRD and TPR results for calcined catalysts. The time evolution of nickel dispersion (D/Dq) and size distributions (Figures 1 and 2) confirms sintering for all catalysts, albeit at different extents. D/Dq vs. time data was fitted to Equation 1. The results are summarized in Table 2. For runs E6 and E13 no satisfactory fitting was obtained, thus the initial sintering rate was calculated from the variation of D/Do up to 5 h.

Figure 6.17 Schematic of the size distribution control mechanism of the hot injection and heat-up methods. In the left boxes, the monomer supply modes are shown as the plots of supersaturation vs. time. In the right boxes, the resulting time evolutions of the nucleation rate, the mean size, and the relative standard deviation are shown. The injection time and the start of the heat procedure are set as t = 0 in the hot injection and the heat-up processes, respectively.

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