Velocity versus efficiency

In Figure 3.49, the minimum liquid superficial velocity versus particle size in order to have a wetting efficiency higher than 90% for water as liquid phase at 25 °C is presented. 

Figure 3 shows a comparison of the model prediction of the overall collection efficiency as a function of superficial gas velocity versus the experimental data of Tardos et al (12). Since the charge acquired on the collectors was not reported, assumed values shown in Figure 3 were employed. It should be noted that this assumed functional dependency between and was not entirely arbitrary, but qualitatively suggested by experimental measurements of the electric potential in the fluidized bed (12). An important aspect of Figure 3 is both the model prediction and experimental... 

Figure 3.49 Minimum liquid superficial velocity versus particle size iu order to have a wettiug efficiency higher than 90% (liquid-phase water at 25 °C).

The alumina zirconia composites processed by the colloidal route present a narrow distribution that is roughly between Dc and D. This leads to a more efficient transformation toughening in the ceramics processed by the colloidal route and to a shift of the crack velocity versus stress intensity factor curve towards higher Ki values for the composites obtained by the colloidal route compared to the composites obtained by a powder-mixing technique [35]. 

A schematic diagram of retardation and mirror velocity versus time is shown in Figure 2.19. This operation is not very efficient as a considerable time in the cycle is not used for the collection of data but is used to decelerate the moving mirror. 

Figure 4-110 depicts an efficiency curve versus velocity ratio for a reaction-type expander. The optimum efficiency will occur at a velocity ratio of. 63. For a velocity ratio considerable greater or less than. 63 a significant efficiency penalty can be expected. Considering the effects on the parameters mentioned above, it is easy to see the importance the velocity ratio has on the performance of the expander. 

FIGURE 10.9 Hood capture efficiency versus normalized cross-draft velocity, ... 

Figure 12-461, Part 3. Stage performance of a compressor is usually represented in a pressure coefficient, n, or M, and efficiency, t), versus Q/N (capacity vs. speed). A given impeller stage design will have a different characteristic depending on the relationship of its operating speed to the inlet sonic velocity of the gas. For higher ratios of speed to sonic velocity, N/A , the head or pressure coefficient curve will be steeper at flows higher than the design. (Used by permission Bui. 423, 1992. Dresser-Rand Company.)...

The curves represent a plot of Log.(/V),(Reduced Plate height)against Log.(v), (Reduced Velocity). The lower the Log.(/7) curve versus the Log.(v) curve the better the column is packed. At low velocities the (B) term dominates and at high velocities the (C) term dominates as in the Van Deemter equation. The best column efficiency is achieved when the minimum is about 2 particle diameters and thus, Log (.ft) Is about 0.35. The minimum value for (H) as predicted by the Van Deemter equation has also been shown to be about two particle diameters. The optimum reduced velocity is in the range of 3 to 5 that is Log.(v ) takes values between 0.3 and 0.5. The Knox equation is a simple and effective method of examining the quality of a given column but, as stated before, is not nearly so useful In column design due to the empirical nature of the constants. 

When the outlet maximum velocity (after eight turns) at a meandering ratio of 4 is plotted versus Re, a curve similar to the dependence of the mixing efficiency on Re is yielded [59], At Re 80, the outlet maximum velocity increases considerably, whereas at low Re it remains nearly constant. 

Van Deemter plot. A graph of column efficiency, expressed as HETP versus linear velocity of the mobile phase. This plot indicates the optimum linear velocity (and, thus, flow rate) for a particular column. 

Carrier gas flow should be optimised for a particular column and a particular carrier gas. This is most important for open tubular columns. Fig. 5 shows the relationship between efficiency expressed as the height equivalent of a theoretical plate versus carrier gas velocity (Van Deemter plot) for a 28 m by 0.25 mm internal diameter wall-coated open tubular column of Carbowax 20M. 

Scientific, Darien, IL). Five compounds—ascorbic acid (dead time marker), hydroquinone, resorcinol, catechol, and 4-methyl catechol—were eluted with a 10/90 (v/v) acetonitrile/water mobile phase containing 0.1 % TFA and were detected with amperometric detection (+1.0V versus Ag/AgCl). The chromatogram was obtained near the optimum linear velocity at a run pressure of 3000 bar. All compounds eluted in less than 8 minutes, with efficiencies ranging from a low of 244,000 plates for 4-methyl catechol to as high as 330,000 plates for hydroquinone. These correspond to about 570,000 and 770,000 plates/m, respectively—much higher than the 150,000 plates/m typically seen with conventional columns. 

The higher the percentage of oxygen, or the higher the deposition temperature, the more complete is the combustion (oxidation) that occurs. The oxidant-to-fuel (solvent) ratio helps to control the flame temperature, size and velocity. Using pure oxygen versus air results in a more efficient and rapid combustion this in turn minimizes the formation of NO, carbon monoxide, and elemental carbon. 

Conversion efficiency is definitely affected by the large void fraction, which is apparent in the results from changes in the total throughput, or space velocity (0.56 versus 1.11 sec ), shown in Fig. 7. In this comparison, the concentration of unconverted hexane increased tenfold when the flow rate was doubled. The impact of improvements in conductive heat transfer, combined with the mass transfer limitations associated with the cell size and honeycomb design, and a catalyst loading that was nearly one-half Chat of commercial pellet catalysts (average, 11.5% versus 19.2%) suggested that both carbon formation and steam/hydrocarbon reactions were better controlled with monolithic supports under the conditions employed. This comparison was made where the extent of the endothermic reaction is equal between the pellet bed and the hybrid cordierite/metal monolith bed. 

Figure 14.4. (a) Simulation results for a continuous initial particle size distribution, with /3 = 4 and size range from 1 nm to 100 /xm initial total mass concentration, 3 mg liter" = 1.5 g cm temperature = 15 C coagulation with a velocity gradient G = 10 s" and a collision efficiency factor a = 0.05 (see Sections 14.4 and 14.8 for the definition of these terms), (b, c) Simulation results for a continuous initial particle size distribution with /3 = 4 and size ranging from 1 nm to 100 pm after 2 days with different initial mass concentrations ranging from 0.01 to 10 mg liter" (p = 2.0 g cm" temperature = 15°C G = 0.5 a. = 0.05). (b) Evolution of particle size versus concentration with ordinates expressed as percentage of initial value for each size class, (c) Evolution of mean size value with concentration. (Adapted from Filella and Buffle, 1993.)... 

It is seen that Eq. (8) is very similar to Eq. (7) except that the velocity used is the outlet velocity, not the average velocity, and that the diffusivity of the solute in the gas phase is taken as that measured at the column outlet pressure (i.e., atmospheric). The shape of the //versus u curve is hyperbolic it has a minimum value of // i at the optimum velocity Uopt (i e., at the optimum velocity, the column will have a maximum efficiency). Expressions for //min and Mopt can be obtained by differentiating Eq. (8) with respect to u and equating to zero, solving for Mop, and substituting Mop, for u in Eq. (8) to obtain // , . 

The influence of the different mass transfer parameters on the overall efficiency of a column is shown in Fig. 2.11, where the efficiency represented by the plate height is plotted versus the mobile phase velocity. 

Figure 3.25 Experimental isotherms of Troger s base enantiomers on microcrystalline cellulose triacetate. Experimental data by frontal analysis (symbols) and best quadratic isotherm (solid line). Experimental conditions column length, 25 cm column efficiency, N = 106 plates phase ratio, F = 0.515 flow velocity 0.076 cm/s, pure ethanol. Column (250 x4.6 mm) packed with cellulose microcrystalUne triacetate (CTA, 15-25ftm), previously boiled in ethanol for 30 min. (a) Isotherm data. Top line, (+)-TB, bottom line, (-)-TB. (b) Plot of q/C versus C. Reproduced with permission from A. Seidel-Morgenstem and G. Guiochon, Chem. Eng. Scl, 48 (1993) 2787 (Figs. 4 and 5).

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