Suspensions density

In all such laboratory studies, plant conditions and compositions should be employed as far as possible. Agglomeration rates tend to increase with the level of supersaturation, suspension density and particle size (each of which will, of course, be related but the effects may exhibit maxima). Thus, agglomeration may often be reduced by operation at low levels of supersaturation e.g. by controlled operation of a batch crystallization or precipitation, and the prudent use of seeding. Agglomeration is generally more predominant in precipitation in which supersaturation levels are often very high rather than in crystallization in which the supersaturation levels are comparatively low. 

Agitator or pump speed and power, whieh are determined by partiele size and suspension density. 

The residence time of the crystallizer in previous example is doubled. If the slurry suspension density is kept constant, calculate the effect of this change on ... 

Slurry suspension density is kept constant. This quantity is given by Mt = (tf pn iGrf... 

A fines removal system is installed on the crystallizer designed in the first example. Assuming that the cut size for the fines removal system is 50 im and the ratio of mean residence times for product and fines, rp/rp( = 7), is 10, calculate the mean product residence time now required to produce the same dominant size of 600 pm at the same production rate and suspension density. 

The experiments of Dou et al. (1991) also indicate that the heat transfer coefficient varied with radial position across the bed, even for a given cross-sectional-averaged suspension density. Their data, as shown in Fig. 20, clearly indicate that the heat transfer coefficient at the bed wall is significantly higher than that for vertical surfaces at the centerline of the bed, over the entire range of suspension densities tested. Almost certainly, this parametric effect can be attributed to radial variations in local solid concentration which tends to be high at the bed wall and low at the bed centerline. 

The data of Fig. 20 also point out an interesting phenomenon—while the heat transfer coefficients at bed wall and bed centerline both correlate with suspension density, their correlations are quantitatively different. This strongly suggests that the cross-sectional solid concentration is an important, but not primary parameter. Dou et al. speculated that the difference may be attributed to variations in the local solid concentration across the diameter of the fast fluidized bed. They show that when the cross-sectional averaged density is modified by an empirical radial distribution to obtain local suspension densities, the heat transfer coefficient indeed than correlates as a single function with local suspension density. This is shown in Fig. 21 where the two sets of data for different radial positions now correlate as a single function with local mixture density. The conclusion is That the convective heat transfer coefficient for surfaces in a fast fluidized bed is determined primarily by the local two-phase mixture density (solid concentration) at the location of that surface, for any given type of particle. The early observed parametric effects of elevation, gas velocity, solid mass flux, and radial position are all secondary to this primary functional dependence. 

The parametric effect of bed temperature is expected to be reflected through higher thermal conductivity of gas and higher thermal radiation fluxes at higher temperatures. Basu and Nag (1996) show the combined effect (Fig. 23) which plots heat transfer coefficients as a function of bed temperature for data from four different sources. It is seen that for particles of approximately the same diameter, at a constant suspension density (solid concentration), the heat transfer coefficient increases by almost 300% as the bed temperatures increase from 600°C to 900°C. 

Figure 21. Significance of local suspension density for heat transfer in fast fluidized beds. (Data of Don, Herb, Tuzla and Chen, 1991.)...

Another parametric effect is the apparent dependence of the heat transfer coefficient on the physical size of the heat transfer surface. Figure 24, from Burki et al. (1993), graphically illustrates this parametric effect by showing that the effective heat transfer coefficient can vary by several hundred percent with different vertical lengths of the heat transfer surface, for circulating fluidized beds of approximately the same particle diameter and suspension density. This size effect significantly contributed to confusion in the technical community since experimental measurements by inves-... 

Figure 24. Dependence of heat transfer coefficient on size of heat transfer surfaces. Dp 9 245 pm Suspension Density 9 50 kg/irf. (From Burki, Hirschberg, Tuzla andChen, 1993.)...

The simplest correlations are of the form shown by Eq. (15), in attempts to recognize the strong influence of solid concentration (i.e., suspension density) on the convective heat transfer coefficient. Some examples of this type of correlation, for heat transfer at vertical wall of fast fluidized beds are ... 

Divilio, R. J., and Boyd, T. J., Practical Implications of the Effect of Solids Suspension Density on Heat Transfer in Large-Scale CFB Boilers, Circ. Fluid. Bed Tech IV, 334-339 (1993)... 

The solvent-mediated transformation of o -L-glutamic acid to the S-form was quantitatively monitored over time at a series of temperatures [248]. The calibration model was built using dry physical mixtures of the forms, but still successfully predicted composition in suspension samples. Cornel et al. monitored the solute concentration and the solvent-mediated solid-state transformation of L-glutamic acid simultaneously [249]. However, the authors note that multivariate analysis was required to achieve this. Additionally, they caution that it was necessary to experimentally evaluate the effect of solid composition, suspension density, solute concentration, particle size and distribution, particle shape, and temperature on the Raman spectra during calibration in order to have confidence in the quantitative results. This can be a substantial experi-... 

Fig. 16.5 Percent of dissolved As(lll), As(V)(3,j, and adsorbed As during As(III) oxidation kinetics on bimessite (suspension density 0.1 g Lin 0.01 M NaCl, and atmosphere) as a function of pH and initial As(lll) concentration, [As(lll)].. (a) pH 4.5, [As(lll)]. = lOOpM (b) pH 4.5, [As(III)]. = 300pM (c) pH 6.0, [As(lll)]. = lOOpM (d) pH 6.0, [As(lll)]. = 300pM. Reprinted with permission from Power LE, Arai Y, Sparks DL (2005) Zinc adsorption effect on arsenite oxidation kinetics at the bimessite water interface. Environ Sci Technol 39 181-187. Copyright 2005 American Chemical Society...

Nucleatlon rates could be estimated from the Increase In the number of particles, obtained from sizings with a 95pm orifice tube, of the low size end of the size distributions. The rate of Increase of numbers In the batch (Figure 11) Is Independent of temperature, and shows an approximate first order dependence on supersaturation. Assuming a first order dependence on suspension density, M, gives the correlating relation as. 

Comparing this equation to that of a single particle (eq. (3.565)), it is evident that in applying the Archimedes principle to a particle in a fluidized suspension, it is an average suspension density, including the particle density, rather than that of the fluid alone, that determines the buoyancy force (Foscolo and Gibilaro, 1984). The gravity force is... 

The significance of the scattering and emission by the particle cloud can be illustrated by the following numerical example [Soo, 1990]. Consider a gas-solid flow through a parallel-plate system. Wall 1 is at 1,111 K with reflectivity of 0.1, and wall 2 is at 278 K with reflectivity of 0.9. The gap between the two plates is 61 mm. The moving particles are 2 p.m iron particles, and the temperature of the particles is maintained at 556 K. The particulate suspension density is 0.16 kg/m3. It can be shown that the net heat flux from wall 1 is about 69.22 kW/m2, whereas the net heat flux into wall 2 is about 5.17 kW/m2. 

Fig. 2. Effect of suspension density on heat transfer coefficients (Basu, 1990).

Figure 4 plots, against suspension density, the heat transfer coefficients measured by Basu (1990) over a wide range of bed temperature for 296 pm sand, by Kobro and Brereton (1986) at a temperature of 850°C for 250 pm sand and by Grace and Lim (1989) at 880°C for 250-300 pm sand. The overall heat transfer coefficient is shown to increase with bed temperature. Before radiation becomes dominant in heat transfer, the observed rise in heat transfer coefficient with bed temperature may be explained as follows. The gas convective component is expected to decrease mainly because of the inverse dependence of gas density on temperature. On the other hand, the particles convective component will increase with temperature, thus leading to an increase in gas conductivity, because the latter is dominant for... 

Figure 26 compares the model predictions with the experimental data of Wu et al. (1989) for a membrane wall surface 1.59 m long at a suspension density of 54 kg/m3. Good agreement, especially at lower bed temperatures (Fig. 26a) is clearly seen. At higher temperatures, because of increase in... 

The bed-to-wall heat transfer coefficient depends mainly on the suspension density in the bed. For specified operating parameters, what needs to be considered is therefore only the transfer between the suspension and the heat transfer surface, although the actual mechanism involves various heat transfer processes. 

In contrast, Richardson and Meikle (1961), Barnea and Mizrahi (1973), Rietema (1982), Rowe (1984), Foscolo et al. (1984), and Gibilaro et al. (1987a, 1987b) have defined the buoyancy force on the basis of average suspension density (p) and... 

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