Continuous mean particle size

Figure 2.1.6 shows the results of such a continuous synthesis process. It shows the variation of the mean particle size during the experiment. The error bars indicate the standard deviation of the particle size distribution of each sample based on the transmission electron micrographs (number distribution). The experiment was performed under the following conditions (A) ammonia, water, and TEOS concentrations were 0.8, 8.0, and 0.2 mol dm-3 7", = 273 K, T2 = 313 K total flow rate was 2.8 cm3 min-1 100 m reaction tube of 3 mm diameter residence time 4 h and (B) ammonia, water, and TEOS concentrations were 1.5,8.0, and 0.2 mol dm- 3 Tx = 273 K, T2 = 313 K total flow rate was 8 cm3 min-1 50 m reaction tube of 6 mm diameter, residence time 3 h. Further details and other examples are described elsewhere (38). Unger et al. (50) also described a slightly modified continuous reaction setup in another publication. 

With the small mean particle sizes (>— 15and less), it was found for underoxidized propellants that pressure increase would cause the burning rate to increase, reach a plateau, decrease, and then possibly extinguish at some critical pressure. Where extinction did not occur, the burning rate would continue to decrease after the plateau, reach a minimum and then again increase monotonically. Further reduction of oxidizer content accentuated the tendency toward plateau behavior. The... 

The growth law (Eq. 15.13) and the continuity equation for the particle-size distribution (Eq. 15.17) lead to the equation for the evolution of the mean particle size ... 

Figure 15 Turnover rate for CO oxidation on Pd particles supported on sapphire. The points represent the experimental data from Rumpf et al. [131]. The symbols ( ) and (O) correspond to mean particle sizes of 3.9nm and 3.7 nm and particles densities of 1.6 x 1010 cm-2 and 1.3 x 1012 cm-2, respectively. The continuous curves represent the experimental fit with Eqs. (3), (4), (5) and (13) using a = 0.46 and E — E = 0.26 eV (from Ref. [144]). The dotted-dashed line represents the fit with non interacting diffusion fields around the Pd particles (from Ref. [131]).

It is important to note that present AccuSizer measurements were obtained with a particle-size threshold of 0.56 pm (the lowest possible size threshold available for this analyzer) and any LPC growth behavior for particles smaller than 0.56 pm could not be seen in these data. MLC pump extensive handling showed a slight increase in mean particle size and PSD of silica-H slurry, as will be discussed later. The above behavior of LPC may be attributed to the cumulative effects of low-intensity continuous shear application to the bulk volume of slurry handled at very high pump speeds in MLC pump. In Fig. 18.21b, the LPC trend for the complete 330 h of Test 1 is very similar to the first 45 h. 

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.)... 

Continuous rotary and batch hydrators are used to produce calcium hydroxide (slaked lime) powder. The continuous version uses a slightly inclined, slowly rotating steel cylinder of about 1 m diameter by 6-7 m in length. The calcium oxide is fed into the upper end and the correct proportion of water is sprayed in, followed by tumbling in the cylinder to produce a uniform product. Open trough-type batch hydrators, in which the reacting components are mechanically combined, provide greater control of hydration rate and temperature and some improvements in the quality of the product. An explosion process in which hydration is conducted in a pressure vessel produces a slaked lime with better flow characteristics, and a smaller mean particle size more suitable for uses such as filters [14]. 

The first improvement in the plant was achieved by reducing the speed of the CBT impeller. A significant increase in mean particle size was achieved ( 50 to 60 p,m), although a bimodal PSD continued to be observed with fines in the 10-20 p,m range. This distribution is shown in Fig. 9-5. Improvements in centrifugation and drying rate were achieved, but the fines content prevented a sufficient increase to achieve the desired productivity. 

The final mean particle size and PSD will be determined by the number of nuclei created by these steps. If nucleation continues throughout the addition, the mean particle size will be small, perhaps < 10 pm, and the PSD will be broad and possibly bimodal because of the large number of nuclei produced and the conditions allowing some crystals to grow while nucleation is creating small crystals. 

The equilibrium or algebraic Eulerian model with a single conditional velocity that is based on the mean particle size small particle Stokes number and limited polydispersity (momentum-balance equation only for the continuous phase if the system is dilute or for the mixture of continuous and disperse phases if the system is dense). 

The resolution and separating efficiency achieved are, as in other forms of chromatography, dependent upon particle size and particle size distribution. The resolution improves as particle size becomes smaller and particle size distribution narrower. The trend towards smaller and more uniform particles continues and the silica gel now commonly in use for TLC studies has a mean particle size of 12 pm with a particle size range of 5-25 pm and a pore diameter of 6nm which gives partial exclusion for compounds between 500 and 1000 Da. Commercially available precoated plates have a mean particle size of 10 pm with a correspondingly narrower particle size range, with thinner layers of 250 pm for increased speed and resolution. The newer technique of HPTLC uses silica gel with a particle size of 5-6 pm. 

Granular Activated Carbon, or GAC has a mean particle size between 1-5 mm. It is usually used in fixed bed adsorbers in continuous processes and with low pressure drops, in both liquid and gas phase applications. Most of the gas phase applications (gas purification, solvent recovery, air filtering and gas masks, gas separation by PSA, catalysis, etc.) use GAC. In addition, GAC is displacing PAC in many liquid phase applications such as gold extraction and drinking water treatment GAC has the advantage, compared to PAC, of offering a lower... 

The reactor vessel is usually a stirred tank. The monomer phase is subjected either to turbulent pressure fluctuations or to viscous shear forces, which break it into small droplets that assume a spherical shape under the influence of interfacial tension. These droplets undergo constant collisions (collision rate >1 s ), with some of the collisions resulting in coalescence. Eventually, a dynamic equilibrium is established, leading to a stationary mean particle size. Individual drops do not retain their unique identity, but undergo continuous breakup and coalescence instead. In some cases, an appropriate dispersant can be used to induce the formation of a protective Aim on the droplet surface. As a result, pairs of clusters of drops that tend to coalesce are broken up by the action of the stirrer before the critical coalescence period elapses. A stable state is ultimately reached in which individual drops maintain their identities over prolonged periods of time [247]. 

Cerium (IV) oxide nanoparticles were synthesized by Masui et al [236] by use of a two-microemulsion technique. One of the microemulsions contained polyoxyethylene(lO) octylphenyl ether (OP-10) as the surfactant, n-hexyl alcohol as the co-surfactant, cyclohexane as the continuous phase, and an aqueous solution of cerium nitrate as the droplet phase. The second microemulsion was the same except that the droplet phase was an aqueous ammonia solution. The two were mixed to cause precipitation the particles thus obtained were gathered by centrifugation and washing under sonication with methanol, deionized water and acetone. The final treatment involved freeze-drying and vacuum drying. The mean particle size varied with experimental conditions in the range 2.5-4.0 nm. 

Continuous particle size distributions can be mixed to improve the packing density. Generally, the mean particle size of the two distributions should be very different and the particle size distribution of the smaller powder should be wider than the larger powder. For a wide particle size distribution where the packing density is already high, little benefit is achieved by mixing with another distribution. 

As shown in section 2.4, there is a bewildering variety of different definitions of mean particle size. Most textbooks quote the definitions either in the form of summations or as integrals, the latter being more appropriate if the particle size distributions are generated as continuous curves. Few textbooks, however, give any hints as to which of the definitions are to be used and when. This is a serious omission because the correct choice of the most appropriate mean is vital in most applications. 

George et al. (17) studied the formation of particulate Ti02 by addition of small quantities of TiCU vapor to a lean CO/O2/N2 flame with a maximum temperature of about 1400 C. According to their observation, chemical reaction was essentially complete 50 ms down stream of the CO flame front and that the particle growth continued for a further 200 ms by the coagulation mechanism. Good agreement with the theoretical prediction of Ulrich (10) was reached with respect to both the development of the mean particle size and the size distribution. 

The mean particle size obtained in a continuous crystallizer can be calculated from the moments of the particle size distribution (Equation 9.3), I = (J rtiilAL)/ wtidl) = (J nj.l dL)/(J nl dl). The mass of particles of size L, thl, can be calculated from Equation 9.7, mi oc L tii = L wo This leads to the average... 

The efficacy of ffiese systems strongly depends on the structure of the vehicle and, especially, on the mean particle size and the particle size distribution (PSD). In fact, in the case of parenteral applications the size of nanoparticles should range between 100 nm and 300 nm in order to avoid undesired interactions with the reticulo-endothelial system, besides guaranteeing an adequate lifetime in the bloodstream, and a continuous and controlled drug release [6,13-15]. 

The kinetic parameters, which were determined from laboratory-scale continuous experiments as a function of the energy input and/or supersaturation, were applied to the semibatch mode of operation without any adjustments or parameter fitting. The SFM slightly underestimates the mean particle size in the range between 0.01 and 1 W/kg, but correctly predicts the smaller particle size obtained experimentally for the 25 1 reactor. On the same scale, the model also predicts a lesser degree of dependence of the particle size on the specific power input due to the interactions of mixing and the precipitation kinetics. This behaviour has also been observed experimentally in this research. 

This shows that a continuous increase of acetone content in the EtOH/AC solvent mixture can be used to gradually decrease the mean particle size of the micronized PVP at otherwise constant parameters from the microscale to the nanoscale. 

Note we are dealing with a discrete function not a continuous function, hence the subscript /.) This approach is needed to treat experimental information on different particle size fractions collected over different size sieves that is, particles collected on a particular size sieve have sizes larger than this sieve opening but smaller than the opening size of the sieve immediately above it through which the particles fell If we can characterize the number of particles of a certain size Tp as Afo , then the mean particle size r is... 

Source sampling of particulates requites isokinetic removal of a composite sample from the stack or vent effluent to determine representative emission rates. Samples are coUected either extractively or using an in-stack filter EPA Method 5 is representative of extractive sampling, EPA Method 17 of in-stack filtration. Other means of source sampling have been used, but they have been largely supplanted by EPA methods. Continuous in-stack monitors of opacity utilize attenuation of radiation across the effluent. Opacity measurements are affected by the particle size, shape, size distribution, refractive index, and the wavelength of the radiation (25,26). 

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