Size distributions by volume

Fig. 2 Particle size distributions, (by volume) of the impeller-batch (top) and the micro-mixer-continuous-flow (bottom) processes when manufacturing the pigment Yellow 12. The cumulative distributions are given as well [11]...

Figure 55 Typical size distributions by volume, for the feed flow and the overflow, if the hydrocyclone is operated for fines removal. The ordinate value is defined by volume percentage divided by interval width.

The mass is related to the cumulative (percent less than) size distribution by volume (or mass), F iL), as follows ... 

Laser diffraction not only provides a particle size distribution by volume but it can also be used to provide a value for volume concentration. Since laser diffraction assumes that all particles are spherical, for plate-like particles, this leads to an overestimation of volume concentration. Particle thickness and aspect ratio can be derived using this information [191]. 

In order to demonstrate that scale-up can be successfully performed from lab to commercial scale, we performed the atomization of inulin (a polysaccharide extracted from chicory root) from NMP solutions (300 g/L) by antisolvent with supercritical CO2 (20 MPa, 40 °C) After the first test a lab scale (XO.l), we prepared samples in three plants 2 g in XI, 20 g in XIO, and 200 g in XlOO (80). As shown in Figure 11, the particle size distributions (by volume) are strictly the same at the three scales in the range for which we want to obtain a nondusty powder. Moreover, this work permits us to show that the fluid/substance ratio ( 50 kg/kg) can be optimized at a much lower value than generally stated in most publications (500-10,000). Extended work is now ongoing on therapeutic molecules and for smaller-sized particles on a large scale. 

If a size distribution by volume is required, a technique that responds principally to the volume of material that has a specific size is chosen. 

By laser diffraction a size distribution by volume is primary obtained, that can be transferred to the intensity and number distribution. Although laser diffraction is sensitive over a broad particle size range, a small number of microparticles will escape determination. It should therefore kept in mind, that the upper limit of the size distribution does not naturally present the real situation, e.g. that particles in the lower m-range may be present although the D99-value was, e.g. determined at 400 nm. Different diameters are normally obtained from size distributions (e.g. mean, mode, median) and only if the particle sizes are Gaussian distributed all these diameters will have the same value. 

Fig. 8. Particle size distribution (by volume) of the products hydrothermally synthesized (at 438 K for 2 h) from the reaction mixtures (hydrogels) having A = 0.001 (A), A = 0.002 (B),...

Fig. 12. Particle size distributions by volume of the products obtained by hydrothermal treatment (at 483 K for 2 h) of the reaction mixtures 0.007/0.56 (A) and 0.007/1.0 (B). (Adopted from Ref. [55] with permission of Publisher)...

The cumulative pore size distribution by volume is obtained by plotting Vj against r ,. This may be differentiated graphically to produce the relative pore size distribution by volume or the calculation may be carried out using the tabulated data. 

If the pore size range is narrow it is possible to plot the cumulative pore size distribution by volume on linear paper and to differentiate the curve to obtain the relative pore size distribution by volume. Graphical differentiating smoothes out experimental errors alternatively, tabular differentiating can be used with a curve smoothing correction. 

For a wide distribution it is preferable to plot the distributions on log-linear paper with V on the linear axis. The pressurizing curve is shown in Figure 4.14. Data extracted from the pressurizing curve are presented in Table 4.3. The data are plotted as cumulative and relative size distribution by volume in Figures 4.IS and 4.16 and the... 

Fig. 4.10 Cumulative pore size distribution by volume by mercury porosimetry for a sample having a narrow pore size range.

Fig. 4.15 Cumulative pore size distribution by volume for a sample with a wide range of pore sizes.

Fig. 4.26 Relative pore size distribution by volume (smoothed curve).

Coalescence Coalescence is the most difficult mechanism to model. It is easiest to write the population balance (Eq. 20-71) in terms of number distribution by volume n v) because granule volume is conserved in a coalescence event. The key parameter is the coalescence kernel or rate constant P(ti,i ). The kernel dictates the overall rate of coalescence, as well as the effect of granule size on coalescence... 

The moment equations of the size distribution should be used to characterize bubble populations by evaluating such quantities as cumulative number density, cumulative interfacial area, cumulative volume, interrelationships among the various mean sizes of the population, and the effects of size distribution on the various transfer fluxes involved. If one now assumes that the particle-size distribution depends on only one internal coordinate a, the typical size of a population of spherical particles, the analytical solution is considerably simplified. One can define the th moment // of the particle-size distribution by... 

MR has been used to measure the pore size distribution by exploiting the dependence of T) and T2 on the surface to volume ratio of water-filled pores [20,... 

Hope, M. J. Bally, M. B. Webb, G. Cullis, P R., Production of large unilamellar vesicles by a rapid extrusion procedure. Characterization of size distribution, trapped volume and ability to maintain a membrane potential, Biochim. Biophys. Acta 812, 55-65 (1985). 

Size exclusion chromatography (SBC) is a separation process by which molecules are fractionated by size on the basis of differential penetration into porous particulate matrices. Blution volume (Vq) of any given molecular species relative to another of different size is dependent on the pore diameter of the matrix, pore-size distribution, pore volume (Vp, interstitial volume (Vq) and column dimensions. Use of SBC to estimate molecular size is achieved by plotting the log of the molecular weight of a series of calibrants against their elution volume. Since Vg is a function of Vg and Vj, its magnitude will be dependent on the geometry of a column. 

Figure 5.11 Particle size distribution by image analysis (a) immediately after sample preparation (b) 24 h after sample preparation. The increase in particle size and the decrease in particle numbers are observed. Volume fraction of DAP increased from (a) 15.6 to (b) 43.5 vol.% DAP. The increase in volume fraction results from the coalescence of submicron particles. Reproduced from Ref. 27, with permission.

The commercial catalyst used in this work contains 12 wt% Ni and 83 wt% a-Al203. It has a BET total surface area of 3.4m /g and a unimodal pore size distribution with volume 0.155 cc/g, mean pore radius 1600 A and void fraction 0.362. Its activation required a reduction which was carried out under atmospheric pressure in situ, for 72 hrs at 850°C by means of a pure dried hydrogen flow of lOO Nl/hr. These severe reduction conditions were required because 20 wt% of the Ni was present as NiAl204-spinel phase, which could only be reduced above 770°C. It led to a very active catalyst, with a specific Ni-surface area of 0.68 m Ni/g.cat. 

The degree of toughness is determined by the crosslink density of the matrix, the elastomer particle size and size distribution, the volume fraction of the elastomeric phase, and the degree of adhesion between the epoxy matrix and the particle. The formulating procedure was found to have as strong an effect on the fracture toughness as the materials themselves.16... 

The volume is closed with a contribution by J. Bibette who describes and illustrates a simplified process of making monodisperse emulsions and emulsion based particles with predictable size and size distribution by a simple shearing device. I regard this very flexible route as important for the conception of many future particle-based systems, devices and procedures, and it is rather the rule than the exception that colloid chemistry nicely integrates mechanical and engineering procedures to access the nanoscale in a rational way. 

The catalyst was removed and analyzed for its coke content, pore size distribution, pore volume, and surface area. All the catalyst samples were analyzed after a Soxhlet extraction with tetrahydrofuran for 24 h and drying in oven at 100 C. The catalyst weight loss due to combustion at 550 C was considered as the coke on catalyst. The catalyst pore characteristics were measured by a Quantachrome Autoscan Porosimeter. 

---