Volume-based particle size distribution

In order to determine the crystal growth rate, volume-based particle size distributions were measured with a Horiba Laser Scattering Particle Size Distribution Analyzer LA-920. Additionally, BET surface area measurements of the seed crystals were undertaken with a Micromeritics Tristar Surface Area Analyzer. The crystal morphology was analyzed with a Philips XL30 PEG SEM. XRD analysis was carried out on a Bruker AXS powder diffractometer. Finally, chemical analysis was conducted with a Dionex ICS 5000 ion chromatograph and a Thermo Scientific iCAP 6000 ICP-MS apparatus. Thermodynamic calculations were conducted with the OLI Stream Analyzer [29]. To ensure reproducibility, the growth kinetics experiments were repeated three times and arithmetic averages were employed in the analysis of the data. 

H. Geers, W. Witt, Direct calculation of the volume based particle size distribution from PCS or PCCS measurements. On the CD-ROM Particulate Systems Analysis 2008, Stratford-Upon-Avon, 02-04 Sept 2008. (available from PCIG, C/o Particle Technology Ltd, Station Yard Industrial Estate, Hatton, Derbyshire, DE65 5DU, United Kingdom), paper 28... 

Figure 7 Volume-based particle size distribution of studied sugar pellets measured by Camsizer XT device.

Figure 2. Histogram of the volume- and number-based particle size distribution of an emulsion.

One of the recent advances in magnetic studies is that it enables not only the estimation of the average volume v of clusters from the LF and HF approximations of the Langevln function, but also enables to compute particle size distribution based on an assumed function. By judiciously combining the parameters of the Langevln and of the "log normal function, we obtained a particle (cluster) size distribution of Y Fe203 in ZSM-5. The essential features of such computation are shown in Fig. 6. 

Model simulations of particle volume concentrations in the summer as functions of the particle production flux in the epilimnion of Lake Zurich, adapted from Weilenmann, O Melia and Stumm (1989). Predictions are made for the epilimnion (A) and the hypolimnion (B). Simulations are made for input particle size distributions ranging from 0.3 to 30 pm described by a power law with an exponent of p. For p = 3, the particle size distribution of inputs peaks at the largest size, i.e., 30 pm. For p = 4, an equal mass or volume input of particles is in every logaritmic size interval. Two particle or aggregate densities (pp) are considered, and a colloidal stability factor (a) of 0.1 us used. The broken line in (A) denotes predicted particle concentrations in the epilimnion when particles are removed from the lake only in the river outflow. Shaded areas show input fluxes based on the collections of total suspendet solids in sediment traps and the composition of the collected solids. 

The particle light scattering coefficient has been continuously measured at this location since 1976. Measurements of the particle size distribution have been made daily since 1978, providing the data base necessary to assess the variability of the normalized aerosol volume distribution. 

The particle size distribution, X(s), above is, unfortunately, not in a form which is useful for most applications. This is because it is a scattered intensity weighted distribution (for brevity, intensity distribution ) rather than a size distribution based on the volume (weight) or number of particles. The difference between distributions weighted in different ways can be most easily explained by relating the various distributions to a number distribution. 

Related Calculations. This procedure can be used to calculate average sizes, moments, surface area, and mass of solids per volume of slurry for any known particle size distribution. The method can also be used for dry-solids distributions, say, from grinding operations. See Example 10.7 for an example of a situation in which the size distribution is based on an experimental sample rather than on a known size-distribution function. 

Many methods are available for determining particle size in pharmaceutical practice, including microscopy, sieving, sedimentation, and determination of particle volume [19]. Sieve analysis with U.S. standard sieves is widely used to determine the particle size distribution based on powder weight. Sieves are classified according to the number of openings (Table 14) and are generally made of wire cloth woven from brass, bronze, or other suitable wire. 

A fundamental extension to the homogeneous nucleation theory was proposed by Lichti et al. [23] and Feeney et al. [24]. Their theory is based on the positive skewness of the particle size distribution (PSD) as a function of volume during Interval II. This impUes that the rate of nucleation during Interval I increases with time until it eventually drops off at the cessation of nucleation. Lichti and Feeney claim that micellar nucleation or one step homogeneous nucleation incorrectly predict either decreasing or constant nucleation rates. 

Figures 7 and 8 show typical particle size distributions for vinyl acetate emulsions produced in a single CSTR. A large number of particles,are quite small with 80 to 90% being less than 500 A in diameter. The large particles, though fewer in number, account for most of the polymer mass as shown by the cumulative volume distributions. Data are also presented on Figures 7 and 8 for the number of particles based on diameter measurements (N ), the average number of free radicals per particle, and the steady state conversion.

Insitec EPCS is covered in detail in section 10.7. They are laser-based instruments for in-line particle measurements that provide information on particle volume concentration and size distribution. Unlike other... 

Insitec now forms part of Malvern Instruments but is still based in California for process and laboratory R D. The EPCS are laser-based instruments for in-line particle measurements that provide information on particle volume concentration and size distribution. EPCS instruments are part of the larger group of electro-optical instruments (MALLS) whose principle of operation is based on light scattering from a group (or ensemble) of particles. Unlike other instruments operating on this principle, the EPCS can perform direct measurements of particle laden flow stream provided the concentration is within operating limits. 

C. Parkinson et al. (17) considered the effect of particle size distribution on viscosity. They studied suspensions of polymethylmethacrylate) spheres in Nujol with diameters of 0.1, 0.6, 1.0 and 4.0 microns with different volume fractions and with different particle size combinations to determine the influence of size-distribution on the viscosity. Each particle size gave a certain contribution to the final viscosity based on the volume fraction and the hydrodynamic coefficient obtained from the empirical equation for that particle size. The contributions were expressed in the same form as in Mooney s model, and the viscosity was calculated from the product of each term, n... 

Usually, in chromatography the volume average partide diameter is employed. For comparison the particle size distribution based on the number and the volume average is shown for the same silica measured by the same technique (see Tab. 3.11). 

The similarity transformation for the particle size distribution is based on the assumption that the fraction of the panicles in a given size range is a function only of particle volume normalized by the average particle volume ... 

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