Particle size distribution functions analysis

Friedlander (11) has examined the effects of flocculation by Brownian diffusion and removal by sedimentation on the shape of the particle size distribution function as expressed by Equation 9. The examination is conceptual the predictions are consistent with some observations of atmospheric aerosols. For small particles, where flocculation by Brownian diffusion is predominant, p is predicted to be 2.5. For larger particles, where removal by settling occurs, p is predicted to be 4.75. Hunt (JO) has extended this analysis to include flocculation by fluid shear (velocity gradients) and by differential settling. For these processes, p is predicted to be 4 for flocculation by fluid shear and 4.5 when flocculation by differential settling predominates. These theoretical predictions are consistent with the range of values for p observed in aquatic systems. 

From the TEM micrographs, particle sizes and the number of particles per unit area could be estimated. Figure 16.6 provides a quantitative analysis of the particle sizes as a function of deposition time. It is evident from the particle size distributions that at low nominal Au thickness (0.13 nm), mean particle diameters are about 1.4 nm and fall in a narrow range of sizes. As the nominal thickness becomes higher, the particle... 

The analysis of the autocorrelation function data by the Coulter Model N4 is carried out by the Size Distribution Program (SDP), which gives the particle size distribution in the form of various output displays (see Section 10.4). The SDP analysis utilizes the computer program CONTIN developed by S.W. Provencher (ref. 467-470 see also Section 10.2). (This program has been tested on computer-generated data, monomodal polystyrene samples, and a vesicle system (ref. 466-468,471).) Since the SDP does not fit to any specific distribution type, it offers the ability to detect multimodal and very broad distributions. 

All the samples measured showed characteristic superparamagnetic behavior with a blocking temperature TB. An independent method of determining the parameters of the particle size distribution g(D) is by means of the analysis of magnetic measurements under equilibrium conditions, i.e. at temperatures above the superparamagnetic blocking temperature Tb- For this purpose we performed magnetization measurements as a function of field M(H) at different temperatures [4,5]. 

In essence, the test battery should include XRPD to characterize crystallinity of excipients, moisture analysis to confirm crystallinity and hydration state of excipients, bulk density to ensure reproducibility in the blending process, and particle size distribution to ensure consistent mixing and compaction of powder blends. Often three-point PSD limits are needed for excipients. Also, morphic forms of excipients should be clearly specified and controlled as changes may impact powder flow and compactibility of blends. XRPD, DSC, SEM, and FTIR spectroscopy techniques may often be applied to characterize and control polymorphic and hydrate composition critical to the function of the excipients. Additionally, moisture sorption studies, Raman mapping, surface area analysis, particle size analysis, and KF analysis may show whether excipients possess the desired polymorphic state and whether significant amounts of amorphous components are present. Together, these studies will ensure lotto-lot consistency in the physical properties that assure flow, compaction, minimal segregation, and compunction ability of excipients used in low-dose formulations. 

Thus, given gparticle size distribution. For narrow size distributions, the autocorrelation function is satisfactorily analyzed by the method of cumulants to give the moments of the particle size distribution.(7) However, the analysis of QELS data for samples with polydisperse or multimodal distributions remains an area of active research.(8)... 

The overall conclusion from the analysis of equation 18 over the complete domain of a is that, in principle, information about the shape of the particle size distribution can be obtained directly from turbidity, or in general, from scattering measurements. However, the discriminating power of the measurements in terms of the particle size distribution depends upon the wavelength range selected for the analysis. The major difficulty in the interpretation of the data arises from the behavior of the extinction itself as function of the size parameter which causes the measurements "see" a different average at every wavelength. 

Beckett described inductively coupled plasma mass spectrometry (ICP-MS) as an off-line detector for FFF which could be applied to collected fractions [ 149]. This detector is so sensitive that even trace elements can be detected making it very useful for the analysis of environmental samples where the particle size distribution can be determined together with the amount of different ele-ments/pollutants, etc. in the various fractions. In case of copolymers, ICP-MS detection coupled to Th-FFF was suggested to yield the ratio of the different monomers as a function of the molar mass. In several works, the ICP-MS detector was coupled on-line to FFF [150,151]. This on-line coupling proved very useful for detecting changes in the chemical composition of mixtures, in the described case of the clay minerals kaolinite and illite as natural suspended colloidal matter. 

A simplified method was proposed by Kundig et al. (9) allowing evaluation of the particle size and the size distribution of a solid by analysis of its spectrum as a function of temperature. By variation of the temperature it is possible to follow the variation of the relative spectral areas of the sextet and doublet. Assuming that particles for which Tj. < Tl and > Tl contribute exclusively to one of the two components (paramagnetic and magnetic), the temperature at which — tl and at which the hyperfine split takes place can be determined V is calculated from Eq. (19) at the temperature T at which the spectral areas of the two components are equal). The dependence of the two spectral areas on temperature in the range in which both components are observed yields the particle size distribution. 

Micromeretics Elzone 5380 has one analysis station features complete sizing and counting capability and reports particle size distribution as a function of number, area or volume. 

Based on a similar approach, a statistical analysis was conducted to determine whether correlations of CO and CH4 emissions could be established with a number of variables including fuel moisture content, fuel particle size distribution, fuel feed rate and excess air ratio. With the limited number of observations, the best model for CO was derived as a function of fuel moisture content (Fig, 1) for the combustor used for these studies. There was no evidence for correlation of the other variables. The measured CH4 contents also had an increasing trend with higher moisture contents of the fuels, but could not to be fitted in any correlation equation. 

If the particles are sufficiently large, it is permissible to pass from the discrete to the continuous particle size distribution and particle current. The basic starting equation for the analysis of the behavior of the stable aerosol in a batch reactor is the continuity relationship (10.33) for the continuous size distribution function. In terms of nj and dp, this can be written... 

Gas-phase molecules in the atmosphere can be converted to the aero.sol phase by homogeneous (gas phase) or heterogeneous aerojtol phase) reactions. Both mechanisms may be operative over different particle size ranges. Information on the dominant growth mechanisms can be inferred by an analysis of aerosol dynamics in power plant plumes (McMurry et al., 1981 Wilson and McMurry. 1981). When homogeneous gas-phase reactions are controlling, there are two possible pathways for the reaction products to enter the size distribution function ... 

Models are constructed which suggest that these optical measurements can be used to determine the effective particle size distribution parameters, mean diameter and sigma. Assumptions include multilayer particle deposit, the lognormal distribution of the diameters of the spherical, opaque particles, and no sorting of size classes during particle deposition. The optical measurement include edge trace analysis to derive the contrast transfer function, and density fluctuation measurements to derive the Wiener spectrum. Algorithms to perform these derivations are outlined. 

A strong positive feature of SEC is that instrumentation is readily available in the form of HPLC apparatus. No special experience is needed for those acquainted with this widely practiced method. Relatively unskilled operators can quickly learn to perform the analysis satisfactorily. Average particle sizes are quickly measured by the peak-position method. However, it is also feasible to determine particle-size distributions if appropriate computer software is available. Separation times are predetermined, because all species elute between the total exclusion and total permeation volumes (provided the desired SEC process is the only retention). No special method development is required, other than ensuring that the proper mobile phase-stationary phase combination is selected. Particle diameter is directly a function of retention or elution times. 

The most complete information that can be obtained in dispersion analysis comes from the determination ofparticle size distributionfunction (in some cases one may be interested in obtaining particle shape distribution). Some methods yield only the information on the average particle size, which in some cases may be accompanied by some conditional distribution width. These terms require a more detailed discussion, as different methods may yield different size distribution functions and average sizes for the same disperse system. 

Sedimentation analysis is commonly used and rather simple method of determining the size and size distribution function, based on the difference in particle settling rates in a gravity field. In this method a pan is placed into a homogeneously mixed disperse system, and the weight of particles, P, that accumulate on the pan, is monitored as a function of time, t (Fig. V-30). 

Size distribution function of the particles in the exhaust pipe as measured by SMPS analysis (16 kW and 19% excess air A metal premix drilled premix O diffusive, continuous line ambient air). 

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