Particle size distribution mass fractions

Most theoretical studies of heat or mass transfer in dispersions have been limited to studies of a single spherical bubble moving steadily under the influence of gravity in a clean system. It is clear, however, that swarms of suspended bubbles, usually entrained by turbulent eddies, have local relative velocities with respect to the continuous phase different from that derived for the case of a steady rise of a single bubble. This is mainly due to the fact that in an ensemble of bubbles the distributions of velocities, temperatures, and concentrations in the vicinity of one bubble are influenced by its neighbors. It is therefore logical to assume that in the case of dispersions the relative velocities and transfer rates depend on quantities characterizing an ensemble of bubbles. For the case of uniformly distributed bubbles, the dispersed-phase volume fraction O, particle-size distribution, and residence-time distribution are such quantities. 

Guillong M, Gunther D (2002) Effect of particle size distribution on ICP-induced elemental fractionation in laser ablation-inductively coupled plasma-mass spectrometry. J Anal At Spectrom 7 831-837 Gunther D (2002) Laser-ablation inductively coupled plasma mass spectrometry. Anal Bioanal Chem 372 31-32... 

Figure 4 presents particle size distributions for six elements which differ among themselves and also from those in Figure 3. Somewhat subjectively, we may identify three patterns in these distributions (a) A coarse mode, typified by Ca and the other elements of Figure 3, which may represent a terrestrial dust origin. This mode can account for coarse particle concentrations observed for Fe, K, Mn, and S. (b) A fine mode with somewhat greater concentrations in the 0.5-1 ymad fraction than in 1-2 ymad particles. The amounts in this <2 ymad range, in excess of those which can be attributed to a coarse crustal aerosol tail with the Ca distribution, show similarities in particle size distributions for Zn, Mn, and possibly Fe. Since the trends shown in Figure 2 point to these elements being characteristic of large scale air masses, their fine modes may be principally due to natural processes.

In a similar study, Allen and co-workers (1996) determined the particle size distribution for 15 PAHs with molecular weights ranging from 178 (e.g., phenan-threne) to 300 (coronene) and associated with urban aerosols in Boston, Massachusetts. As for BaP in the winter (Venkataraman and Friedlander, 1994b), PAHs with MW >228 were primarily present in the fine aerosol fraction (Dp < 2 /Am). A study of 6-ring, MW 302 PAH at the same site showed bimodal distributions, with most of the mass in the 0.3- to 1.0-/zm particle size size range a smaller fraction was in the ultrafine mode particles (0.09-0.14 /xm) (Allen et al., 1998). For PAHs with MW 178—202, the compounds were approximately evenly distributed between the fine and coarse (D > 2 /am) fractions. Polycyclic aromatic hydrocarbons in size-segregated aerosols col-... 

Up to this point, the evidence for two particle populations has been based solely on the refractory specific activity. Additional confirmation is based on the observed particle size distribution by mass of an aerial filter sample. A portion of the aerial filter sample designated as 2 in Table I, was separated into size fractions, and the weight distribution of the fraction is shown in Figure 3. The ordinate values are simply ... 

The chain model corresponding to the closed circuit milling system with localised models of all its elements is presented in Fig. 2. It can be constructed in different ways, but first let us examine the model shown in Fig. 2a. Every column of the set of cells corresponds to an element of the circuit a mill a classifier or an absorber. The cells within columns correspond to fraction numbers with the total number of fractions equal to r. The fraction size decreases with increasing fraction number. The state of the system is characterised by the set of probabilities f, to occupy the cells, every of which can be interpreted as the relative mass content of particles in the cell ij. In particular, the set fj, I = 1,2,.. .r, corresponds to the particle size distribution in the hold-up of the /111 element of the circuit. 

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. 

Consider a particle size distribution determination by mass where the fractional masses (volume =f) of particles of mean diameters (d ) are determined. For a sieve analysis, for example, the measured diameters are... 

Conventionally, the calculation of quantitative sizes following fractionation requires a mass detector, usually a UV detector. The resulting particle size distributions have been found by subsequent MATS analyses to be far too broad. 

Other samples of alkaline slurry were subjected to particle size analysis by sedimentation. With the —43 xm + 1.2 [im fraction this analysis was done in a 50-mm-diameter settling column of dilute slurry with a tared pan at the base to record continuously the mass of sedimented solid. The data were analyzed by the method of Oden (8), and the particle size distribution (Stokesian diameter), expressed on a mass percent basis, was calculated. 

The particle size distribution for the humic acid fraction is depicted in Figure 4. No material sedimented out until the most extreme conditions were applied (40,000 rpm for 24 hr), when some lightening of color at the top of the solution was observed. The sedimented particles had a Stokesian diameter of around 2 nm, which means that a particle size gap of three orders of magnitude exists between these and the next largest particles detected (5 xm). From the experimentally determined coal particle density of 1.43 g/cm, it was calculated that a solid sphere of diameter 2 nm would have a molecular mass of 4000. If the molecules were rod-shaped, even smaller molecular masses would be predicted. Literature values of the molecular mass of regenerated humic acids range between 800 and 20,000, with the values clustering around 1,000 and 10,000 (i5, 16, 17). 

Macromolecular or particulate samples fractionated by the FFF are usually not uniform but exhibit a distribution of the concerned extensive or intensive parameter [8] or, in other words, a polydispersity. Molar mass distribution (MMD), sometimes called molecular weight distribution (MWD), or particle size distribution (PSD) describes the relative proportion of each molar mass (molecular weight), M, or particle size (diameter), d, species composing the sample. This proportion can be expressed as a number of the macromolecules or particles of a given molar mass or diameter, respectively, relative to the number of aU macromolecules or particles in the sample ... 

Another separation technique of particular application for proteins, high-molar-mass molecules, and particles is the general class known as field-flow fractionation (FFF) in its various forms (cross-flow, sedimentation, thermal, and electrical). Once again, MALS detection permits mass and size determinations in an absolute sense without calibration. For homogeneous particles of relatively simple structure, a concentration detector is not required to calculate size and differential size and mass fraction distributions. Capillary hydrodynamic fractionation (CHDF) is another particle separation technique that may be used successfully with MALS detection. 

Particle size distributions were measured 20 nozzle diameters downstream of the nozzle exit, on the Jet centerline (Fig. 10.10). At low DBP vapor concentrations, the size distributions were unimodal with count mean diameters of 0.4 to 0.5 fjLtn and mass mean diameters of about 3 /zm. As the vapor mole fraction increased, the count mean diameter... 

Particle-size and mass distribution curves, along with information on particle porosity, density, shape, and aggregation, can be obtained for submicrometer- and supramicrometer-size silica materials suspended in either aqueous or nonaqueous media by field-flow fractionation (FFF). Narrow fractions can readily be collected for confirmation or further characterization by microscopy and other means. Among the silicas examined were different types of colloidal microspheres, fumed silica, and various chromatographic supports. Size distribution curves for aqueous silica suspensions were obtained by both sedimentation FFF and flow FFF and for nonaqueous suspensions by thermal FFF. Populations of aggregates and oversized particles were isolated and identified in some samples. The capability of FFF to achieve the high-resolution fractionation of silica is confirmed by the collection of fractions and their examination by electron microscopy. 

---