Aerosol distribution

The kinetic theory and the diffusion theory may be used for certain aerosol distributions. However, these two theories begin to deviate from the hybrid theory as the aerosol polydispersity increases. Use of either the kinetic theory or the diffusion theory may therefore result in large errors. 

The aerosol distributions are calculated in terms of a single mode, without attempting to resolve them into a major large mode and a minor very small (unattached) mode. The unattached mode is very much smaller in diameter (of molecular cluster dimensions) than the major mode of the aerosol and in underground mines its peak height is very small. To resolve such a mode would require more than the three diffusion batteries used for the measurements. 

Since the subsequent B-decays of Pb-212 and Pb-214 4- Bi-214 do not result in significant recoil (Mercer, 1976), the alpha measurement of Po-214 and the Pb-212 daughters is in reality tracing the aerosol distribution of a Rn-220 daughter atom (Pb-212) which has condensed only once and a Rn-222 daughter atom (Pb-214) that has probably condensed more than once. This stability of the Pb isotopes is the basis for our generic reference to Pb-212 and Pb-214 distributions. 

Fig. 1. Deposition of inhaled particles of different sizes (mass median aerodynamic diameters) in the three regions of the respiratory tract. Each shaded area indicates the variability of deposition when the aerosol distribution parameter, o, (geometric standard deviation) was varied from 1.2 to 4.5. The assumed tidal volume was 1450 cm3. (Reproduced from Health Physics, vol. 12, pp. 173-207,1966 by permission of the Health Physics Society).

Analyzing inhalation chamber atmospheres to characterize aerosol distributions with a new generation system. 

The submicron aerosol populations in the European background air are variable from location to location. The concentrations and variability of aerosol distributions do, however, show similarities over large geographical areas (Fig. 11). The particle number concentrations are generally lower in more northern and higher mountain locations, naturally as they are generally located farther from the emission areas. 

Since atmospheric aerosols comprise particles with a wide range of sizes, it is often convenient to use mathematical models to describe the atmospheric aerosol distribution (Seinfeld and Pandis, 1998). A series of mathematical models have been proposed, of which the lognormal distribution has been the most used in atmospheric applications (Seinfeld and Pandis, 1998 Horvath, 2000). Useful discussions of the various aerosol size distribution models are provided by Seinfeld and Pandis (1998) and Jaenicke (1998). In general, atmospheric aerosols size distributions are shown graphically in terms of the volume (or mass) distributions, surface area distributions, or number distributions as a function of particle size (Jaenicke, 1998). 

In general, if the aerosol distribution is wide enough and the mass mediam diameter (MMD) is within the range of the device, D50S can provide reasonably accurate estimates of the aerosol-distribution parameters. Efficiency curves for impactors are sigmoidal, however, and collection efficiency for particles of all sizes is non-zero. Thus, when the size distribution is narrow, as in aerosols modified by particulate-control devices, the amount of mass attributed to the larger particles may be incorrect. As a rule, the size of the... 

Recent estimates of direct radiative forcing by tropospheric aerosols have employed aerosol distributions from global-scale chemical transport models and assumed aerosol properties typical of the several aerosol types. These estimates contain uncertainties both in the modeled aerosol... 

Laube, B.L., Norman, P.S. and Adams, G.K. (1992). The effect of aerosol distribution on airway responsiveness to inhaled methacholine in patients with asthma. J. Allerg. Clin. Immunol. 89, 510-518. 

Lee Z, Berridge MS, Finlay WH, Heald DL. Mapping PET-measured triamcinolone acetonide (TAA) aerosol distribution into deposition by airway generation. Int J Pharm 2000 199(1) 7-16. 

Atmospheric aerosol distribution functions may also be plotted in the form ]og dN/d log dp) versu.s log dp (Fig. 13.2), but the area under the curve does not have a direct physical interpretation. However, the slope of the curve on the log-log plot is often approximately constant over one or two decades in the particle diameter, and the. size distribution function can be represented by a power law ... 

A value of p -4 C Junge" distribution) provides a useful approximation for many continental aerosol distributions over the size range 0.2 < dp < 10 The power law form also simplifies Mie theory calculations oflight scattering (Chapter 5). Small deviations from the power law in the range around I to 3 /rm lead to the bimodal volume distributions of Fig. 13.1. 

An aerosol particle can be considered to consist of an integer number k of molecules or monomers. The smallest aerosol particle could be defined in principle as that containing two molecules. The aerosol distribution could then be characterized by the number concentration of each cluster, that is, by Nk, the concentration (per cm3 of air) of particles containing k molecules. Although rigorously correct, this discrete method of characterizing the aerosol distribution cannot be used in practice because of the large number of molecules that make up even the smallest aerosol particles. For example, a particle with a diameter of 0.01 pm contains approximately 104 molecules and one with a diameter of 1 pm, around 1010. 

In the previous section, the value of the aerosol distribution n, for a size interval i was expressed as the ratio of the absolute aerosol concentration IV, of this interval and the size range ADp. The aerosol concentration can then be calculated by... 

The use of arbitrary intervals ADp can be confusing and makes the intercomparison of size distributions difficult. To avoid these complications and to maintain all the information regarding the aerosol distribution, one can use smaller and smaller size bins, effectively taking the limit ADp —> 0. At this limit, ADp becomes infinitesimally small and equal to dDp. Then one can define the size distribution function n (Dp), as follows ... 

FIGURE 8.5 The same aerosol distribution as in Figure 8.4, plotted against the logarithm of the diameter. 

FIGURE 8.6 The same aerosol distribution as in Figures 8.4 and 8.5 expressed as a function of log Dp and plotted against log Dp. Also shown are the surface and volume distributions. The areas below the three curves correspond to the total aerosol number, surface, and volume, respectively. 

Expressing the aerosol distributions as functions of In Dp or log Dp instead of Dp is often the most convenient way to represent the aerosol size distribution. Formally, we cannot take the logarithm of a dimensional quantity. Thus, when we write In Dp, we really mean In (Dp/1), where the reference particle diameter is 1 pm and is not explicitly indicated. We can therefore define the number distribution function neN r Dp) as... 

These aerosol distributions can also be expressed as functions of the base 10 logarithm log Dp, defining n (logDp), n°s( ogDp), and n°v( og Dp). Note that neN, and n°N are different mathematical functions, and, for the same diameter Dp, they have different arguments, namely, Dp, In Dp, and log Dp. The expressions relating these functions will be derived in the next section. 

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