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It is obvious that a similar size distribution function can be given for the surface, volume and mass of aerosol particles. Thus, e.g. the volume concentration (aerosol volume per unit volume of air) distributes according to particle radius in the following way:

with the condition

It goes without saying that the number size distribution may be converted to volume size distribution, given an assumed particle shape. Furthermore by using a constant particle density the size distribution of particle mass can be calculated from equation [4.9] by a simple calculation.

It is customary, in the interconversion of these distribution functions, to assume that the particles are spherical; this simplifies the mathematics, but is somewhat questionable physically. The method of measurement determines the nature of the reported radii of these hypothetical spheres; e.g. in the case of microscopic sizing, the so-called "surface radius" is obtained, which is the radius of a circle having the same surface area as the orthogonal projection of the particle.

On the basis of his atmospheric impactor measurements Junge (1963) proposed a power law to describe the size distribution of large and giant particles:

dr where C, and fi are constant. Considering the large range of particle size, equation [4.11] is best rewritten in the following form:

d log;r4-12J

In this formula C2 is a function of concentration, while fi characterizes the slope of the distribution curve. According to Junge (1963), /i is about 3 under continental conditions.

More recently, Whitby (1978) has analyzed the results of much more numerous size distribution observations carried out mainly by his group who used a combination of expansion chamber, electrical mobility and optical counter techniques. This analysis clearly shows that the complete size distribution is composed of three separate log-normal distributions as demonstrated in Fig. 26. Whitby speculates that the first distribution, the nuclei mode, is controlled by the condensation of vapour, (predominantly H2S04) formed by chemical reactions. Thus, the concentration of these small particles was found to be very significant in irradiated polluted atmosphere. On the other hand, the so-called accumulation

Fig. 26

Number size distribution of aerosol particles under urban conditions according to Whitby (1978). N : number of particles; </,,: diameter of particles; fT. total volume concentration; r. correlation coefficient between power law given in the figure and experimental data. (By courtesy oi Atmospheric Environment)

Fig. 26

Number size distribution of aerosol particles under urban conditions according to Whitby (1978). N : number of particles; </,,: diameter of particles; fT. total volume concentration; r. correlation coefficient between power law given in the figure and experimental data. (By courtesy oi Atmospheric Environment)

mode is due to the coagulation of primary particles or to the vapour condensation on secondary particles formed by coagulation or on existing aerosol particles. It follows from this idea that the accumulation mode is a consequence of aging of the primary aerosol. In the air far from gaseous sources the nucleation mode may well be partly or totally missing. The third log-normal distribution consists of particles formed mostly by mechanical disintegration of the material of the Earth's surface. This is the coarse particle mode, which is independent of the first two distributions. For this reason the chemical composition of the coarse particles is different from the composition of the smaller particles (see later), called "fine" particles.

Fig. 27

Size distribution of the volume of aerosol particles (solid line) according to Whitby (1978). Dotted line corresponds to the power law of Fig. 26. V: particle volume; n: nuclei mode a. accumulation mode; < . coarse particle mode; ilrGV: geometric volume mean size. (By courtesy of Atmospheric EnvironmentI

### Fig. 27

Size distribution of the volume of aerosol particles (solid line) according to Whitby (1978). Dotted line corresponds to the power law of Fig. 26. V: particle volume; n: nuclei mode a. accumulation mode; < . coarse particle mode; ilrGV: geometric volume mean size. (By courtesy of Atmospheric EnvironmentI

To gain further insight into the character of particle size distribution, the volume distribution calculated from the curve of Fig. 26 is also presented in Fig. 27. It can be seen that on a volume basis the nuclei mode, which determines the particle number, cannot be identified owing to the small size of the primary particles. One can also see that a large fraction of the aerosol mass is found in the range of coarse particles. However, the mass of particles in the accumulation mode is also significant. In our case the particle volume in the two modes is nearly the same. Generally speaking 2/3 of the total mass is in the coarse and 1/3 in the accumulation mode. Finally, Figs 26 and 27 show that, while the number size distribution of large and giant particles can be well approximated by the power law, Junge's formula is very poor for characterizing the volume distribution. In other words this means that minor deviations from the power law in the number distribution cause significant deviations in the volume distribution.

It should be mentioned that the size distributions presented in Figs 26 and 27 are typical of a polluted atmosphere. Unfortunately, very little information is available about the background aerosol filling 80-90 % of the troposphere. These background particles can be studied over oceanic areas remote from continents if we disregard sea salt particles. The other possibility for such a study is the direct sampling above a height of about 5 km in the troposphere. Examples of the first method are provided by the work of Junge and Jaenicke (1971), A. Meszaros and Vissy (1974) and Tymen et al. (1975).

Fig. 28

Size distribution of atmospheric aerosol particles under various conditions. (/). urban (2). continental; (i); tropospheric background; (4). continental at 3000 m above inversions; N: total number of particles with radius larger than 0.03 /tm. (Data of A. Meszaros)

### Fig. 28

Size distribution of atmospheric aerosol particles under various conditions. (/). urban (2). continental; (i); tropospheric background; (4). continental at 3000 m above inversions; N: total number of particles with radius larger than 0.03 /tm. (Data of A. Meszaros)

Curve 3 of Fig. 28 represents the size distribution of atmospheric aerosol particles obtained by A. Meszaros and Vissy (1974) from samples collected on membrane filters over the oceans of the Southern Hemisphere. The samples were evaluated by optical and electron microscopy in the radius range of 0.03-64 /im8. The total concentration of these particles is also shown. It can be seen that the maximum of the distribution occurs around 0.1 pm radius, a value in the range of the

### 8 This means that the nuclei mode was not studied.

accumulation mode. The coarse mode is practically missing since the curve does not contain the distribution of sea salt particles (see later). It should be mentioned that the form of this spectrum agrees fairly well with the distributions found over the North Atlantic by other workers (Junge and Jaenicke, 1971; Tymen et al., 1975). However, the maximum of the distribution over the Northern Hemisphere is shifted to smaller sizes probably as a result of indirect anthropogenic effects. We have to note in this respect that Junge and Jaenicke (1971) identified, by the diffusion channel technique, another maximum in the aerosol particle spectrum below 0.01 pm which proves the presence of primary particles formed by reaction and subsequent condensation (nuclei mode). No such measurements were performed by A. Meszaros and Vissy (1974). However, comparison between the concentration of particles with radii larger than 0.03 /im and the total particle concentration (~400 cm"3) make evident the presence of the nuclei mode even over the Southern Hemisphere.

Fig. 29

Size distribution of large and giant particles at various altitudes (Bliflord, 1970). (By courtesy of the

American Geophysical Union)

Fig. 29

Size distribution of large and giant particles at various altitudes (Bliflord, 1970). (By courtesy of the

American Geophysical Union)

Also shown in Fig. 28 are three other size distributions. Curve I was measured near Budapest, Hungary in a locally polluted atmosphere(A. Meszaros, 1977), while spectrum 2 refers to rural air, also in Hungary. Finally, the curve labelled 4 is the size distribution of large and giant particles observed at an altitude of 3 km above inversion layers over Central Europe by A. Meszaros (1969). It is seen by comparing these size distributions that the aerosol structure varies considerably as a function of the pollution of the place considered. The difference between curves 1 and 3 is particularly great in the range of smaller particles. The coarse particle mode is also evident in distributions / and 2. The concentration of coarse (or giant) particles is 0.40 and 0.12 cm"3, respectively. Unfortunately, when distribution 4 was measured, only optical microscopic evaluation was made. However, comparison of curves J and 4 shows that the distribution of large and giant particles at an altitude of 3 km over continents practically coincides with the spectrum of aerosol particles measured in remote oceanic areas. This fact also supports the concept of a tropospheric background aerosol.

In the upper troposphere the size distribution of large and giant particles was investigated by Soviet (Kondratyev et at.. 1969) and American (Blifford, 1970) research workers. Particles were collected by impactors in both cases. Figure 29 shows Blifford's size distributions for different altitudes, obtained over Nebraska, U.S.A. An interesting feature emerging from the distributions presented is the decrease in the steepness of the slope in the distributions (that is the value of (i in equation [4.12] decreases). It is very difficult to explain this peculiarity of aerosol behaviour. However, it is believed that the removal of aerosol particles by cloud elements (Chapter 5) plays an important role in control of the size distribution of aerosol particles in the troposphere.