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d

" From Whitby and Sverdrup (1980).

h Note that the diameter—number, surface, or volume—changes depending on the type of distribution used, whereas crg remains constant for each of the three modes. See text. ' Same as derived from the number distribution. '' Same as derived from the surface distribution.

" From Whitby and Sverdrup (1980).

h Note that the diameter—number, surface, or volume—changes depending on the type of distribution used, whereas crg remains constant for each of the three modes. See text. ' Same as derived from the number distribution. '' Same as derived from the surface distribution.

Sverdrup (1980) based on the normal distributions in the three size ranges in Fig. 9.6.

The examples used so far are generally based on surface measurements. The particle concentration and size distribution also depend on altitude. Typical vertical distributions are discussed, for example, by Jaenicke (1992).

3. Particle Motion

One of the important properties of particles that contributes to both the observed size distribution and the number concentration of aerosols in the atmosphere is the motion they undergo when suspended in air. This includes gravitational settling and Brownian diffusion.

a. Gravitational Settling

In the free troposphere, particles are subjected to gravitational forces. They also can be subjected to electrical forces in nature as well as in the course of detection and measurement. When such forces are applied, the particle moves relative to the gas and hence is subjected to a resistance force. Stokes' law gives the force (FR) acting on smooth spherical particles due to the laminar flow of air over them:

17 is the gas viscosity, v is the particle velocity relative to the gas, and D is the particle diameter. When a force such as gravity is applied to the particle, it speeds up until the frictional force equals the applied force; it then moves with a constant velocity known as the terminal velocity.

One can apply Stokes' law to atmospheric particles to calculate how fast they will settle out of the air when subjected to gravity alone. Thus the terminal settling velocity occurs when the frictional and gravitational forces are balanced, that is,

where m is the mass of the particle and g is the acceleration due to gravity (9.8 m s 2 at sea level). One can apply the relationship between mass, volume (77D3 6), and density (p) of the particle. Equations (M) and (N) combine to give Eq. (O):

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