## X

s and where s is the mean free path of the atoms, or molecules, in the air.

In the other extreme, the Stokes regimen ceases to be applicable for particles with high Reynolds numbers, Re:

Re = D X v X -h where v is the particle velocity. Correction factors need to be applied to aerosols with particles or droplets in the regimes with Re > 1 [22].

When deposition is governed primarily be impaction and sedimentation, the independent variable that is used to relate to these processes is called the aerodynamic diameter, Dae [22,23]. It is defined as the diameter of a sphere of unit density that has the same terminal sedimentation velocity as the particle in question. Therefore, the sedimentation velocity in terms of the aerodynamic diameter can be rewritten as follows:

18 X h c where d0 is unit density (i.e., 1 g/cm3 or 1 kg/dm3). For spherical particles that are sufficiently large compared to the mean free path in the gas so that the slip correction, Cc, does not need to be applied, Dae is simply related to the actual diameter of the sphere D and its density, d:

For nonspherical particles, Dae, in addition to the size and density, depends on particle shape. For relatively simple geometries, Dae can be estimated from a theoretical expression [22,24,25].

One problem with Dae is that it does not provide a unique, one-to-one correspondence to deposition. Impaction for particles with the same Dae will vary depending on the flow rate, Q. A different composite variable, the impaction parameter d X D2Q, was found to predict uniquely the deposition in the human mouth and nose. Deposition increases with an increase of this variable, that is, as the particle size, density, and velocity become larger [26].

When the particles become sufficiently small, their deposition by diffusion becomes a significant mechanism. The rate of diffusion is proportional to the diffusion coefficient, Dif, that can be calculated from the Stokes-Einstein equation:

where k is Boltzmann's constant and T is absolute temperature [22]. In contrast to impaction and sedimentation, diffusional deposition increases with decreasing size of the particle and is independent of the particle density. Hence, diffusion coefficient should be a more suitable independent variable to describe the deposition of ultrafine particles than aerodynamic diameters.

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