Aerodynamic diameter, definition

In many practical cases Leith s approach to the definition of the aerosol shape factor has greatly simplified the understanding of this correction to Stokes law. For example, consider again the aerodynamic diameter of a fiber having a cross-sectional diameter df, length L, and density p. This can be approximated by using Eqs. 5.17 and 5.18 for the case of long axis motion parallel to the flow as... 

Show that Eqs. 5.20 and 5.21 can be derived from Eq. 5.17 and the definition of aerodynamic diameter. In this derivation, assume that the aspect ratio is sufficiently large that... 

As can be seen from the above table, the ACGIH definition of respirable dust is almost identical with that of the AEC, differing only for a 2-(im-aerodynamic-diameter particle. Lippmann (1989) points out that this difference appears to be a recognition by the ACGIH of the characteristics of real particle separators. 

Definitions of particle diameters derived by different methods have been described in detail [4]. The aerodynamic diameter is defined as the diameter of a unit-density sphere having the same settling velocity, generally in air, as the particle. This encompasses particle shape, density, and physical size, all of which influence the aerodynamic behavior of the particle. As a dynamic parameter, it can generally be linked with aerosol deposition and specifically with that in the lung [5]. 

Ultrafine particles have been defined as those, which are smaller than 0.1 pm. Another classification is into submicrometre particles, which are smaller than 1 pm, and supermicrometre particles, which are larger than 1 pm. The terminology that has been used in the wording of the ambient air quality standards, and also for characterisation of indoor and outdoor particle mass concentrations, includes PM2.5 and PM fractions and the total suspended particulate (TSP). PM2.5 (fine particles) and PM, are the mass concentrations of particles with aerodynamic diameters smaller than 2.5 and 10 pm, respectively (more precisely the definitions specify the inlet cutoffs for which 50% efficiency is obtained for these sizes). TSP is the mass concentration of all particles suspended in the air. There have been references made in the literature to PMj or PMq 1 fractions, which imply mass concentrations of particles smaller than 1 and 0.1 pm, respectively. These terms should be used with caution, as particles below 1 pm, and even more those below 0.1 pm, are more commonly measured in terms of their number rather than their mass concentrations, and therefore these terms could be misleading. 

Definition The aerodynamic diameter of a particle is the diameter of a fictitious sphere of unit density which, under the action of gravity, settles with the same velocity as the particle in question. 

Where d is the aerodynamic diameter, is the particle density, and dp is its physical diameter. For a sphere, dp is the sphere s diameter for an irregular particle, dp will depend on particle shape. By definition, a water droplet with density of 1 g/cnP will have the same aerodynamic and physical diameter. It is the aerodynamic size distribution which is measured as the in vitro surrogate for inhalation aerosols. 

The aerodynamic behaviour of aerosol particles depends on their diameter, density and shape. To compare the behavioiu of particles that have different properties with each other, the aerodynamic diameter (Da) has been introduced, which standardises for particle shape and density. By definition the aerodynamic diameter of a particle is the diameter of a sphere with unit density having the same terminal settling velocity as the particle in consideratimi. Only for aqueous droplets with a spherical shape and unit density the aerodynamic diameter equals the geometric diameter. For non-spherical particles, the aerodynamic diameter can be expressed in terms of equivalent volume diameter (De), particle shape factor (x) and particle density (p) (see definitions) Da = De.(p/x)° ... 

This is the act of bringing an aerosol particle in contact with the airway wall. Different deposition mechanisms exist and it depends primarily on the particle s aerodynamic diameter (see definition) and velocity in which part of the airways an aerosol particle is most likely to be deposited. 

Equation (1) points to a number of important particle properties. Clearly the particle diameter, by any definition, plays a role in the behavior of the particle. Two other particle properties, density and shape, are of significance. The shape becomes important if particles deviate significantly from sphericity. The majority of pharmaceutical aerosol particles exhibit a high level of rotational symmetry and consequently do not deviate substantially from spherical behavior. The notable exception is that of elongated particles, fibers, or needles, which exhibit shape factors, kp, substantially greater than 1. Density will frequently deviate from unity and must be considered in comparing aerodynamic and equivalent volume diameters. 

As with most questions on particle size, the answer is very dependent on the definition used and the experimental technique. For a dynamic aerosol cloud, the correct definition is the aerodynamic particle size, which is the diameter of an equivalent sphere of unit density. An equivalent sphere is a conventional assumption in particle sizing, but for the aerodynamic size, the density is included to account for the momentum of the particle, i.e., both mass and velocity are important. The technique chosen for measurement must include these parameters, and impaction is the normally chosen technique, which also reflects the major deposition mechanism in the lung. A schematic of an impaction plate is given in Figure 10.3. 

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