Diameter, aerodynamic Stokes

From the standpoint of collector design and performance, the most important size-related property of a dust particfe is its dynamic behavior. Particles larger than 100 [Lm are readily collectible by simple inertial or gravitational methods. For particles under 100 Im, the range of principal difficulty in dust collection, the resistance to motion in a gas is viscous (see Sec. 6, Thud and Particle Mechanics ), and for such particles, the most useful size specification is commonly the Stokes settling diameter, which is the diameter of the spherical particle of the same density that has the same terminal velocity in viscous flow as the particle in question. It is yet more convenient in many circumstances to use the aerodynamic diameter, which is the diameter of the particle of unit density (1 g/cm ) that has the same terminal settling velocity. Use of the aerodynamic diameter permits direct comparisons of the dynamic behavior of particles that are actually of different sizes, shapes, and densities [Raabe, J. Air Pollut. Control As.soc., 26, 856 (1976)]. 

When the size of a particle approaches the same order of magnitude as the mean free path of the gas molecules, the setthng velocity is greater than predicted by Stokes law because of molecular shp. The slip-flow correc tion is appreciable for particles smaller than 1 [Lm and is allowed for by the Cunningham correc tion for Stokes law (Lapple, op. cit. Licht, op. cit.). The Cunningham correction is apphed in calculations of the aerodynamic diameters of particles that are in the appropriate size range. 

Inertial impaction is the method of choice for evaluating particle or droplet size delivery from pharmaceutical aerosol systems. This method lends itself readily to theoretical analysis, ft has been evaluated in general terms [39] and for specific impactors [40]. Inertial impaction employs Stokes law to determine aerodynamic diameter of particles being evaluated. This has the advantage of incorporating shape and density effects into a single term. 

Another type of diameter commonly used is the Stokes diameter, If. This is defined as the diameter of a sphere that has the same density and settling velocity as the particle. Thus Stokes diameters are all based on settling velocities, whereas the aerodynamic diameter (Da) also includes a standardized density of unity. 

Stokes diameter Diameter of a sphere of the same density as the particle in question having the same settling velocity as that particle. Stokes diameter and aerodynamic diameter differ only in that Stokes diameter includes the particle density whereas the aerodynamic diameter does not. 

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... 

Given a particle made up of a two-sphere cluster, each sphere having a density of 2 g/cm3 and a diameter of 1 pm, find the aerodynamic and Stokes diameter of the cluster. 

Another example is the aerodynamic diameter this diameter is used to characterize aerosolized particles for which the density is difficult to determine. Thus, one assumes that the particle density equals 1 and does the Stokes" Law calculations for the sphere of unit density and having the same settling velocity as the particle in question (8). 

The stages are arranged to allow jet velocity to increase with each succeeding stage (by successive reduction in jet diameter or width) and to thereby cause particles of progressively smaller sizes to be impacted. In effect, the cascade impactor classifies particles according to their aerodynamic size. The aerodynamic diameter can be expressed in terms of Stokes diameter as... 

Dividing (9.108) by (9.106), one can then find the relationship between the classical aerodynamic and the Stokes diameter as... 

Classical Aerodynamic Diameter, D a- The diameter of unit density sphere (/O, = 1 g cm ) having the same terminal velocity as the particle. Given the Stokes diameter Ds, the classical aerodynamic diameter D a is given by... 

The internal impaction of aerosol particles with an aerodynamic diameter, tip, on a specific stage i can be described by the Stokes number St(tip) ... 

An experimental set-up used for characterising a particle trap impactor is shown in Figure 6.18. Figure 6.19 shows the penetration efficiency curves for the different nozzle diameters. Systems I and II have the acceleration nozzle diameter of 2.6 and 2.2 mm, respectively, while the sampling flow rates and S/D values of both systems are the same 5 Lmin and 1.3, respectively. Penetration curves are expressed as a function of the aerodynamic particle diameter (a) and the square root of the Stokes number (b), respectively. 

Nanofibers can be classified by an aerodynamic diameter via inertial impaction or centrifugation [5-9]. Inertial impactors, as illustrated in Figure 9.1, classify particles based on the Stokes number, a nondimensional grouping of parameters defined as [10]... 

The impaction of spherical particles depicted in Figure 9.1 depends on the fluid properties and the particle diameter and density as described by the Stokes number. Those particles with an aerodynamic diameter larger than a well-defined cutoff size will collide with an impaction plate due to their larger inertia. Smaller particles will follow the flow field and pass by the plate. The impaction of nanoflbers, however, depends on their length in addition to diameter and density. Cheng et al. [14] have outlined a theoretical approach to this and confirmed their theory via experimental studies. For nanofibers, the aerodynamic equivalent diameter is defined as... 

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