Dynamic shape factor

The apphcation of the laser diffraction technique is sometimes questioned becanse it measures geometric instead of aerod5mamic particle diameters. However, the aerod5mamic diameter can be calcnlated when the dynamic shape factor and density are known. Moreover, the dynamic shape factor (x) of micronized particles will often be only shghtly higher than 1 and so is the tme particle density (1.0 < pp < 1.4 g cm ). As a conseqnence, the aerodynamic diameter differs only slightly from the eqnivalent volume diameter (see Eq. 3.1). 

To use Stokes law with chains or fibers, several approaches are available. Traditionally a correction factor k, known as the dynamic shape factor, is defined such that... 

Fuchs [30] introduced a dynamic shape factor, y/p, to relate volume and Stokes diameters ... 

The dynamic shape factor /ris defined as the ratio of the resistance to motion of a given particle divided by the resistance of a spherical particle of the same volume. 

Stoeber W. Dynamic shape factors of nonspherical aerosol particles. In Assessment of Airborne Particles Mercer TT, Morrow PE, Stoeber W, eds. Charles C Thomas Springfield, IL, 1972 249-289. 

Allen, M.D., Moss, O.R., and Briant, J.K.. 1978. Dynamic shape factors for LMFBR mixed-oxide fuel aggregates, J. Aerosol Sci.. 10. pp. 43-48. 

In the above, <7C is the equivalent volume diameter, i.e. the diameter of a sphere having the same volume as an irregular particle. As Hinds (1982) points out The equivalent volume diameter can be thought of as the diameter of the sphere that would result if an irregular particle were melted to form a droplet <7C is calculated from microscopic measurement of the actual particles being considered, while x is the dynamic shape factor which is included to allow for the effects of shape on terminal velocity. For example, talc dust is characterized by a dynamic shape factor (/ ) of 1.88, sand particles by 1.57, etc. Spheres have a dynamic shape factor of 1.0 while cubes have a dynamic shape factor of 1.08. 

Note that for all particles with a density greater than that of water and with a dynamic shape factor > 1.0, diX will be greater than [Pg.40]

The dynamic shape factor is almost always greater than 1.0 for irregular particles and flows at small Reynolds numbers and is equal to 1.0 for spheres. For a nonspherical particle of a given shape % is not a constant but changes with pressure, particle size, and as a result of particle orientation in electric or aerodynamic flow fields. 

The dynamic shape factor for flow in the continuum regime is equal to 1.08 for a cube, 1.12 for a 2-sphere cluster, 1.15 for a compact 3-sphere cluster, and 1.17 for a... 

Stokes Diameter What is the relationship connecting the volume equivalent diameter and the Stokes diameter of a nonspherical particle with dynamic shape factor X for Re < 0.1 ... 

Calculate the Stokes diameter of the NaCl particle of the previous example. The two approaches (dynamic shape factor combined with the volume equivalent diameter and the Stokes diameter) are different ways to describe the drag force and terminal settling velocity of a nonspherical particle. The terminal velocity of a nonspherical particle with a volume equivalent diameter Dve is given by (9.104),... 

Zelenyuk, A., Cai, Y., and Imre, D. (2006) From agglomerates of spheres to irregularly shaped particles Determination of dynamic shape factors from measurements of mobility and vacuum aerodynamic diameters, Aerosol Sci. Technol. 40, 197-217. 

For non-spherical particles, microscopies and light scattering can provide shape information, as discussed in Section 2.3. Shape information can also be obtained from the influence of particle shape on, for example, sedimentation. One such me asure is the dynamic shape factor (j), which is given by the square of the equivalent diameter divided by the aerodynamic diameter x = X 1-00 for a... 

FIGURE 2.32 Dynamic shape factor (a term for the relative cross section common in aerosol science) measured using DMA for PSL dimers with spheres of various diameters, as labeled. (From Zelenyuk, A., Imre, D., Aerosol Sci. TechnoL, 41, 112, 2007.)... 

Hansson, H.C., Ahlberg, M.S., Dynamic shape factors of sphere aggregates in an electric field and their dependence on the Knudsen number. J. Aerosol Sci. 1985,16, 69. 

Kousaka, Y., Endo, Y., Ichitsubo, H., Alonso, M., Orientation-specific dynamic shape factors for doublets and triplets of spheres in the transition regime. Aerosol Sci. Technol. 1996, 24, 36. 

Sedimentation velocities of aerosol particles depend on particle shape. The models of aerosol behaviour that are now available are derived for perfect spheres that have no porosity. The deviations of real particles from this ideal are handled by correction factors called shape factors. In the case of gravitational settling, the dynamic shape factor is used to account for deviations from sphericity and for porosity. These shape factors are not known well and frequently are estimated by back calculation from experimental data for simulant aerosols. This, of course, is not a reliable procedure. There have been some attempts to predict shape factors based on the fractal nature of particles that have grown by coagulation [A-7b]. 

The ratio of the resistance of a given particle to that of a spherical particle having the same volume is called the dynamic shape factor of the particle, K. The radius of an equal volume sphere is referred to as the equivalent radius re. Clearly,... 

A. J. Medalia, Dynamic Shape Factors of Particles, Powder Technology, 4 (1970-1971) 117-138. 

The dynamic shape factor %) is used to correct for the influence of shape on the resistance force or drag experienced by a particle moving through a fluid. For micron-sized particles this term can be expressed as ... 

Table 4 Dynamic Shape Factors of Natrojarosite Particles...

The utility of microscopic size measurements of irregular particles often depends on the ability to convert the measured sizes to other equivalent diameters that describe the behavior rather than the geometry of the particles. The most useful of these diameters is the equivalent volume diameter, which can be combined with the dynamic shape factor (Section 3.5) to describe the aerodynamic properties of a particle. The volume shape factor relates the voliune of a particle, v, to one of the silhouette diameters described before and is defined, for the projected area diameter, by... 

I dynamic shape factor with long axis perpendicular to the flow X I dynamic shape factor with long axis parallel to the flow... 

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