Aerodynamic shape factor

The aerodynamic diameter dj, is the diameter of spheres of unit density po, which reach the same velocity as nonspherical particles of density p in the air stream Cd Re) is calculated for calibration particles of diameter dp, and Cd(i e, cp) is calculated for particles with diameter dv and sphericity 9. Sphericity is defined as the ratio of the surface area of a sphere with equivalent volume to the actual surface area of the particle determined, for example, by means of specific surface area measurements (24). The aerodynamic shape factor X is defined as the ratio of the drag force on a particle to the drag force on the particle volume-equivalent sphere at the same velocity. For the Stokesian flow regime and spherical particles (9 = 1, X drag... 

Particle sphericity, ip aerodynamic shape factor, x- crystal density, p aerosolized powder bulk density, pg volume mean diameter, dy aerodynamic mean volume diameter, d total (Hildebrand) solubility parameters of the cohesive (drug-drug), 6c, and adhesive (drug carrier), 6a, interactions. 

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. 

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). 

Dg is the geometric diameter, pp is the density of the particle, neglecting the buoyancy effects of air, p is the reference density (1 g cm 3), and k is a shape factor, which is 1.0 in the case of a sphere. Because of the effect of particle density on the aerodynamic diameter, a spherical particle of high density will have a larger aerodynamic diameter than its geometric diameter. However, for most substances, pp 10 so that the difference is less than a factor of 3 (Lawrence Berkeley Laboratory, 1979). Particle densities are often lower than bulk densities of pure substances due to voids, pores, and cracks in the particles. 

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... 

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. 

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. 

Deposition in the thoracic region is the sum of aerodynamic and thermodynamic deposition of particulate material. Aerodynamic deposition depends on aerodynamic particle size, total volumetric flow rate, anatomical dead space, tidal volume, functional residual capacity (FRC) (combined residual and expiratory reserve volume or the amount of air remaining in the lungs after a tidal expiration) and diameter of the airways. Thermodynamic deposition depends on anatomical and physical characteristics, such as tidal volume, anatomical dead space, functional residual capacity and the transit time of air within each region. Thermodynamic particle size, which is derived from the diffusion coefficient, particle shape factor and the particles mass density, influence thermodynamic deposition. 

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... 

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)° ... 

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... 

The functional requirements of the ablative heatshield must be well understood before selection of the proper material can occur. Ablative heatshield materials not only protect a vehicle from excessive heating, they also act as an aerodynamic body and sometimes as a stmctural component (2,3). Intensity and duration of heating, thermostmctural requirements and shape stabiUty (4,5), potential for particle erosion (6), weight limitations (7—10), and reusabiUty (11) are some of the factors which must be considered in selection of an ablative material. 

Inhaled particles vary both in shape and density and these factors affect their capacity to be deposited by sedimentation. The behaviour of such particles can be determined by converting their actual diameter(s) to their aerodynamic diameters). What does this mean Imagine a low-density particle of irregular shape - this will be characterized by a certain terminal velocity as it settles in air. The aerodynamic diameter of the particle is defined as the actual diameter of a spherical particle of unit density with the same terminal velocity. 

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