Geometric diameter

Consider again the simple motion of a sphere. In this case, the equivalent diameter of a sphere, d, is equal to its geometric diameter, d. Equating the above expressions and replacing 5 by d (and denoting the Euler umber, Eu, by Y), we obtain an expression for the resistance force ... 

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. 

FIGURE 9.28 Size distribution of particle geometric cross section (A) as a function of geometric diameter for a typical rural aerosol (adapted from Hegg et at., f993). 

The collision diameters of the oxide vapor molecules must be estimated. For many common vapor molecules, the collision diameters are roughly twice the average geometrical diameters as determined by molecular or atomic radii. By use of estimated molybdenum-oxygen bond distances and a proposed configuration of the Mo309 vapor molecule (5),... 

Mie s Theory. Mie applied the Maxwell equations to a model in which a plane wave front meets an optically isotropic sphere with refractive index n and absorption index k [1.26]. Integration gives the values of the absorption cross section QA and the scattering cross section Qs these dimensionless numbers relate the proportion of absorption and scattering to the geometric diameter of the particle. The theory has provided useful insights into the effect of particle size on the color properties of pigments. 

Other possible geometrical diameters can be used to determine the mean particle diameter of a polydisperse system. Examples are the surface average, ds, and volume average diameters, dv where ds is defined as the diameter of a sphere having the same surface area as the particle and dw is the diameter of a sphere having the same volume as the particle. These are given by ... 

The recovered liposomes possess a mean geometric diameter of 0.2 p.m. The aerodynamic diameter of these particles, when emitted from an ultrasonic nebulizer, is 1 xm. 

In the aerosol solvent extraction system (ASES), the protein is dissolved in a compatible solvent (i.e., water or DMSO) and then introduced by atomization into supercritical CO2 (12,13). The solvent is extracted from the droplet, and the protein precipitates to form particles with appropriate sizes for pulmonary delivery (see Note 3). CO2 is then removed by venting off and the particles are collected. Insulin powders (see Note 4) made by this method possess a mean geometric diameter of 9.6 xm, and 22% of the powder was in the respirable range (0.5-6 p,m) (12). 

A solution of insulin is added to an aqueous suspension of Technosphere particles. The insulin is adsorbed to the surface of the particles to form TI. The solvent is then removed from the suspension by lyophilization to produce the bulk drug powder. TI has a mean geometric diameter of 2.0 p,m and an aerodynamic diameter of 2.5 xm. 

AIR particles are low-density lipid-based particles that are produced by spray drying lipid-albumin-drug solutions. These particles are characterized by their porous surface characteristics and large geometric diameter while having a low aerodynamic diameter [176,177], This technology has been used to produce porous particle powder formulations of L-dopa that have been investigated for the treatment of Parkinson s disease [178],... 

Fig. 2. Size distriburions of laboratory-produced soot particles (propane soot), d, — mean geometrical diameter.

The in situ produced aerosol has a characteristic bimodal distribution dS/dlgr. The first mode is determined by Aitken particles themselves (r < 0.1 pm). The second, coagulative mode (0.1 pm < r < 1 pm) is constantly supplied with heterogeneously coagulating Aitken particles and, for these particles, it is the last form of existence before the aerosol particles in question leave the atmosphere. The parameters of the coagulative mode are dg (mean geometrical diameter) = 0.37 pm, o = 2.00... 

Geometric diameter Transmission electron microscope (TEM) Use of electron beam to directly measure size, shape, aggregation, composition of dried collected particles ... 

From the eccentricity definition, the geometric radius and geometric diameter can immediately characterize a molecule. The radius of a molecule is defined as the minimum geometric eccentricity, and the diameter is defined as the maximum geometric eccentricity in the molecule, according to the following ... 

Whenever the airborne substance is deposited on the linings of the respiratory tract, its new biological environment will react to it. For inhaled particles, a major factor that influences deposition is size. A particle s characteristics may alter its size for example, if the particle is hygroscopic, it can be expected to grow substantially while still airborne within the respiratory tract and will be deposited based on its hydrated size. The deposition probability for particles with geometric diameter 0.5 pm is governed... 

Three primary mechanisms govern the deposition of aerosols in the respiratory tract inertial impaction, sedimentation, and diffusion (Fig. 7). Early work by Landahl and coworkers showed that both sedimentation and inertial impaction in the mouth, throat, and lungs uniquely depend on the particle aerodynamic diameter [220], Deposition by diffiisional transport is independent of particle density and limited primarily to particles with geometric diameters smaller than 0.5 p,m [221],... 

Particles with aerodynamic diameters between 2 and 3 pm are ideal for deep lung delivery (76). This aerodynamic diameter depends primarily on the geometric diameter and bulk density (77). Particles with bigger size ( 10 pm) and lower bulk density aerosolize better and avoid lung macrophage clearance. 

Geometric diameter The standard diameter of a perfect circle or sphere... 

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