Particle Size Distributions

PARTICLE SIZE DISTRIBUTIONS

Inhalation toxicology experiments often involve generating aerosols for deposition in various portions of the respiratory tract. Particles (of the density of water or greater) that are ten microns (µm) or larger tend to be captured in the nose or in the tracheal and bronchial regions of the respiratory tract. The primary mechanisms of capture are inertia and gravitational sedimentation. Particles smaller than a tenth of a micron are retained in the alveolar region, captured in the tiny air spaces of the lungs. The primary mechanism of capture here is diffusion (Brownian motion). Particles in the range of 0.1 to 1µm are captured with the least efficiency, but most are still captured, rather than exhaled. Thus, the distribution of sizes for the generated aerosol can be quite important, in terms of biological endpoints measured in the lung.

There are several ways to measure the "size" of a particle, and these may give different results for the same particle. Usually, the results are reported in terms of an "equivalent" sphere.

For example, the aerodynamic diameter controls the rate of sedimentation in a gas or the tendency to be captured due to inertia (such as being captured on a fiber from an air stream flowing past the fiber, as in a filter, or being captured at the apex of a flow bifurcation, as occurs in the lung). Ignoring the "slip correction" (important for particles 1µm and smaller), one can calculate the aerodynamic diameter d' of a sphere of diameter d and density rho from

d' = sqrt(rho'/rho) d

where rho' is the density of the particle material and rho is the density of water. [The aerodynamic diameter can also be calculated from the settling velocity or inertial behavior or the particle.] Thus, a silica particle 1µm in diameter would have an aerodynamic diameter close to 2µm, etc.

Diffusion by Brownian (thermal) motion is determined by the mobility diameter, which is the physical (geometric) diameter d, independent of material density.

Optical particle counters use a bright beam of light to illuminate single particles and to count and size them by the scattering of light from the particles. The size determined by optical particle counters is generally the equivalent scattering diameter, the size of a sphere of reference material (often polystyrene latex) that has an index of refraction of n. Generally, scattering from a particle is proportional to size raised to the second power (geometric scattering) to the sixth power (molecular scattering). The scattering by real particles will depend on size, shape, refractive index, orientation, the wavelength and polarization of the illuminating beam and the details of the optics. A bacterium and a dust particle of the same size could appear to be very different in size by their optical behavior. One can use calibration techniques to find equivalent aerodynamic diameters for the inhalation challenges chosen.

Microscopy, optical or electron, is often used for particle sizing, sometimes with the help of automated image analyzers. A sample on a filter is treated to enhance contrast, if necessary, then the image is analyzed. The size of spheres, as determined by microscopy, would be their diameters. For cubes, it would be their side lengths. For irregular particles, the size is ambiguous. They may not be captured in random orientations, so that plate-like particles would not have their thinnest dimension measured, for example. Some common options include taking their longest chords in one direction (a chord is a straight line drawn from one boundary to the other) or the maximum chord or the diameter of a circle with the same apparent cross-sectional area. Each choice would give a somewhat different value for the size of an irregular particle. Fibers represent another challenge, in that both their lengths and their widths can be of significance.

A size distribution is a description of how much of the aerosol is in each of a set (or continuum) of size intervals. As noted above, "size" is not a trivial concept. Neither is "how much." One can count the number of particles in the size interval or one can weigh them. [These are the two most common approaches.] Ten spheres of 2µm diameter have the same count as ten spheres of 1µm diameter but they have eight times the weight (mass). Thus, count methods emphasize smaller particles than mass methods do, and methods that are sensitive to cross-sectional area (such as light scattering or extinction) fall between these two.

A standard approach to determining the respirable fraction of an aerosol is to use an inertial impactor or a cyclone to capture particles larger than a certain "cut diameter," representing an approximate aerodynamic diameter below which diameter particles penetrate to the lung and above which diameter they do not. A cyclone is a device that causes air to spiral in the interior of a cylinder or cone (or combination), with the larger particles being thrown to the walls and the smaller particles being withdrawn through a small central exit mounted axially. Impactors direct a jet of particle - laden air at a surface, often coated, such that the larger particles tend to strike and adhere to the surface, while the smaller particles tend to follow the airflow away from the surface.

Dose is the number or mass of the aerosol particles that is determined to have been inhaled by the target, once factors such as particle size and target respiration rates are taken into account. Sometimes, dose is defined as the product of concentration and time, with the amount inhaled by the target to be calculated from this product.

Finally, an aerosol with a certain size distribution under one set of conditions may have a different size distribution under a second set of conditions. Prime examples of this are hygroscopic (water - attracting) aerosols such as soluble salts or acid or alkaline droplets that swell or shrink as the relative humidity increases or decreases. That is, they will swell as they go from the ambient air to the inner spaces of the respiratory tract.

These complications can largely be accommodated for in inhalation tests, once they are taken into account.

Douglas W. Cooper, Ph.D.