On-line measurement of ultrafine aggregate surface area and volume distributions by electrical mobility analysis: I. Theoretical analysis

Electrical mobility analyzers are usually calibrated for spherical particles, and provide number, area and volume distributions for spherical particles. However, these instruments cannot be directly used to obtain the surface area and volume distributions for aggregates. Aggregates are important in technological applications, such as the manufacture of fine powdered materials, and in air pollution and atmospheric sciences. Thus, nanoparticle chain aggregates of low fractal dimension are another important limiting case, in addition to spheres; a method is described which makes it possible to relate aggregate surface area and volume distributions to the electrical mobility diameter. This is accomplished by equating the migration velocity of an aggregate to that of a sphere. Particles of equal migration velocities will trace similar paths in the mobility analyzer and have the same mobility diameter (neglecting the Brownian diffusive spread). By equating the migration velocities of a sphere and aggregate, the number and size of the primary particles composing the aggregate can be related to the diameter of a sphere with the same migration velocity. The calculation of aggregate surface areas and volumes requires two theoretical “modules”, one for the drag on the aggregates and the other for aggregate charging efficiency. Two modules selected from the literature were used. The results indicate that the surface area distributions of aggregates with random orientation are somewhat over-predicted when calculated directly from the mobility diameter. However, the volume distributions are greatly over-predicted, up to a factor of ten compared with values based on the mobility diameter. The affect of aggregate orientation on surface area estimates was also examined.