Aerosol diffusion battery: The retrieval of particle size distribution with the help of analytical formulas

Abstract

A new algorithm is proposed for the determination of aerosol particle size distribution from a set of screen diffusion battery penetrations. The idea is to determine the size spectra of the fractions of particles separated by the sections of diffusion battery, so the total size distribution is the sum of the spectra of fractions. The spectrum of each fraction is approximated by the lognormal function, which is defined by two parameters: the standard geometric deviation (SGD) and geometric mean diameter. The SGD value is chosen to be 1.35 for each fraction. The geometric mean diameters of fractions are calculated from the diffusion battery penetrations. For this purpose, analytical formulas are derived to link the mean single-fiber collection efficiency for each fraction with the experimentally measured penetrations. Then the mean diameters of fractions are calculated from the collection efficiencies using the fan model filtration theory. To achieve a better size resolution, numerical approach is proposed to calculate the particle size spectrum using the analytical solution as an initial approximation. The validity of the analytical and numerical solutions is investigated by comparing them with the spectra determined by means of transmission electron microscopy and gravity settling. For this purpose, the aerosol is generated using the evaporation-nucleation technique, Collison-type nebulizer, and hot-wire bulb generator. It is found that the analytical solution demonstrates a good sizing accuracy but relatively poor size resolution, while the numerical approach results in both good sizing accuracy and good size resolution for the two-mode aerosol.

Data inversion methods to determine sub-3 nm aerosol size distributions using the particle size magnifier

“…Some inversion methods rely on a presumed particle size distribution formula (Fuchs et al, 1962;Raabe, 1978;Ramachandran and Kandlikar, 1996) or prior information on the detection efficiencies (e.g. Onischuk et al, 2018). However, approximating various shapes of the observed sub-3 nm particle size distributions or the PSM detection efficiency curves using a specific formula may lead to relatively large uncertainties.…”

Determination of the aerosol particle size distribution by means of the diffusion battery: Analytical inversion

“…In this work (as well as in our previous one [Onischuk et al 2018]), we use the diffusion battery comprising nine consecutive sections, which are filled with the stacks of woven nylon screens. The number of screens is 2, 2, 4, 8, 16, 32, 64, 128, and 256 for the section numbers 1, 2, … , 9, respectively.…”

“…The aerosol passes through the battery starting from section 1. The aerosol concentrations are measured by a Condensation Particle Counter (CPC) at the inlet of diffusion battery and downstream of each section using T-junctions (for more detail see (Onischuk et al 2018)). The particle diameter distribution function f(D) can be calculated from the DB penetrations g i :…”

“…However, to retrieve the particle size distribution from aerosol penetrations through screen stacks, one should solve an inverse problem, which is mathematically complex and ambiguous, as many different spectra can result from the same set of penetrations. Graphical, analytical, and numerical approaches were elaborated to determine the aerosol size spectrum from DB measurements (see the references and the discussion in more detail in Onischuk et al (2018)). However, the graphical/analytical methods are either too much laborious or limited by a single-mode size distribution.…”

“…In our previous work (Onischuk et al 2018), we proposed a new method to determine the aerosol size distribution from the diffusion battery penetrations. The central idea of this method was to obtain the particle diameter frequency distribution using simple analytical formulas (analytical inversion).…”