Uncertainty propagation using the Monte Carlo method in the measurement of airborne particle size distribution with a scanning mobility particle sizer

Abstract

Scanning Mobility Particle Sizer (SMPS) is a high resolution nanoparticle sizing system that is widely used as the standard method to measure airborne particle size distributions in the size range 1 nm -1 µm. This paper addresses the problem to assess the uncertainty associated with the particle size distribution (PSD) when the Differential Mobility Analyzer (DMA) operates under scanning mode. The sources of uncertainty are described and then modeled either through experiments or knowledge extracted from the literature. Special care is brought to model the physics and to account for competing theories. Indeed, it appears that the modeling errors resulting from approximations of the physics can largely affect the final estimate of this indirect measurement especially for quantities that are not measured during the day-to-day experiments. Monte-Carlo method is used to compute the uncertainty associated with the PSD. The method is finally tested against real data sets that are monosize Polystyrene Latex Spheres (PSL) with nominal diameters of 100 nm, 200 nm and 450 nm. The median diameters and associated standard uncertainty of the aerosol particles are estimated as 101.22 nm ± 0.18 nm, 204.39 nm ± 1.71 nm and 443.87 nm ± 1.52 nm with the new approach. Other statistical parameters such as the mean diameter, the mode and the geometric mean and associated standard uncertainty are also computed. These results are finally compared with the results obtained by SMPS embedded software.

Absolute Quantification of Bionanoparticles by Electrospray Differential Mobility Analysis: An Application to Lipoprotein Particle Concentration Measurements

“…The number size distributions measurement uncertainties were expressed as the standard deviation calculated on the basis of Monte Carlo simulations. The equations, physical models and parameters used in this software are thoroughly described in the work of Coquelin et al , and summarized in the Supporting Information. Briefly, all the parameters involved in the equations for SMPS signal inversion and correction (temperature, pressure, gas flows, ionic pathways, penetration factors, or DMA column dimensions, for example) are listed in the software.…”

Uncertainty assessment for the airborne nanoparticle collection efficiency of a TEM grid-equipped sampling system by Monte-Carlo calculation

“…The experimental dispersion due to fluctuations among samples requires calibration. The calibrated data can be modeled as samples drawn from a Multivariate normal vector whose parameters are inferred from the raw measured particle counts [46]. The uncertainty is described using the MC method with a 95% confidence region over the nine diameters.…”

“…The pressure Pr set in DMA was 100 kPa. The pressure of aerosol passing through the TEM gird is modeled by an arcsine distribution (100-0.1 kPa, 100+0.1 kPa) [46].…”

“…Table 2 summarizes some recently published values of these coefficients recommended by standard ISO 15900 [52]. Using simulations of L. Coquellin [46], the coefficients are modeled as truncated Gaussian distributions A, B, C, respectively. Let , , = ( ), , , = ( ), , , = ( ), , , = ( ), , , = ( ).…”

Airborne nanoparticle collection efficiency of a TEM grid-equipped sampling system

“…Where a = 1.165, b = 0.483, and c = 0.997 are experimentally determined coefficients given by Kim et al (2005) with the help of a nano DMA (Coquelin et al 2018).…”