Stochastic Modeling of a New Spectrometer

Abstract

A new spectrometer for classifying aerosol particles according to specific masses is being considered . The spectrometer consists of concentric cylinders which rotate. The instrument is designed so that an electric field is established between the cylinders. Thus, aerosol particles injected into the spectrometer are subjected to a centrifugal force and an electric force. Depending on the balance between these two forces, as well as Brownian motion, charged particles either pass through the space between the cylinders or stick to either cylinder wall. Particles which pass through are detected. Given the rotation rate, voltage drop and physical dimensions of the device, we calculate the probability of detection in terms of particle density, diameter and charge. This is the transfer function. In this work, the focus is on situations where Brownian motion is significant. To solve for the transfer function, the trajectory of a particle in the spectrometer is modeled with a stochastic differential equation. Laminar flow is assumed. Further, attention is restricted to spherical particles with uniform density. The equation is solved using both numerical and Monte Carlo methods. The agreement between methods is excellent.

Design Considerations and Performance Evaluation of a Compact Aerosol Particle Mass Analyzer

“…Particle Brownian motion within the APM is expected to shift the APM transfer function to the larger mass side (Hagwood et al 1995), and hence it cannot explain the observed disagreement. In our separate study (Sakurai et al 2010), we investigated size change of Stantovac and poly-alpha-olefin (PAO) particles before and after the APM by using a scanning mobility particle sizer, but observed no size change even at 10 nm.…”

“…Theoretically, an APM spectrum can be calculated according to where n(m) = dC N /dm is the mass distribution of particles at the APM inlet, and APM (m; V) is a function of m with V as a parameter, representing the APM transfer function for singlycharged particles when the classification voltage is V. In the present study, we neglect the effects of particle Brownian motion on the transfer function (Hagwood et al 1995). Assuming n(m) to be described by a certain function containing a few adjustable parameters, and fitting C N (V) in Equation (19) to an experimental spectrum, we can determine n(m).…”

Online Nanoparticle Mass Measurement by Combined Aerosol Particle Mass Analyzer and Differential Mobility Analyzer: Comparison of Theory and Measurements

“…The APM transfer function for uniform and laminar flows are plotted in Figure 1. Unlike our case, the shape of the transfer function reported by Hagwood et al (1995) for parabolic flow was not unimodal. This is because the transfer function used by Hagwood et al (1995) was based on the ratio of probabilities rather than the ratio of fluxes; that is, the velocity term in Equation (8b) was not included.…”

“…The method was also previously used for both the DMA (Hagwood et al 1999) and APM transfer functions (Hagwood et al 1995). Here p(V , s, r) = 1 when z ≥ L and r 1 < r < r 2 , and p(V , s, r) = 0 when z ≥ L and r ≥ r 2 or r ≤ r 1 .…”

The Nano-Particle Mass Classifier (Nano-PMC): Development, Characterization, and Application for Determining the Mass, Apparent Density, and Shape of Particles with Masses Down to the Zeptogram Range

“…Diffusion is described in the model with a stochastic algorithm, analogous to that used for the original APM design (Hagwood et al 1995;Lall et al 2009). …”