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3.2.1 Stochastic Modeling of Aerosol Trajectories

Kevin J. Coakley

Statistical Engineering Division, ITL

Kensei Ehara

National Research Laboratory of Metrology, Japan

Under the auspices of the 1980 Japan-US Science pact, Kensei Ehara of Japan's National Laboratory of Metrology visited NIST. During this visit, he proposed a new kind of spectrometer which separates aerosol particles according to their mass to charge ratio. Aerosol particles are injected into the space between two corotating cylinders. A voltage difference is applied between the cylinders. Electrical and centrifugal forces act on the particles. Further, Brownian motion effects are significant for particles with small mass. In earlier work (in collaboration with C. Hagwood and A. Negiz), we computed the probability that a particle of a given mass and diameter will pass through the spectrometer or stick to either the inner or outer cylinder wall. This probability, i.e. the transfer function, depends on the adjustable rotational rate and applied voltage.

In new work, we estimate the concentration of aerosols within the spectrometer. The space between the inner and outer walls of the spectrometer is discretized into pixels. For a given random initial position at the inlet boundary, a trajectory is computed. When a trajectory enters a particular pixel, the cumulative visitation time for that pixel is updated. Based on many random trajectories, a visitation time histogram is computed. By normalizing this histogram, we estimate the spatial concentration distribution.

Near the boundaries, the concentration is complex. Typically, when solving the diffusion equation for concentration, simple boundary conditions on concentration are typically assumed. Hence, the new work suggests that such simple boundary conditions are not appropriate.


Figure 11: Upper left: computed relative concentration of spherical aerosol particles with diameter 0.1 micron and density of 1g cm-1. The radii of the cylinders are 160 and 166 mm. The axial length of the cylinders is 200 mm. The rotation rate is 4000 RPM and the applied voltage is 580 V. The other plots show estimated concentration near the boundaries. At the inlet boundary, the initial concentration is uniform.

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Date created: 7/20/2001
Last updated: 7/20/2001
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