STOCHASTIC MODELING OF A NEW SPECTROMETER

A new spectrometer for classifying aerosol particles according to spec ific masses is being considered (Ehara et al. 1995). The spectrometer consists of concentric cylinders which rotate. The instrument is desig ned so that an electric field is established between the cylinders. Th us, aerosol particles injected into the spectrometer are subjected to a centrifugal force and an electric force. Depending on the balance be tween 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 r otation rate, voltage drop and physical dimensions of the device, we c alculate the probability of detection in terms of particle density, di ameter and charge. This is the transfer function. In this work, the fo cus is on situations where Brownian motion is significant. To solve fo r the transfer function, the trajectory of a particle in the spectrome ter is modeled with a stochastic differential equation. Laminar dow is assumed. Further, attention is restricted to spherical particles with uniform density. The equation is solved using both numerical and Mont e Carlo methods. The agreement between methods is excellent.