Stochastic Modeling of a New Spectrometer

A new spectrometer for classifying aerosol particles according to specific masses is being considered (Ehara et aI. 1995). 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.