Continuum field-diffusion theory for bipolar charging of aerosols

Abstract

Continuum regime field-diffusion theory for the acquisition of charge by particles exposed to bipolar ions is developed. An approximate numerical solution to the governing equations is described which, in the limit as the external field approaches zero, yields results within 1% of exact solutions. The numerical method is used to calculate particle charge as a function of time, external electric field strength, ratio of positive to negative ion conductivity, particle radius and particle dielectric constant. With increasing time, charge is predicted to approach a steady state value asymptotically. For a given conductivity ratio, steady state charge is predicted to increase almost linearly with increasing external electric field. For a given charging time and field strength, charge asymptotically approaches unipolar levels with increasing conductivity ratio. Predictions based on theory generally show good agreement with experiment, typically being within ± 10–15%. The exception to this is for intermediate conductivity ratios, where theory exceeds experiment by as much as 30°.