Continuum theory for ionic field charging of spheroidal aerosols in nonuniform electric field

Abstract

Classical theory for the ionic field charging previously developed for a spherical particle in a uniform electric field is extended for prolate and oblate spheroidal particles in uniform and nonuniform electric fields. Spheroidal particles are either dielectrics or perfect conductors. The nonuniform electric field is modeled as a two-dimensional linear field commonly developed in wire-cylinder and wire-plate electrodes systems. Assuming that the particle orientation remains unchanged during the charging process the saturation charge and the time evolution of the particle charge are determined as functions of the aspect ratio and orientation of the particle. Although the saturation charge depends strongly on the particle shape and orientation, the results for spherical particles apply to within an order of magnitude to spheroidal particles in most cases. For a collection of spheroidal particles with a uniform orientation distribution the ensemble averages for the saturation charge and the time evolution of the particle charge are also determined. A simple formula is proposed as an approximate expression for the ensemble average for the saturation charge. It is found that the ensemble average for the time evolution of the relative saturation for a spheroidal particle with a moderate aspect ratio can be approximated using the well-known formula for a spherical particle in a uniform electric field.