Theoretical Study of Equilibrium Bipolar Charge Distribution on Nonuniform Primary Straight Chain Aggregate Aerosols

Abstract

A general theory describing the equilibrium bipolar charge distribution for straight chain aggregate aerosols consisting of primary spheres of different diameters was derived from a theory previously developed for linear chain aggregate of uniform spheres. The present theory is based on the assumptions that (1) the individual primary particles of a straight chain aggregate are charged independently, (2) the probability that a particular primary particle has acquired q elementary charges is governed by the Gaussian distribution predicted by Boltzmann's law, based on particle size; and (3) the resultant charge of a straight chain aggregate is the algebraic sum of the charges carried by the constituent primary spheres. The present theory can be stated as follows: The equilibrium bipolar charge distribution of straight chain aggregate aerosols with nonuniform primary spheres can be expressed by Boltzmann's law with an equivalent diameter such that d_eL = Σ ⁿ _i=1 d_i . The limitations imposed by the assumptions are also discussed.