Brownian Dynamics Determination of the Bipolar Steady State Charge Distribution on Spheres and Non-spheres in the Transition Regime

A Brownian Dynamics (BD) method to calculate the steady state charge distribution on spherical and non-spherical aerosol particles is presented which circumvents ion-particle collision rate calculation. BD calculations are performed using both monodisperse and measured polydisperse ion properties under atmospheric pressure, room temperature conditions. Calculations reveal that for spherical particles in both the nano- and submicrometer size ranges, the fractions of charged particles are noticeably underpredicted by flux matching theory-based regression expressions. In the examination of non-spherical particles (aggregates, linear chains and cylinders), two models for accumulated particle charge are employed: (1) accumulated charge distributes itself along a particle surface, and (2) accumulated charge is immobile. Independent of model, it is found that particles having a Projected Area (PA) to diffusion based surface area (πR_s²) ratio close to unity behave similar to a sphere of the same mobility diameter. However, model specific behavior is observed for highly non-spherical particles (PA/πR_s²<0.5). With distributed charge, highly non-spherical particles acquire more charges than an equivalent mobility sphere in the sub 100 nm range, yet acquire less charge than spheres in the submicrometer range. Conversely, with immobile charges, non-spherical particles are found to be more charged than equivalent mobility diameter spheres in both the nano- and submicrometer size ranges. The results of BD calculations are used to develop accurate regression expressions for the charge distribution on spherical and non-spherical particles considering three situations: conducting particles (where both Coulomb and image potentials are accounted for), non-conducting particles where charge is distributed, and non-conducting particles where charge is immobilized.