The unipolar diffusion charging of particles, i.e. the net increase in particle charge through ion-particle collisions, is an important process in a number of aerosol systems. Accurate methods are hence needed to predict the unipolar charging rate, not only for spherical particles, but also particles of arbitrary geometry. In this work, the unipolar charging (described by the particle-ion collision kernel) of conducting, arbitrary shaped particles is studied theoretically. Through a combination of dimensional analysis, Brownian dynamics (BD), and molecular dynamics (MD), the collision kernel is found to be described accurately by a simple-to-use expression across the entire diffusive Knudsen number KnD range (from the continuum regime to the free molecular regime), where KnD is the ratio of the ion mean persistence path to a well-defined particle length scale (proportional to the ratio of orientationally averaged projected area PA to the Smoluchowski radius Rs). In the developed collision kernel expression, the effect of repulsive Coulomb and attractive image potential interactions between the ion and the particle are parameterized by the coulomb potential energy to thermal energy ratio, ψE, and image potential energy to thermal energy ratio, ψI. It is found that the changes in collision rates due to potential interactions in the continuum (KnD→0) and free molecular (KnD→∞) regimes collapse to particle geometry independent functions, expressed in terms of ψE and ψI. In the transition regime, the dimensionless collision kernel H is shown to be geometry independent, and is a function of a suitably defined KnD only. Comparison is made between the predictions of the proposed expression and the flux matching model of Fuchs; for non-spherical particles, theories available in the literature are examined and commented upon. Finally, sample calculations of the mean charge acquired by selected particle geometries are presented and discussed.
Bibliographical noteFunding Information:
This work was supported by the University of Minnesota Center for Filtration Research . We also thank the Minnesota Supercomputing Institute (MSI) for the allocation of high performance computer time to perform to noted BD and MD calculations and Mr. Chonglin Zhang (University of Minnesota Aerospace Engineering and Mechanics) for assistance in generating contour plots. R.G. acknowledges support from a University of Minnesota Doctoral Dissertation Fellowship .
- Collision kernel
- Knudsen number
- Unipolar charging