Comment on the Calculation of the Steady-State Charge Distribution on Aerosols < 100 nm by Three Body Trapping Method in a Bipolar Ion Environment

Abstract

The theory of Fuchs (1963) is widely used for calculation of the steady-state charge distribution on (submicron) aerosol particles in a bipolar ion environment. Hoppel and Frick (1986) and others showed that the Fuchs theory is no longer valid for particle diameters in the order of magnitude of the ionic mean free path. In their 1986 and 1990 papers, Hoppel and Frick published a new calculation method based on the concept of thee-body trapping, which is applicable for small particles down to the size of ions. Some print and procedure mistakes were made in the named publications. Additionally some important calculation information was not given. In this article, the relevant equations are shown, corrected and appended. A recalculation of the charge distributions for small particles based on three-body trapping shows a pronounced difference in comparison to data calculated according to the theory of Fuchs.

Charged meteoric smoke as ice nuclei in the mesosphere: Part 1—A review of basic concepts

“…The three body trapping method (Hoppel and Frick, 1986;Stommel and Riebel, 2007) aims at a better description of the collisional influence of air molecules on the charge capture. This is of minor importance for our conditions, since the charging of smoke in the upper mesosphere is to a good approximation governed by the orbital motion limit, i.e.…”

The formation and growth of Fe2O3 nanoparticles from the photo-oxidation of iron pentacarbonyl

“…To check the validity of this, we compared the a values to those reported for DZ1 nm from both Fuchs theory and the 'three body trapping' or TBT treatment of the ionic charging of small particles (e.g. Hoppel & Frick, 1986;Stommel & Riebel, 2007). We also used a smoke particle growth model described in our earlier study of ironcontaining aerosol systems (Saunders & Plane, 2006a), to best-fit a number of measured particle distributions produced under different experimental conditions, and thereby derived values of a consistent with such model fits to the EMS data.…”

“…. 'EMS' refers to values in the instrument software, extrapolated below $ 3 nm from the data of Reischl et al (1996), 'Model' refers to values determined from particle growth modelling fits in this study (see top panel), 'TBT' refers to the three body trapping approach of Hoppel and Frick (1986), and 'Fuchs' refers to data from the 'limiting sphere' theory of Fuchs, revised and reported by Stommel and Riebel (2007).…”

Ions in the Terrestrial Atmosphere and Other Solar System Atmospheres

“…The greater relative variability in n − /n + than μ + /μ − illustrates that, in relative terms, ion concentrations vary more than ion compositions. For smaller aerosol particles the Gunn assumption of no image forces breaks down, and a more sophisticated theory is required (Fuchs 1963;Hoppel and Frick 1986;Jensen and Thomas 1991;Stommel and Riebel 2007). A simple mathematical approximation …”