Evaluation of Select Approximations for Calculating Particle Charging Rates in the Continuum Regime

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Abstract
Select approximations for particle charge acquisition in the continuum regime were evaluated by comparison with numerical calculations of continuum field-diffusion theory. Charging rates as calculated by five approximations—White, diffusion, field, Klett, and Wang—were evaluated as a function of dimensionless particle charge, ν, and dimensionless field, ω, over the domains - 20 ≤ ν ≤ 20 and 0.01 ≤ ω ≤ 100. None of the approximations was found to be valid over the full domain of charge and field strength encountered in aerosol charging applications, and the subdomains over which each of the approximations is accurate were determined. Based on these results, various combinations of approximations and polynomial curve fits were evaluated. A combination consisting of the diffusion and field approximations along with a polynomial curve fit was found to yield good estimates of the charging rate over the full domain of charge and field. Sample calculations using this combination to determine charge as a function of time under unipolar conditions compared well with calculations based on field–diffusion theory, and the combination is recommended for continuum regime charging calculations. For estimating steady-state bipolar charge, an empiricism formed by the average of two approximations, one developed by Klett and one consisting of the superposition of the diffusion approximation and the field approximation, is recommended.