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Particle charging in the afterglows of non-thermal plasmas typically take place in a non-neutral space charge environment. We model the same by incorporating particle-ion collision rate constant models, developed in prior work by analyzing particle-ion trajectories calculated using Langevin Dynamics simulations, into species transport equations for ions, electrons and charged particles in the afterglow. A scaling analysis of particle charging and additional Langevin Dynamics calculations of the particle-ion collision rate constant are presented to extend the range of applicability to ion electrostatic to thermal energy ratios of 300 and diffusive Knudsen number (that scales inversely with gas pressure) up to 2000. The developed collision rate constant models are first validated by comparing predictions of particle charge against measured values in a stationary, non-thermal DC plasma from past PK-4 campaigns published in Phys. Rev. Lett. 93(8): 085001 and Phys. Rev. E 72(1): 016406). The comparisons reveal excellent agreement within ±35% for particles of radius 0.6,1.0,1.3 μm in the gas pressure range of ~20-150 Pa. The experiments to probe particle charge distributions by Sharma et al. (J. Physics D: Appl. Phys. 53(24): 245204) are modeled using the validated particle-ion collision rate constant models and the calculated charge fractions are compared with measurements. The comparisons reveal that the ion/electron concentration and gas temperature in the afterglow critically influence the particle charge and the predictions are generally in qualitative agreement with the measurements. Along with critical assessment of the modeling assumptions, several recommendations are presented for future experimental design to probe charging in afterglows.
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