Space charge and ion transport in aerosol neutralization: Toward a concentration-dependent alternative to the $N_it$ product

TL;DR

This paper develops a self-consistent, axisymmetric model of space-charge–affected aerosol neutralization, coupling ion transport with aerosol charging and transport via Poisson’s equation. It shows that even small net charges generate internal electric fields that substantially alter ion drift and charge relaxation, especially at high particle densities, invalidating the traditional $N_i t$ metric. The authors derive a concentration-dependent mean-charge relaxation expression and introduce a neutralization-time metric that captures the two-timescale dynamics arising from coupled ion–aerosol evolution. The framework provides actionable insights for designing neutralizers in laboratory, industrial, and atmospheric contexts where electrostatic effects govern aerosol behavior.

Abstract

In this study, we quantify how charged particle concentration affects the neutralization rate of aerosol particles, focusing on the role of ion dynamics shaped by internal electric fields arising from net space charge. Conventional neutralizer performance is typically evaluated using the $N_it$ product, which assumes quasi-neutral conditions and neglects electric fields from small charge imbalances. We demonstrate that internal electric fields become increasingly important at high aerosol concentrations and significantly influence neutralization dynamics. We develop a coupled ion--aerosol transport model in a two-dimensional axisymmetric geometry that includes ion generation, convection, diffusion, recombination, attachment to aerosols, and wall loss, with self-consistent electric fields obtained from the Poisson equation. Results show that even small net charges generate electric fields that enhance ion drift and accelerate neutralization, effects not captured by traditional $N_it$-based approaches. Using a neutralization time metric, we find that neutralization becomes slower with increasing aerosol number concentration $N_p$, higher initial particle charge $q_0$, and smaller particle diameter $d_p$ when space charge is absent. When space charge is included, the influence of $q_0$ and $d_p$ diminishes, while $N_p$ becomes the dominant factor governing neutralization behavior. Accordingly, we propose a concentration-dependent analytical expression for mean charge relaxation that captures coupled ion--aerosol transport and space charge effects. The modeling framework presented here is applicable to laboratory instruments, industrial processes, and atmospheric environments where electrostatic interactions govern aerosol behavior.

Figures (10)

• Figure 1: Schematic of space-charge-assisted neutralization. Charged aerosols enter along the axis, while ions are uniformly generated throughout the volume. The electric field induced by net space charge (indicated by arrows) drives ion drift, which facilitates aerosol neutralization, especially in the central region of the flow domain.
• Figure 2: Time evolution of the mean number of charges per particle ($\bar{q}$) at the center (solid lines) and boundary (dotted lines) of the neutralizer. Simulations are shown for four initial aerosol number concentrations: $N_p|_{t=0} = 10^{9}~\mathrm{m}^{-3}$ (blue), $10^{10}$ m$^{-3}$ (orange), $10^{11}$ m$^{-3}$ (green), and $10^{12}$ m$^{-3}$ (pink). Panel (a) shows results without space charge (SC) effects, and panel (b) includes SC effects. All simulations were conducted at an ion concentration of $N_i = 10^{12}~\mathrm{m}^{-3}$, assuming a monodisperse aerosol population with a particle diameter of $d_p = 1~\mu\mathrm{m}$.
• Figure 3: Charge distribution ($q_{\text{frac}}$) on aerosols at the center and boundary of the neutralizer at two time points (0.1 s and 1 s), for varying initial aerosol number concentrations ($N_p|_{t=0} = 10^{9}$ to $10^{12}~\mathrm{m}^{-3}$). Panels (a)–(d) correspond to simulations with space charge (SC) effects included, while panels (e)–(h) represent the corresponding cases without SC. All simulations were conducted at a fixed ion concentration of $N_i = 10^{12}~\mathrm{m}^{-3}$, assuming a monodisperse aerosol population with a particle diameter of $d_p = 1~\mu\mathrm{m}$.
• Figure 4: Time evolution of positive and negative ion concentrations ($N_i^+$ and $N_i^-$) at the center (solid lines) and boundary (dotted lines) of the neutralizer, for four initial aerosol number concentrations: $N_p|_{t=0} = 10^{9}~\mathrm{m}^{-3}$ (blue), $10^{10}$ m$^{-3}$ (orange), $10^{11}$ m$^{-3}$ (green), and $10^{12}$ m$^{-3}$ (pink). Panels a and b show negative ion concentrations without and with space charge effects, respectively. Panels c and d show the corresponding positive ion concentrations without and with space charge effects. All simulations were conducted at an ion concentration of $N_i = 10^{12}~\mathrm{m}^{-3}$, assuming a monodisperse aerosol population with a particle diameter of $d_p = 1~\mu\mathrm{m}$.
• Figure 5: Time evolution of total aerosol number concentration ($N_p|_t$) at the center (solid lines) and boundary (dotted lines) of the neutralizer shown as a function of the transit time ($t$), for different initial aerosol concentrations: $N_p|_{t=0} = 10^{9}~\mathrm{m}^{-3}$ (blue), $10^{10}$ m$^{-3}$ (orange), $10^{11}$ m$^{-3}$ (green), and $10^{12}$ m$^{-3}$ (pink). Panel a shows results without space charge effects, and panel b includes space charge effects. All simulations were conducted at an ion concentration of $N_i = 10^{12}~\mathrm{m}^{-3}$, assuming a monodisperse aerosol population with a particle diameter of $d_p = 1~\mu\mathrm{m}$.