Charge Accumulation

The Charge Accumulation feature is used to compute the charge accumulated at a surface of a particle in a background of ions as a function of time. Charging models can be classified according to charging polarity (unipolar or bipolar), aerosol regime (continuum, free molecular, or transition regime), and charging mechanism (diffusion charging and/or field charging). The charging models used in this feature are unipolar, meaning that the ions in the background are either positively or negatively charged. The different models categories are summarized in Table 5-4 as a function of the particle diameter for STP conditions. The Knudsen number is defined as

, where λ (SI unit: m) is the ion mean free path and rp (SI unit: m) is the particle radius. For reference, the mean free path at atmospheric pressure of small ions such as oxygen and nitrogen is about 100 nm, and of larger ions such as water and methane agglomerates is around 10 nm.

Table 5-4: charging regimes and models used as a function of the particle radius at STP
Free molecular	Transition	Continuum
Kn>>1	Kn~1	Kn<<1
0.5 nm	5 nm - 50 nm	0.5 μm
Kinetic models	Limiting sphere models	Diffusion and field charging models

Ionic charging of particles is usually described in terms of diffusion charging or field charging. Diffusion charging occurs when the particle acquires a charge by virtue of the random thermal motion of ions and their collision and adherence to the particles. Field charging occurs when the electric flux lines deflect toward the particle resulting in the capture of ions. As the particle becomes charged, ions begin to be repelled by the particle, reducing the rate of charging. Eventually, the particle will reach a saturation charge and charging will cease (Ref. 33).

Diffusion charging is the dominant mechanism for small particles or low fields, while field charging is dominant for large particles and high fields. At intermediate sizes, diffusion and field charging can coexist; a simple way to estimate the total charging rate is to simply add the contributions from the two charging mechanisms. Lawless (Ref. 34) developed a more elaborate model to combine diffusion and field charging that reduces the diffusional component as the field becomes stronger, giving a distinctive diffusion charging rate above the saturation charge.


	All the charging models here presented can increase the charge of a particle by fractional amounts of the elementary charge. This presents a problem for particles small enough that physically can only collect one charged ion or none. That is, the quantization of charge is neglected.