## Field Charging

The presence of particles with a dielectric constant greater than unity causes a localized deformation in the electric field (see Figure 5.17.4). Gas ions travel along electric field lines, and because the lines intercept the particle matter, the ions collide with these particles and charge them. When the particle reaches a saturation charge, additional ions are repelled and charging stops. The amount of charge q on a particle is the product of the number of charges n and the electronic charge e (q = ne). The following equation gives the rate of particle charging:

b) Particle Partially Charged

FIG. 5.17.4 Distortion of an electric field around an aerosol particle.

b) Particle Partially Charged

FIG. 5.17.4 Distortion of an electric field around an aerosol particle.

r02 ln

On integration, this equation yields the number of charges on a particle as a function of time as follows:

On integration, this equation yields the number of charges on a particle as a function of time as follows:

where ns is the saturation charge given by (3e/e + 2) (d2E/4e). The saturation charge is the maximum charge that can be placed on a particle of diameter d by a field strength E. The value is the dielectric constant of the particle. The value Te is a time constant for the rapidity of charging and is equal to (lAneZN), where Zi is the ion mobility and N is the ion concentration.

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