Electrodynamics

Aerosols Charging and Their Kinetics

Most aerosol particles carry some electrical charges.  In an electric field of strength E, a charged particle experiences a force, which is given by

.                                                                                      (4)

Here    

                                                                                          (5)

where e is the elementary unit of charge and  is the number of elementary units carried by the particle.  ( coulombs (MKS)=  Statcoulombs (electrostatic  cgs unit).)

Particle Mobility

Particle mobility is defined as the velocity that it will acquire when subjected to an electric field of unit strength. Equating the drag and Columbic forces, it follows that

                                                                             (6)

For , the mobility becomes

                                                                               (7)

Particle Charging

Aerosol particle can be electrified by a number of different processes. Among the important ones are: Direct ionization, static electrification, electrolytic effects (liquids of high dielectric constant exchange ions with metals), contact electrification, spray electrification, frictional electrification, collisions with ion, diffusion, and field charging.

Under equilibrium conditions, the aerosols approach the Boltzmann charge distribution.  Accordingly, the fraction of particles having unites of charge of one sign, , is given by

.                                                             (8)

For , the approximate expression for the charge distribution becomes

.                                                                (9)

For a room temperature of , (9) reduces to

      in          for        .                (10)

The average number of charge per particle is given by

           for        .               (11)

Electric Field of a Point Charge

The electric field strength of a point charge at a distance r is given by

,                                                                                                            (12)

where  for cgs or electrostatic unit with  being the dielectric constant of the medium.  For air, , , and  (for MKS).