Charging mechanisms based on the conductivity data

The conductivity of a liquid medium containing ions is well understood [5]. Usually the thermal motion is not strong enough to dissociate the molecule and the motion of molecule will contribute to the conductivity. Due to the collision from neighboring molecules, the molecule will travel in a distance in (he scale of its size and then slay there. The relative number of the molecules staying at the ground state and the free Slate or activation state determine the conductivity. Suppose that the potential at ground state is L l, and that at the activation state is Ui, and the number of molecules per unit volume is no, then  

For a low dielectric constant liquid, Uo is very large, kgT, making a O. Without an external elcetrie field, the moleeulc motion is random. 

The number of molecule in one of three perpendicular axes in a space is 

The applied electric field is far less than 5.18 xlO V/mm, making the assumption, AU kgT, always valid. So Eq. (86) can be approximated by 

The velocity of the excess amount of ions moving along the electric field is the relative number of the excess amount of ions multiplying the moving distance per second 

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