The separation of ions according to their mobility in gas phase is called ion mobility spectrometry, in liquid phase it is called electrophoresis.
When a charged particle in a gas or liquid is acted upon by a uniform electric field, it will be accelerated until it reaches a constant drift velocity according to the formula
[1] This means that a sodium ion in an electric field of 1 V/m would have an average drift velocity of 5.19×10−8 m/s.
Such values can be obtained from measurements of ionic conductivity in solution.
Electrical mobility is proportional to the net charge of the particle.
Electrical mobility is also inversely proportional to the Stokes radius
This is true because the solvated ion moving at a constant drift velocity
For different ions with the same charge such as Li+, Na+ and K+ the electrical forces are equal, so that the drift speed and the mobility are inversely proportional to the radius
[2] In fact, conductivity measurements show that ionic mobility increases from Li+ to Cs+, and therefore that Stokes radius decreases from Li+ to Cs+.
This is the opposite of the order of ionic radii for crystals and shows that in solution the smaller ions (Li+) are more extensively hydrated than the larger (Cs+).
through an exact (thermodynamically required) equation known as the Einstein relation:
where If one defines the mean free path in terms of momentum transfer, then one gets for the diffusion coefficient
is often defined as the diffusional mean free path, by assuming that a simple approximate relation is exact:
is the root mean square speed of the gas molecules:
This approximate equation becomes exact when used to define the diffusional mean free path.
Electrical mobility is the basis for electrostatic precipitation, used to remove particles from exhaust gases on an industrial scale.
The particles are given a charge by exposing them to ions from an electrical discharge in the presence of a strong field.
The particles acquire an electrical mobility and are driven by the field to a collecting electrode.
Instruments exist which select particles with a narrow range of electrical mobility, or particles with electrical mobility larger than a predefined value.
This technique is applied in scanning mobility particle sizers.