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# Electrical mobility

Electrical mobility is the tendency of charged elementary particles (such as electrons or protons) to move, other than engaging in a stationary orbit (for example within a given atom or molecule}. 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:

$\,v_d = \mu E$

where

$\, v_d$ is the drift velocity (m/s)
$\, E$ is the magnitude of the applied electric field (V/m)
$\, \mu$ is the mobility (m^2/(V.s))

In other words, the "electrical mobility" of the particle is defined as the ratio of the drift velocity to the magnitude of the electric field:

$\,\mu = \frac{v_d}{E}$

The separation of ions according to their mobility in gas phase is called Ion mobility spectrometry, in liquid phase it is called Electrophoresis.

Electrical mobility is proportional to the net charge of the particle. This was the basis for Robert Millikan's demonstration that electrical charges occur in discrete units, whose magnitude is the charge of the electron.

Electrical mobility of spherical particles much larger than the mean free path of the molecules of the medium is inversely proportional to the diameter of the particles; for spherical particles much smaller than the mean free path, the electrical mobility is inversely proportional to the square of the particle diameter.

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. The former are generally referred to as "differential mobility analyzers". The selected mobility is often identified with the diameter of a singly-charged spherical particle, thus the "electrical-mobility diameter" becomes a characteristic of the particle, regardless of whether it is actually spherical.

## References

• E. O. Knutson and K. T. Whitby (1975). "Aerosol classification by electric mobility: Apparatus, theory, and applications". J. Aerosol Sci. 6: 443-451.