### Electrophoresis

**Electrophoresis** is the movement of an electrically charged substance under the influence of an electric field. This movement is due to the Lorentz force, which may be related to fundamental electrical properties of the body under study and the ambient electrical conditions by the equation given below. **F** is the Lorentz force, *q* is the charge carried by the body, **E** is the electric field :

.
The resulting electrophoretic migration is countered by forces of friction such that the rate of migration is constant in a constant and homogeneous electric field:

Where *v* is the velocity and *f* is the frictional coefficient.

The electrophoretic mobility μ is defined as followed.

The expression above applied only to ions at a concentration approaching 0 and in a non-conductive solvent. Polyionic molecules are surrounded by a cloud of counterions which alter the effective electric field applied on the ions to be separated. This render the previous expression a poor approximation of what really happens in an electrophoretic aparatus.

The mobility depends on both the particle properties (e.g., surface charge density and size) and solution properties (e.g., ionic strength, electric permittivity, and pH). For high ionic strengths, an approximate expression for the electrophoretic mobility is given by the Smoluchowski equation,

,
where ε is the dielectric constant of the liquid, _{} is the permitivitty of free space, is the viscosity of the liquid, and is the zeta potential (i.e., surface potential) of the particle.

### Applications

Gel electrophoresis is an application of electrophoresis in molecular biology. The content of the buffers (solutions) and gels used to enhance viscosity greatly affects the mobility of micromolecules. This process is used to determine the different size of High density lipoproteins in order to establish a more accurate representation of their effectiveness.

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