Dielectrophoresis

Dielectrophoresis (or DEP) is a phenomenon in which a force is exerted on a dielectric particle when it is subjected to a non-uniform electric field. This force does not require the particle to be charged. All particles exhibit dielectrophoretic activity in the presence of electric fields. However, the strength of the force depends strongly on the medium and particles' electrical properties, on the particles' shape and size, as well as on the frequency of the electric field. Consequently, fields of a particular frequency can manipulate particles with great selectivity. This has allowed, for example, the separation of cells or the orientation and manipulation of nanoparticles and nanowires.

Background and Properties
Publications on dielectrophoresis go as far back as the 1950's, by Herbert Pohl. Recently, dielectrophoresis has been revived due to its potential in the manipulation of microparticles, nanoparticles and cells.

Pohl wrote in his book defining dielectrophoresis as the translational motion of neutral matter caused by polarization effects in a nonuniform electric field. The phenomenological bases are catalogued below:
 * 1) The dielectrophoresis force can be seen only when particles are in the nonuniform electric fields.
 * 2) Since the dielectrophoresis force does not depend on the polarity of the electric field, thus the phenomenon can be observed either with AC or DC excitation.
 * 3) Particles are attracted to regions of stronger electric field when their permittivity exceeds that of the suspension medium.
 * 4) When permittivity of medium is greater than that of particles, this results in motion of particles to lesser electric field.
 * 5) DEP is most readily observed for particles with diameters ranging from approximately 1 to 1000 μm. Above 1000 μm gravity, and below 1 μm Brownian motion, overwhelm the DEP forces.

Phenomena associated with dielectrophoresis are electrorotation and traveling wave dielectrophoresis (TWDEP). Dielectrophoresis can be enhanced using multiple frequencies, in what is known as multiple-frequency dielectrophoresis (MFDEP).

Dielectrophoretic force
For a field-aligned prolate ellipsoid of radius $$r$$ and length $$l$$ ($$r>l$$) with complex dielectric constant $$\varepsilon_p^*$$ in a medium with complex dielectric constant $$\varepsilon_m^*$$ the time-dependent dielectrophoretic force is given by :
 * $$F_\mathrm{DEP} = \frac{\pi r^2 l}{3}\varepsilon_m \textrm{Re}\left\{\frac{\varepsilon^*_p - \varepsilon^*_m}{\varepsilon^*_m}\right\}\nabla \left|\vec{E}\right|^2 $$

The complex dielectric constant is $$\varepsilon^* = \varepsilon + \frac{\sigma}{j\omega}$$, where $$\epsilon$$ is the dielectric constant, $$\sigma$$ is the electrical conductivity, $$\omega$$ is the field frequency, and $$j$$ is the imaginary number.

This equation is accurate for highly elongated ellipsoids when the electric field gradients are not very large (e.g., close to electrode edges). The equation only takes into account the dipole formed and not higher order polarisation. When the electric field gradients are large, higher order terms become relevant, and result in higher forces. To be precise, the time-dependent equation only applies to lossless particles, because loss creates a lag between the field and the induced dipole. When averaged, the effect cancels out and the equation holds true for lossy particles as well. An equivalent time-averaged equation can be easily obtained by replacing E with Erms, or, for sinusoidal voltages by dividing the right hand side by 2.

For a homogeneous sphere of radius $$r$$ and complex permittivity $$\varepsilon_p^*$$ in a medium with complex permittivity $$\varepsilon_m^*$$ the (time-dependent) DEP force is :
 * $$F_\mathrm{DEP} = 2\pi r^3\varepsilon_m \textrm{Re}\left\{\frac{\varepsilon^*_p - \varepsilon^*_m}{\varepsilon^*_p + 2\varepsilon^*_m}\right\}\nabla \left|\vec{E}\right|^2$$

The factor in parentheses is known as the complex Clausius-Mossotti function and contains all the frequency dependence of the DEP force. Once again, a time-averaged force can be achieved by using Erms.

Dielectrophoresis Field-Flow Fractionation (DEP-FFF)
The utilization of the difference between dielectrophoretic forces exerted on different particles in nonuniform electric fields is known as DEP separation. The exploitation of DEP forces has been classified into two groups: DEP migration and DEP retention. DEP migration uses DEP forces that exert opposite signs of force on different particle types to attract some of the particles and repel others. DEP retention uses the balance between DEP and fluid-flow forces. Particles experiencing repulsive and weak attractive DEP forces are eluted by fluid flow, whereas particles experiencing strong attractive DEP forces are trapped at electrode edges against flow drag.

Dielectrophoresis Field-Flow Fractionation, introduced by Davis and Giddings, is a family of chromatographic-like separation methods. In DEP-FFF, DEP forces are combined with drag flow to fractionate a sample of different types of particles. Particles are injected into a carrier flow that passes through the separation chamber, with an external separating force (a DEP force) being applied perpendicular to the flow. By means of different factors, such as diffusion and steric, hydrodynamic, dielectric and other effects, or a combination thereof, particles (<1 μm in diameter) with different dielectric or diffusive properties attain different positions away from the chamber wall, which, in turn, exhibit different characteristic concentration profile. Particles that move further away from the wall reach higher positions in the parabolic velocity profile of the liquid flowing through the chamber and will be eluted from the chamber at a faster rate.