Dielectrophoresis (DEP) , travelling-wave dielectrophoresis (TWD) and electrorotation (ER) utilise differences in the electric polarizability of particles and the surrounding liquid. If a dielectric particle is exposed to an external electric field it polarises. The size and direction of the induced dipole depend on field frequency and dielectric properties (conductivity and permittivity ). This is schematically shown in the following figure.
Depending on field frequency and passive dielectric properties of
particles and the external medium the particles polarise in direction
(symbolised by arrows in the particles 1-3) of the electric field, E,
or opposite to it (particle 4). In an inhomogeneous field this causes
a force due to the interaction of induced dipole and external field.
The particles 1-3 show negative and particle 4 shows positive DEP.
Similarly, dielectric particles can be moved in electric fields due to a gradient in the field phase. This effect is used in TWD and ER and is due to a phase lag between the external field and the induced dipole. Local field minima can be created within a liquid, far from any surfaces, by using appropriate electrode configurations. This allows negative DEP to create closed field cages for particles and cells without feedback. Unlike elementary particle traps, dielectrophoretic cages do not require particle spinning or the application of additional forces. Particle spinning induced in rotating electric fields can, however, be used for particle characterisation (dielectric spectroscopy).
The situation becomes more complex in dense particle suspension due to the interaction of the induced dipoles. Particles can attract each other (e.g. particle 1 and 2, or 2 and 4) or repel each other (e.g. particle 3 and 4, or 1 and 3). As a consequence, particles can form the so called pearl-chains or compact aggregates. Additionally, particle interactions can produce spinning (this is obvious for the particles 1 and 4, or 2 and 3).
A good introduction with special respect to nanotechnology is give in an online paper of M.P. Hughes.
Some applications can be found in a small pdf-file (180k) summarizing a talk given at the IOP conference "Bio-dielectrics: theories, mechanisms and applications" held in Leicester in 2006. See also the special issue of the Journal of Physics D.
Note, that due to the small difference in magnetic susceptibility between cells and water, magnetic forces can be neglected. However, Geim and co workers (High Field Magnet Laboratory University of Nijmegen) have shown that whole organisms can be levitated by magnetic fields in air.