Review of the theory of generalised dielectrophoresis.

Generalised dielectrophoresis (gDEP), including conventional dielectrophoresis (cDEP), electrorotation (ER) and travelling wave dielectrophoresis (twDEP), is an effective tool for particle (cell) manipulation and characterisation, even down to the level of nano-sized objects such as DNA, proteins and viruses. All the disciplines of gDEP are originated from the interaction of an applied electric field with its polarisation effect on the particle and can be studied systematically in a unified approach under electrostatics. In this review, the authors discuss both the quasi-static and transient theory of gDEP in an unbounded medium for both spherical and ellipsoidal particles. Then the quasi-static theory of wall effect is discussed on gDEP for a spherical particle. The wall effect is minor for ER, twDEP and cDEP parallel to wall(s), but could be significant for cDEP normal to wall(s). Force and torque expressions in terms of electric potential and its derivatives are provided and suggested for a robust calculation of the twDEP force and DEP torque. Discussions are provided for the application of the theory to nano-sized particles. The authors also illustrate some features of the Clausius-Mossotti factor using erythrocyte as an example, including both the crossover (DEP) and peak frequencies (ER) at low and high-frequency limits.