Non-uniform spatial distributions of both the magnitude and phase of AC electric fields determine dielectrophoretic forces.

It is well known that the conventional dielectrophoretic force acting on a polarised particle in a non-uniform AC electric field is proportional to the in-phase component of the induced dipole moment and the non-uniformity of the field strength. In contrast, the travelling-wave-dielectrophoretic force that acts on a particle subjected to a travelling electric field is proportional to the out-of-phase component of the induced dipole moment. We derive a theory that unifies the description and interpretation of conventional dielectrophoretic and travelling-wave-dielectrophoretic forces. We show that a particle in a non-uniform AC electric field experiences a dielectrophoretic force due to spatial non-uniformities of the magnitude and the phase of the field interacting, respectively, with the in-phase and out-of-phase components of the induced dipole moment. The theory is used to explain the translational effects observed for particles in the presence of standing, travelling and rotating fields in several experimental electrode configurations. The good agreement found between the experimental observations and the theoretical predictions validate the theory.