Dielectrophoresis and deformation of a liquid drop in a non-uniform, axisymmetric AC electric field

Analytical theory for the dielectrophoresis and deformation of a leaky dielectric drop, suspended in a leaky dielectric medium, subjected to non-uniform, axisymmetric Alternating Current (AC) fields is presented in the small deformation limit. The applied field is assumed to be a combination of a uniform part and a quadrupole component. The analysis shows that the magnitude and the sign of the steady and time-periodic dielectrophoretic velocity depend upon the frequency of the applied voltage. The frequency of oscillatory motion is twice that of the applied frequency and the phase lag is a consequence of charge dynamics. A deformed drop under non-uniform axisymmetric AC fields admits Legendre modes l = 2, 3, 4. The deformation has a frequency-dependent steady and time-periodic parts due to charge and interface dynamics. The steady deformation can be zero at a certain critical frequency in leaky dielectric systems. The time-periodic deformation also has a frequency which is twice the frequency of the applied voltage. In perfect dielectric systems, unlike the steady state deformation which is a balance of Maxwell and curvature stresses, the time-periodic deformation additionally includes viscous stresses associated with the oscillatory shape changes of the drop. A consequence of this effect is a phase lag that is dependent on the charge and interface hydrodynamics and a lag of pi/2 at high frequencies. It also results in vanishing amplitude of the oscillatory deformation at high frequencies. The study should lead to a better understanding of dielectrophoresis under non-uniform axisymmetric AC fields and better electrode design to affect drop breakup.