  Non-uniform fields are commonly used to study vesicle dielectrophoresis and
can be used to hitherto relatively unexplored areas of vesicle deformation and
electroporation. A common but perplexing problem in vesicle dynamics is the
cross over from the entropic to enthalpic (stretching) tension during vesicle
deformation. A lucid demonstration of this concept is provided by the study of
vesicle deformation and dielectrophoresis under axisymmetric quadrupole
electric field. Small deformation theory incorporating the Maxwell stress
approach is used (employing area and volume conservation constraints) to
estimate the dielectrophoretic velocity. The entropic and enthalpic tensions
are implemented to understand vesicle electrohydrodynamics in low and high
tension limits. The shapes obtained using the entropic and the enthalpic
approaches, show significant differences. A strong dependence of the final
vesicle shapes on the ratio of electrical conductivities of the fluids inside
and outside the vesicle as well as on the frequency of the applied quadrupole
electric field is observed which could be used to estimate electromechanical
properties of the vesicle. Moreover, an excess area dependent transition
between the entropic and enthalpic regimes is observed. The Maxwell stress
approach, used in this work, indicates that Clausius-Mossotti factor obtained
by the dipole moment method together with the drag on a rigid sphere explains
vesicle dielectrophoresis. Interestingly, the coupling of hydrodynamic and
electric stress, important in drops is absent in vesicle dielectrophoresis to
linear order.
