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. low electric field [33]. This has led to research in designing effective non-uniform electric fields by judicious design of electrodes, often in microfluidic/nanofluidic chips by microfabrication techniques [36,16,35] has gained prominence.Giant Unilamellar Vesicles (Liposomes) (GUVs) have emerged as a very reliable bio-memetic system and has been used to understand the DEP response of cells [37,38]. Unlike biological cells, there are very few experimental [37,39,40] and theoretical [41] investigations on the DEP of vesicles . Korlach et al., [42] created a 3D electric field cage to study vesicle deformation and electro-rotation by trapping a vesicle using optical tweezers. Studies on the modification of the electrical properties of GUVs to serve them as test particle for DEP study [43], high-frequency DEP response of vesicles to estimate upper and lower crossover frequency at different interior conductivity and membrane electric properties [38] and DEP studies on surface-modified liposomes in AC fields [39], have also been reported . A vesicle under non-uniform, axisymmetric quadrupole electric field, not only exhibits dielectrophoresis, but can also deform. Although several experimental and theoretical papers have demonstrated vesicle deformation under AC [44,45,46,47], pulsed DC[48], DC fields [49,50], these fields are mostly uniform. A uniform field leads to prolate and oblate spheroidal (dipolar) deformations, and these have bee...