An apparatus separating a polarizable analyte using dielectrophoresis includes a vessel including a membrane having a plurality of nano- to micro-sized pores, the membrane disposed inside the vessel, electrodes generating spatially non-uniform electric fields in the nano- to micro-sized pores of the membrane when an AC voltage is applied to the electrodes, and a power source applying the AC voltage to the electrodes, wherein a sectional area of the pores varies along a depth of the pores. A method of separating a polarizable material uses the apparatus.