Higher-order dielectrophoresis of nonspherical particles.

Higher-order terms of dielectrophoretic (DEP) force are commonly ignored by invoking the simplifying dipole approximation. Concurrently, the trend towards micro- and nano-electrode structures in DEP design is bringing about an increasing number of instances where the approximation is expected to lose reliability. The case is severe for nonspherical particles (the shape of many biological particles) due to the shape-dependent nature of dielectric polarization. However, there is a lack of analytical means to determine multipole moments of nonspherical particles, numerical calculations of the same are regarded as unreliable, and there is a prevalence for higher-order force considerations to be ignored. As a result, the dipole approximation is used and/or nonspherical particles are approximated as spheres. This work proves the inefficacy of current qualitative criteria for the reliability of the dipole approximation and presents a quantitative substitute, with verified accuracy, that enables precise determination of the extent to which the dipole approximation would be reliable, and if found unreliable, corrects the approximation by adding second- and third-order terms of the DEP force. The effects of field nonuniformity, electrode design, and particle shape and aspect ratio on the significance of higher-order DEP forces is quantitatively analyzed. The results show that higher-order DEP forces are indeed of substantially increased significance for nonspherical particles; in the cases examined in this work, multipolar terms are seen to constitute more than 40% of the total force on ellipsoidal and cylindrical particles. It is further shown that approximating nonspherical particles as spheres of similar dimensions is subject to substantial error. Last, the substantial importance of the electrode design in influencing higher-order forces is shown.