Quantified evaluation of the significance of higher order effective moments and dielectrophoretic forces

Abstract

In analysis of electric field interactions with dielectrics, higher order moments and dielectrophoretic force terms are commonly ignored in what has become known as the dipole approximation. The very few multipolar studies in the literature have either confined analysis to spherical particles or modelled non-spherical particles as spheres of similar dimensions. A major obstacle in analysing the significance of higher order moments has been the limitedness of multipole moment determination techniques. Analytic derivations for higher order moments are only available for spherical particles. This work addresses this roadblock and presents a hybrid numerical-analytical method for determination of the first three effective moments of particles of any shape subjected to electric fields of arbitrary geometry. Results of applying this method for determining higher order dielectrophoretic force terms have been verified by comparison against total force calculations using the Maxwell stress tensor method, known for its mathematical rigorousness in accounting for all interaction between an applied electric field and subject dielectric(s). It is shown that the dipole approximation is particularly unreliable for non-spherical particles, importantly comprising the vast majority of bioparticles. It is shown that higher order terms can constitute up to half the dielectrophoretic force on dielectric particles in suspension. With the current trend toward micro- and nano-electrode geometries used for single particle analysis, and a consequent increase in the number of instances where invoking the dipole approximation can be highly inaccurate, this work offers a computationally inexpensive and verifiably accurate means for determining higher order moments and dielectrophoretic forces.

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ORCID for Nicolas G Green: orcid.org/0000-0001-9230-4455

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