Energy landscapes for ellipsoids in non-uniform AC electric fields

We report a closed-form analytical model for energy landscapes of ellipsoidal particles in non-uniform high-frequency AC electric fields to identify all possible particle positions and orientations. Three-dimensional equilibrium positions and orientations of prolate (r_x = r_y < r_z), oblate (r_x = r_z > r_y), and scalene (r_x≠r_y≠r_z) ellipsoids are reported vs. field frequency and amplitude, which are determined from energy landscape minima. For ellipsoids within non-uniform electric fields between co-planar parallel electrodes, the number of configurations of position and orientation is 6 for prolate, 5 for oblate, and 9 for scalene ellipsoids. In addition, for coplanar electrodes, conditions are identified when particles can be treated using a quasi-2D analysis in the plane of their most probable elevation near an underlying surface. The reported expressions are valid for time-averaged interactions of ellipsoid particles in arbitrary AC electric field configurations, such that our results are applicable to electromagnetic tweezers interacting with particles having an appropriate material property contrast with the medium in the frequency range of interest.