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.

中文翻译：

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非均匀交流电场中椭球的能量分布图†

我们报告一个椭圆形的粒子在不均匀的高频交流电场中的能量景观的封闭形式的分析模型，以识别所有可能的粒子位置和方向。三维平衡位置和扁长（方位- [R _X = - [R _ý < ř _Ž），扁圆（[R _X = - [R _ž > ř _Ý）和不等边（[R _X ≠ ř _ý ≠ ř _Ž）椭球被报告与场频率和幅度，这是根据能量分布的最小值确定的。对于共面平行电极之间不均匀电场内的椭球，扁长形的位置和方向的构型数为6，扁球形为5，斜角形椭球为9。此外，对于共面电极，可以确定何时可以使用准2D分析在其接近表面的最可能高程平面中处理粒子的条件。报告的表达式对于任意交流电场配置中的椭球粒子的时间平均相互作用都是有效的，因此我们的结果适用于电磁镊子，该镊子与具有适当材料特性且与感兴趣的频率范围内的介质形成对比的粒子相互作用。