Electro-rotation of spheroids in fluids under linear-polarized AC electric field: A dynamic model

Abstract

Under a linear-polarized AC electric field, a spheroid suspended in fluids typically aligns one of its axes with the field. The time-averaged torque model is widely used to predict the orientation of the spheroid with respect to the field. Different from the AC case, the dynamical behaviors including stable orientation, stable spinning, and the limit cycle of spheroids under the DC electric field are much richer. An inconsistency exists between the two cases, and a criterion for the validity of the time-average torque model is also missing. In this article, the dynamic model for the DC electric field was adapted to its AC counterpart and the full dynamics of spheroids under the AC field were studied. We bridged the DC and AC dynamics of spheroidal particles and widened the frequency range for applying the time-averaged torque model. It was found that the phase diagram at the DC limit is a very instructive guiding map for predicting the dynamical behavior at the AC field and ωτη ∼ 1 ( ω: angular frequency of the electric field, τη: characteristic time of particle rotation) appears to be a universal criterion for the time-averaged model to be effective. The flipping of particle orientation was explained with bifurcations of the periodic solutions and the irregular dynamics at low frequencies were uncovered with the Poincaré map and the power spectrum analysis. Our study sheds light on even richer dynamical behaviors of the particles under the AC electric field and may help realize other unconventional dynamical behaviors of particles in the future.