Levitation and oscillations of neutral particles in a constant electric field

We investigate oscillations of polarized particles embedded in a host liquid and subjected to a constant electric field. In the considered range of parameters there exist repulsion forces between particles which can cause particle levitation and oscillations in the system. We study the eigenfrequencies of oscillations of the levitated particle and demonstrate that oscillations frequency decreases when the amplitude of the electric field grows. Consequently, the lower frequency cut-off of the excited oscillations is determined by the maximum strength of the external electric field whereby the particle motion is not overdamped. The upper bound of the oscillations frequency is determined by the minimum strength of the electric field which is required for particle levitation. We analyze two simple geometrical configurations when a spherical particle is levitated by another immobilized spherical particle and the particle is levitated above the plane interface between two half-spaces with different permittivity and electric conductivity.