Instability of the orientation of a speroidal particle in a leaky dielectric medium in the AC electric field

We study a system consisting of an ellipsoidal particle with permittivity ε₂ and conductivity σ₂ immersed into a host medium with permittivity ε₁ and conductivity σ₁ in the AC external electric field with a strength E₀ ^→ and frequency ω. We determined conditions when 1) orientation of a spheroidal particle with a finite electric conductivity at t → ∞ coincides with the orientation of the ideal dielectric spheroid; 2) orientation of a spheroid at t → ∞ is normal to the orientation of the ideal dielectric spheroid and 3) orientation of particle is not affected by the external electric field. We found the direct connection between the final orientation of the particle and the existence of two time intervals, T ₁ (ω) and T₂ (ω), such that during time interval T₁ an equilibrium orientation of the particle is the same as the equilibrium orientation of an ideal dielectric particle while during time interval T₂ the direction of the stable equilibrium orientation is normal to the equilibrium orientation of an ideal dielectric particle. The values T₁ and T₂ depend on the frequency of the external field ω, and T = T₁(ω)+ T₂(ω), where T = 2π/ω.