Electrorotation of a leaky dielectric spheroid immersed in a viscous fluid

We study rotation of a spheroidal dielectric particle immersed into a viscous dielectric fluid and subjected to a constant external electric field. The electrorotation is caused by the mechanical torque due to a fluid shear flow and by the electric moment due to the difference between electric conductivities and permeabilities of a particle and a host fluid. We consider effect of a shear flow on the orientation of the spheroid in a case of an ideal dielectric and for the finite electric conductivities of the spheroid and a host medium. We determined the critical magnitude of the shear flow velocity whereby spheroid cannot be held by the external electric field with a given strength and found the dependencies of the Euler angles of the spheroid vs the strength of the electric field. In a case of a system with a finite electric conductivity we considered two types of the nonideal dielectrics, namely, negative electroviscosity particles and positive electroviscosity particles. For a given magnitude of shear velocity and for two types of particles we determined the critical strengths of the electric field whereby rotation regime changes qualitatively in a case of rotation around the symmetry axis and in a case when the orientation of the axis of symmetry changes.