A numerical analysis of Quincke rotation

This paper deals with the Quincke rotation of small particles. It is usual to explain this DC electorotation looking at the action of the free charges present in the liquid which under the application of an electric field accumulate at the surface of the insulating object. Then it acquires a dipole moment in the direction opposite to that of the field. In turn the particle begins to rotate in order to flip its dipole moment. We present a numerical study of the rotation of and infinite cylinder whose axis is perpendicular the DC E field. Using a finite element method, we solve the conservation equations for the positive and the negative ions coupled with the Stokes equation. Doing so, we determine the charge distribution around the rotating particle and the fluid velocity field. Then, we deduce the angular velocity of the cylinder and we show that, contrary to what is usually assumed, the spin rate of the rotor can depend on its size. This dependence is particularly significant for small rotor whose typical dimension is smaller than few microns.