This paper deals with the Quincke rotation of small insulating particles. This dc electrorotation ofinsulating objects immersed in a slightly conducting liquid is usually explained by looking at theaction of the free charges present in the liquid. Under the effect of the dc electric field, the chargesaccumulate at the surface of the insulating particle which, in turn, acquires a dipole moment in thedirection opposite to that of the field and begins to rotate in order to flip its dipole moment. In theclassical Quincke model, the charge distribution around the rotor is supposed to be purelysuperficial. A consequence of this assumption is that the angular velocity does not depend on therotor size. Nevertheless, this hypothesis holds only if the rotor size is much larger than thecharacteristic ion layer thickness around the particle. In the opposite case, we show thanks tonumerical calculations that the bulk charge distribution has to be accounted for to predict theelectromechanical behavior of the rotor. We consider the case of an infinite insulating cylinderwhose axis is perpendicular to the dc electric field. We use the finite element method to solve theconservation equations for the positive and the negative ions coupled with Navier–Stokes andPoisson equations. Doing so, we compute the bulk charge distribution and the velocity field in theliquid surrounding the cylinder. For sufficiently small cylinders, we show that the smaller thecylinder is, the smaller its angular velocity is when submitted to a dc electric field. This size effectis shown to originate both in ion diffusion and electromigration in the charge layer. At last, wepropose a simple analytical model which allows calculating the angular velocity of the rotor whenelectromigration is present but weak and diffusion can be neglected.
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