Torque density measurements on vortex fluids produced by symmetry-breaking rational magnetic fields

We have recently reported on the discovery that an infinite class of triaxial magnetic fields is capable of producing rotational flows in magnetic particle suspensions. These triaxial fields are created by applying a dc field orthogonally to a rational biaxial field, comprised of orthogonal components whose frequencies form a rational ratio. The vorticity axis can be parallel to any of the three field components and can be predicted by a careful consideration of the symmetry of the dynamic field. In this paper we not only test the field-symmetry predictions, but also quantify fluid vorticity as a function of the field parameters (strength, frequency ratio, phase angle and relative dc field strength) and particle shape. These measurements validate the symmetry predictions and demonstrate that rational fields are as effective as vortex fields for producing strong fluid mixing, yet have the advantage that small changes in the frequency of one of the field components can change the vorticity axis. This approach extends the possibilities for noncontact control of fluid flows and should be useful in areas such as microfluidics, and the manipulation and mixing of microdroplets.