Theory of strong intrinsic mixing of particle suspensions in vortex magnetic fields

Recent experiments have shown that a type of triaxial magnetic field we call a vortex field can induce strong mixing in a magnetic particle suspension. A vortex triaxial field consists of a rotating magnetic field in a horizontal plane, with a dc field applied normal to this. The mixing torque is found to be independent of the field frequency and fluid viscosity over a broad range; scales as the square of the applied field; and is strongest for a balanced triaxial field—one in which the root-mean-square amplitudes of the three field components are equal. In this paper we show that these anomalous effects are consistent with the formation of volatile particle chains that have a precessionlike motion. Theoretical results are given for both particle chains and magnetic rods for arbitrary vortex field angles. A key conclusion is that the mixing torque is independent of particle size, making this mixing technique scale adaptive, and thus suitable for microfluidics applications.