In laboratories around the world, scientists use magnetic stirrers to mix solutions and dissolve powders. It is well known that at high drive rates the stir bar jumps around erratically with poor mixing, leading to its nick-name 'flea'. Investigating this behaviour, we discovered a state in which the flea levitates stably above the base of the vessel, supported by magnetic repulsion between flea and drive magnet. The vertical motion is oscillatory and the angular motion a superposition of rotation and oscillation. By solving the coupled vertical and angular equations of motion, we characterised the flea’s behaviour in terms of two dimensionless quantities: (i) the normalized drive speed and (ii) the ratio of magnetic to viscous forces. However, Earnshaw’s theorem states that levitation via any arrangement of static magnets is only possible with additional stabilising forces. In our system, we find that these forces arise from the flea’s oscillations which pump fluid radially outwards, and are only present for a narrow range of Reynold's numbers. At slower, creeping flow speeds, only viscous forces are present, whereas at higher speeds, the flow reverses direction and the flea is no longer stable. We also use both the levitating and non-levitating states to measure rheological properties of the system.
- Industrial and Applied Mathematics Seminar