Magnetically driven hydrodynamic interactions of magnetic and non-magnetic particles

The influence of magnetic forces on (i) the motion of magnetisable particles in a non-magnetisable fluid and (ii) the motion of non-magnetisable particles in a magnetisable fluid was investigated. A nonuniform magnetic field was used to induce a strong magnetic field gradient. The study was conducted at low particle Reynolds numbers allowing independent evaluation of the hydrodynamic forces along the tangential and normal directions, which in turn were used to deduce the strength and variation of the magnetic forces. Two iron spheres placed in a non-magnetisable fluid showed strong mutual attraction in the normal direction, consistent with an inverse distance to the power four law. The velocity of each sphere in the tangential direction prior to aggregation was constant. Upon aggregation, the velocity of the dumbbell in the tangential direction was approximately two times higher. This sudden increase in velocity was attributed to an increase in the magnetisation following aggregation of the two spheres. It was concluded that a dumbbell has a larger concentration of matter along the direction of the magnetic field and hence, with respect to motion in the tangential direction, a higher magnetisation. For the two acrylic spheres in a magnetised fluid the attractive force was found to be negligible, most probably because of the low magnetisation of the paramagnetic salt solution used. The two spheres did migrate towards each other because of the local field gradients that develop in the normal direction. Interestingly, the spheres developed a constant velocity prior to aggregation, which was also maintained after aggregation. Two acrylic spheres glued together also travelled in the tangential direction at the velocity observed for the individual spheres. It was concluded that there was no change in the magnetisation of the fluid following the aggregation of the spheres.