Magnetic field effect on the sedimentation process of two non-magnetic particles inside a ferrofluid

The behaviours of non-magnetic particles inside a ferrofluid have a significant effect on the performance of ferrofluid-based biosensors, such as antibody detection. The present work numerically investigates the sedimentation process of two non-magnetic spherical particles inside a ferrofluid under a uniform external magnetic field. A three-dimensional lattice Boltzmann model coupled with the bounce-back schemes is employed to simulate the corresponding flows. The present work particularly focuses on the effects of the magnetic field orientation and intensity on the sedimentation behaviours. The results show that the two particles are accelerated in a vertical magnetic field due to the reduction of drag, but decelerated in the magnetic field with the orientation of 30 degrees <= theta <= 90 degrees. The inter-particle collision is encouraged by the attractive dipole force for 0 degrees <= theta <= 45 degrees, resulting in an earlier occurrence of the 'kissing' stage, but is suppressed by the repulsive dipole force for 60 degrees <= theta <= = 90 degrees, leading to a postponement or even the absence of the 'kissing' stage. Meanwhile, it is found that the time duration of the 'drafting' stage decreases with the increasing of the magnetic field intensity. When the magnetic field intensity is beyond a critical value, the two particles self-assemble into a 'dumbbell-like' structure and the 'tumbling' stage will disappear during the sedimentation process. The present work demonstrates that the sedimentation behaviour of non-magnetic particles immersed in a ferrofluid can be controlled by varying the orientation and intensity of the external magnetic field, which can provide a valuable technical guidance for the industrial applications of ferrofluids.