Dynamics of a pair of paramagnetic particles in shear flows under a uniform magnetic field

We numerically investigated the particle-particle interaction and relative motion of a pair of equal-sized magnetic particles in simple shear and plane Poiseuille flows. Two-dimensional numerical models were created by using direct numerical simulations, which are based on the finite element method and arbitrary Lagrangian-Eulerian approach with full consideration of particle-particle, particle-magnetic field, particle-flow field interactions. The effects of direction and strength of magnetic field on the dynamics of the particles in simple shear and plane Poiseuille flows were investigated, respectively. In the simple shear flow, the presence of magnetic field can show stabilizing or destabilizing effect on the particle trajectories, depending on the direction of the magnetic field. Specifically, the particles initially located at closed trajectories moved closer and closer when the magnetic field is applied at 0 degrees and 135 degrees, while they moved further apart and separated when the field is applied at 90 degrees. In the plane Poiseuille flow, the magnetic field changed the relative motion of two particles: it induced two particles to form a chain when a strong magnetic field is applied at 0 degrees and 135 degrees; it separated the two particles when a strong magnetic field is applied at 45 degrees and 90 degrees. This work offers insights toward understanding the mechanisms of particle-particle interaction in magnetorheological fluids in simple shear or plane Poiseuille flows under a uniform magnetic field.