Transverse gradient diffusion in a polydisperse dilute suspension of magnetic spheres during sedimentation

Abstract

In this work we investigate the pair interaction of magnetic particles in a dilute polydisperse sedimenting suspension. The suspension is composed of magnetic spherical forms of different radii and densities immersed in a Newtonian fluid, settling due to the gravity. When in close contact, the particles may exert on each other a magnetic force due to a permanent magnetization. We restrict our attention to dispersions of micromagnetic composite with negligible Brownian motion. The calculations of the relative particle trajectories are based on direct computations of the hydrodynamic interactions among rigid spheres in the regime of low particle Reynolds number. Depending on the relative importance of the interparticle forces and gravity, the collisions may result in aggregation or simply in a breaking of the particle relative trajectory time reversibility. After summing over all possible encounters, the transverse self-diffusion and down-gradient diffusion coefficients that describe the cross-flow migration of the particles are calculated. Our calculation shows first evidence and the significance of the diffusion process arising from magnetic interactions in dilute non-Brownian suspensions.

Symmetry breaking of particle trajectories due to magnetic interactions in a dilute suspension

“…When this happens, we say that this trajectory of the particle is irreversible. We verify here the results of Cunha and Couto [6,7] that magnetic interactions can break the symmetry of relative trajectories in creeping flows, as mentioned previously in this work.…”

“…The main differences of the present study and previous calculations (e.g. [6,7]) are: firstly, we consider particle rotation due to dipoledipole interactions. This adds a new equation for the orientation of the particles, for which the torque balance on the particles has to be known.…”

“…8 reversibility diagrams for the case in which the particles have infinite rotational inertia, that is, they do not rotate while moving and the orientation of the dipoles remain constant throughout time evolution. This is carried out in the simulations by not solving the angular momentum of the particles [6,7]. We can see from these plots that configuration 1 gives a more regular and isotropic shape, and configuration 2 conserves the dumbbell shape with an anisotropic ratio I¼1.5.…”