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

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.