Hydrodynamic dispersion and aggregation induced by shear in non-Brownian magnetic suspensions

In this paper, we examine a two-particle problem in order to study transport phenomena on magnetic suspensions such as the shear-induced hydrodynamic diffusion and the shear-induced aggregation in the regime of non-Brownian particles and creeping flow. New results are presented for the shear-induced hydrodynamic diffusivities and the rate of particle doublet formation, resulting from the diffusive and aggregative irreversible trajectories produced by particle magnetic interactions. The numerical computation of the particle shear-induced diffusivities and the rates of particle aggregation are performed by using a Monte Carlo integration scheme for different values of the relevant magnetic parameter α. This parameter represents the non-dimensional strength of the dipole-dipole magnetic interactions between the particles. For small values of α, the shear-induced self-diffusivity is remarkably described by a slight adaptation of the asymptotic theory for rough spherical particles interacting hydrodynamically [F. R. Cunha and E. J. Hinch, “Shear-induced dispersion in a dilute suspension of rough spheres,” J. Fluid Mech. 309, 211 (1996)]. We just replace the roughness parameter ϵ with α5/4, giving for the self-shear-induced diffusivity for small values of α, 0.156γ̇a2ϕα0.547log(1/α5/4)+1.347−0.701, where γ̇ is the applied shear rate, a is the radius of the magnetic spheres, and ϕ is the particle volume fraction. In addition, a root-square law dependence is obtained for the rate of particle aggregation as (1.830/π)ϕ1N1γ̇α1/2, where N1 and ϕ1 are, respectively, the number and the volume fraction of the isolated particles in the suspension. A comparison shows that the root-square law prediction is in excellent agreement with the results of the numerical simulations for all values of the parameter α investigated.