On the magnetization of a dilute suspension in a uniform magnetic field: Influence of dipolar and hydrodynamic particle interactions

•Hydrodynamic and dipolar interactions in MR Fluids.•Non-Brownian magnetic suspension in strong flows.•Influence of particle interactions on magnetization.•Magnetization dependence on particle volume fraction. In this work, the magnetization of a dilute magnetic suspension undergoing a shear flow and a uniform field in the presence of dipolar and hydrodynamic interactions is investigated. Firstly, the problem of a single magnetic particle in a simple shear flow in the presence of an external uniform magnetic filed is examined. From this solution, we study the influence of non-equilibrium effects on the magnetization at condition of strong flows, including the spinning behavior of the particles. Next, we use a non-renormalized cluster expansion in order to derive the magnetization O(ϕ2) in a sheared suspension of non-Brownian magnetic from a solution of a creeping flow problem of two magnetic spherical particles interacting magnetically and hydrodynamically in the presence of a uniform applied magnetic field, where ϕ is the particle volume fraction. The numerical results suggest that under condition of strong flows the aggregative nature of the dipolar interactions may lead to a decrease in the magnetization component in the field direction. In contrast, the dispersive character of the viscous hydrodynamic interactions produces a substantial increase in the same component of magnetization even under the condition of strong flow. This result is attributed to the misalignment produced by the hydrodynamic disturbances on the particle dipoles orientated with the flow direction.