Three‐dimensional modelling and simulation of magnetorheological fluids

A magnetorheological fluid (MR fluid) is a type of smart fluid composed of micrometer‐sized magnetizable particles suspended in a carrier fluid. The rheological properties of an MR fluid can be greatly altered upon application of an external magnetic field. This paper presents a computational framework for the numerical study of MR fluids, in which a two‐stage modelling and simulation strategy is proposed to achieve reasonable accuracy and computational efficiency. At the first stage for simulating the particle chain formation, the particle dynamics plays a major role whereas the hydrodynamics of the fluid flow is of secondary importance. Thus an MR fluid is modelled in the context of the discrete element method and the simple Stokes formula is adopted for the hydrodynamic interaction. At the second stage, the formulated particle chains are applied as the initial configuration for simulating the rheological properties of the fluid under different shear loading conditions. A combined lattice Boltzmann and discrete element approach is employed to fully resolve the fluid field and the hydrodynamic interactions between the fluid and the particles. Some relevant magnetic models are comprehensively reviewed and the mutual dipole model is employed in this work to account for the magnetic interactions between the particles. The proposed solution procedure is illustrated via a set of numerical simulations for a representative volume element of an MR fluid. Copyright © 2010 John Wiley & Sons, Ltd.