Simulations of Particle Dynamics in Magnetorheological Fluids

We present particle dynamics simulations for the response of magnetorheological (MR) uids upon application of a magnetic eld. The particles motion is considered to be governed by magnetic, hydrodynamic and repulsive interactions. Fluid-particle interactions are accounted for via Stokes' drag while inter-particle repulsions are modeled through approximate hard-sphere rejections. In accordance with their greater signii-cance, on the other hand, (linear) magnetic interactions are fully simulated. The time evolution is considered to be magnetically quasi-static and magnetostatic forces are derived from the solution of (steady) Maxwell's equations, recomputed at each instant in time. For this we use a potential theoretic formulation where the boundary integral equations are solved with a fast multipole approach. We show that the resulting numerical codes can be eeectively used to study a number of experimental observables such as eeective magnetic permeabilities and response timescales which are of crucial importance in the design of MR uids.