Rheological properties of magnetic fluids with the formation of clusters: Analysis of simple shear flow in a strong magnetic field

Abstract

An analysis of rheological properties of magnetic fluids is made in the case of a steady simple shear flow in a strong magnetic field perpendicular or parallel to a shearing plane. It is assumed that the particles in magnetic fluids form rigid linear aggregates to make clusters. First a governing equation for an orientational distribution function and a stress tensor are derived from physical arguments on forces acting on the cluster in an arbitrarily directional magnetic field. Numerical calculation is then made to obtain an approximate solution of the governing equations in the three cases of magnetic field direction. It is clearly shown that an apparent viscosity of magnetic fluids increases significantly with the number of particles forming a cluster and with the effective diameter of the particles for the case of the magnetic field perpendicular to the shearing plane. Furthermore, it is clarified that the magnetic fluids show non-Newtonian behavior over a certain value of a shear rate for all cases of magnetic field direction.