On the effect of particle couples on the motion of a dilute suspension of spheroids

Abstract

This paper is concerned with the effect on the bulk motion of applying torque by external means to the particles of a suspension. Our investigation is based upon theoretical consideration of the motion of a dilute suspension of permanently magnetized spheroids, in the presence of a uniform magnetic field, for cases in which the motion of a Newtonian fluid would be uni-directional. For convenience, we have divided the work into two parts: in the first, the particles are assumed to be perfectly spherical and the magnetic field strength to be arbitrary; in the second, the particles are taken as arbitrary spheroids (with their magnetic dipole axis coincident with the axis of revolution), but the magnetic field is assumed to be strong enough to ensure that the magnetic dipole axis of each particle is effectively aligned with the field vector H. We concentrate attention on the development of general criteria which allow an a priori determination as to whether the bulk motion remains uni-directional in the presence of particle couples, and (when the motion is uni-directional) whether the resultant velocity profile has the same form as for a Newtonian fluid. In addition, we evaluate the effective viscosity of the suspension for several representative cases in which the velocity field is Newtonian in form. Finally, as an example of the general situation in which the bulk velocity field does not remain uni-directional, we obtain the solution for the motion through a circular tube when the magnetic particles are spherical and the magnetic field is applied at right angles to the tube axis.