Rheology of a dilute suspension of dipolar spherical particles in an external field. II. Effects of Rotary Brownian motion

Abstract

A previous treatment of the rheological properties of ferrofluids (and of dipolar spherical-particle suspensions in general) is here extended to include the effects of rotary Brownian motion. A second-order partial differential equation is derived which expresses the steady-state distribution of dipole orientations in terms of the angle between the directions of the external field and the fluid vorticity vector, the external field strength, and the rotary diffusivity—each of the latter being rendered dimensionless with the shear rate. This equation for the orientational distribution function is solved numerically for a variety of values of these three parameters. Several asymptotic perturbation solutions are also developed, and shown to agree with the numerical results. Knowledge of the distribution function is used to calculate the theological properties of a dilute suspension of spherical particles containing permanent embedded dipoles in a simple shearing flow, in terms of the relevant parameters. An attempt is made to compare the theoretical predictions with experimental data.