Rheology of a dilute suspension of dipolar spherical particles in an external field

Abstract

A theoretical analysis is presented of the effects of an external field on the rheological properties of a dilute suspension of spherical particles containing embedded dipoles. These permanent dipoles may be gravitational, magnetic, or electrical in nature. Rotary Brownian motion is assumed negligible. Free rotation of the suspended particles resulting from the shear is hindered by the action of the field. This gives rise to a system of body couples and, hence, to a state of antisymmetric stress. In particular, the suspension is non-Newtonian and displays shear-thinning. The dynamical theory is applied to a diverse variety of fluid motions including Couette flow, two- and three-dimensional Poiseuille flows, and the flow arising from the translation of a macroscopic sphere through the suspension. The apparent viscosity is shown to vary with the orientation of the viscometer relative to the direction of the external field.