Rheological Theories · Measuring Techniques in Rheology Test Methods in Rheology · Fractures Rheological Properties of Materials · Rheo-Optics · Biorheology pp 1398-1398 | Cite as

# The bulk stress in a suspension of spheres to order *c*^{2}

## Abstract

An exact formula is obtained for the term of order *c* ^{2} in the expression for the bulk stress in a suspension of force-free spherical particles in Newtonian ambient fluid, where *c* is the volume fraction of the spheres and *c* ≪ 1. The particles may be of different sizes, and composed of either solid or fluid of arbitrary viscosity. The method of derivation circumvents the familiar obstacle, of non-absolutely convergent integrals representing the effect of all pair interactions in which one specified particle takes part, by the judicious use of a certain quantity which is affected by the presence of distant particles in a similar way and whose mean value in known exactly. The bulk stress is in general of non-Newtonian form and depends on the statistical properties of the suspension which in turn are dependent on the type of bulk flow.