Introduction

The previous chapters primarily discussed dispersions of spherical particles, but real particles are seldom perfectly spherical. Anisometric crystalline particles would be one example. Particles come in a wide range of shapes, as illustrated in Figure 5.1. Fibers and platelets constitute two simple shapes that represent typical deviations from sphericity. When such particles are subjected to shear flow they will, as with spherical particles, be dragged along and rotate. With non-spherical particles, however, the hydrodynamic stresses will depend on the relative orientations of the particles with respect to the direction of flow. Hence, the stresses will vary during rotation, causing a time-dependent motion of the particle in steady shear flow. Consequently, the rheology of a suspension of non-spherical particles will depend on particle orientation. As rotation and orientation depend on particle shape, particle motion and rheology will be strongly coupled.

The behavior in flow of individual, non-Brownian particles with arbitrary shape has been studied in particular by Brenner [1]. To gain insight into shape effects in suspension rheology it is, however, more suitable to limit the discussion to rather simple shapes. Only axisymmetric particles, i.e., those with rotational symmetry, will be considered here. More specifically this includes rods (including fibers), circular disks, and spheroids (Figure 5.1). All these shapes can be characterized by an aspect ratio pa, defined as the ratio of the dimension along the symmetry axis to that in the cross direction. The aspect ratio can be larger or smaller than unity; spheroids are then prolate or oblate, respectively (Figures 5.1(a) and (b)). Because of the strong influence of sharp edges on the drag on a particle, cylinders and spheroids with identical aspect ratios (i.e., L/d = a/b) will move differently in the flow field. To compare other axisymmetric shapes with spheroids, an effective aspect ratio pa,e that results in identical rotational behavior can be used [2]. Other mapping procedures between shapes are possible; see, e.g., [3].