Steady and Transient Motion of Spherical Particles in Viscoelastic Liquids

1. Introduction The motion of a spherical particle through a fluid with non-Newtonian rheological properties is a well-studied problem with a broad range of practical application from sedimentation of muds and slurries to processing of filled polymer melts. As a benchmark problem for computational rheology and the evaluation of numerical codes (cf. Hassager, 1988), the sedimentation of a sphere in an elastic fluid has become one of the most studied problems in non-Newtonian fluid mechanics. Almost 10 years ago, in the first edition of this book, Walters & Tanner (1992) provided a comprehensive overview of the state of knowledge at that time. Over the past decade, significant advances have been made in numerical algorithms for steady and transient computation of viscoelastic flows and also in quantitative experimental techniques for non-invasively resolving the spatial and temporal characteristics of both the particle motion and the velocity field within the fluid. These advances, when combined with careful rheological characterization of the test fluids studied and simulated, have led to a greater understanding of the motion of particles in complex fluids. This chapter focuses on these recent developments rather than comprehensively reviewing the early literature and should thus be regarded as complementary to the earlier reviews of Walters & Tanner (1992) and Chhabra (1993). We focus almost exclusively on motion in viscoelastic liquids, since these are the most common types of non-Newtonian fluids encountered and because the interactions of viscosity, elasticity and particle inertia give rise to some of the most complex and unexpected classes of phenomena. The motion of spheres through inelastic fluids such as power-law, Carreau or Bingham fluids is covered elsewhere in this book. In order to avoid the additional complications arising from fluid inertia, most fundamental studies over the past decade have focused on the creeping motion of a sphere at low Reynolds numbers. In addition to its central role as a benchmark problem for rheologists and fluid dynamicists, such a problem continues to be of great practical relevance due to modern technological developments in, for example, highly-filled polymeric nanocomposites containing submicron spherical (or other shaped) particles and the use of submicron spherical beads as