Aggregation and Dispersion of Spheres Falling in Viscoelastic  Liquids

D. D. Joseph,  Y. J. Liu, M. Poletto, and J. Feng
J. Non-Newtonian Fluid Mech. 54, 45-86 (1994)

Abstract - This paper focuses on the settling of one sphere near another or near a wall. We find maximum differences between Newtonian and viscoelastic liquids, with repulsion between nearby bodies in the Newtonian case and attraction in the viscoelastic case. Side-by-side arrangements of sedimenting spheres are unstable in exactly the same way that broadside-on settling of long bodies is unstable at subcritical speeds in a viscoelastic fluid. The line of centers between the spheres rotates from across to along the stream as the spheres are sucked together. The resulting chain of two spheres is a long body which is stable when the line between centers is parallel to the fall, but this configuration breaks up at supercritical speeds where inertia again dominates. To explain the orientation of particles in the subcritical case, we correlate the aggregative power of a viscoelastic fluid with a zero shear value of the ratio of the first normal stress difference to the shear stress and for exceptional cases we introduce the idea of the memory of shear-thinning leading to corridors of reduced viscosity.