The Motion of Solid Particles Suspended in Viscoelastic Liquids under Torsional Shear
J. Feng and D. D. Joseph
J. Fluid Mech. 324, 199-222 (1996)
Abstract - This paper presents an experimental study of the behavior of single particles and suspensions in polymer solutions in a torsional flow. Four issues are investigated in detail: the radial migration of a spherical particle, the rotation and migration of a cylindrical particle, the particle-particle interaction and microstructures in a suspension of spheres and the microstructures in a suspension of rods. Newtonian fluids are also tested under similar flow conditions for comparison. A spherical particle migrates outward at a constant velocity unless the polymer solution is very dilute. A rod in a viscoelastic fluid has two modes of motion depending on its initial orientation, aspect ratio, the local shear rate and the magnitude of normal stresses in the fluid. In the first mode, the rod rotates along a Jeffery-like orbit around the local vorticity axis. It also migrates slowly inward. The second mode of motion has the rod aligned with the local stream at all time; the radial migration is outward. A hypothesis proposed by Highgate & Whorlow (1968) on the radial force on a particle in a cone-and-plate geometry is generalized to explain the variation of migration speed in torsional flows. Spheres form chains and aggregates when the suspension is sheared. The chains are along the flow direction and may connect to form circular rings; these rings migrate outward at a velocity much higher than that for a single sphere. Rods interact with one another and aggregate in much the same way, but to a less extent than spheres. It is argued that the particle interaction and aggregation are not direct results of the shear flow field. Two fundamental mechanisms discovered in sedimentation are applied to explain the formation of chains and aggregates. Finally, the competition between inertia and elasticity is discussed. A change of type is not observed in steady shear, but may happen in small-amplitude oscillatory shear.