The Motion and Interaction of Solid Particles in Viscoelastic Liquids

Abstract

Abstract In this paper we present numerical and experimental results on the motion and interaction of solid particles in polymeric fluids. The two-dimensional numerical work investigates the viscoelastic effects on the sedimentation of a particle in the presence of solid walls or another particle. The Navier-Stokes equations coupled with an Oldroyd-B model are solved using a finite element method, and the particles are moved according to their equations of motion. In a vertical channel, a particle settling close to one side wall experiences a repulsion from the wall; a particle settling farther away from the wall is attracted to it. Two particles settling in tandem attract and form a doublet if their initial separation is not too large. Two particles settling side by side approach each other and the doublet also rotate till the line of centers is aligned with the direction of fall. The experimental part studies the behavior of single particles and suspensions in polymer solutions in a torsional flow. Four issues are investigated: the radial migration of a spherical particle, the rotation and migration of a cylindrical rod, the particle-particle interaction and microstructures in a suspension of spheres and the microstructures in a suspension of rods. A spherical particle migrates outward at a constant velocity unless the polymer solution is very dilute. A rod has two modes of motion depending on its shape, initial orientation, the local shear rate and the magnitude of normal stresses in the fluid. When a suspension is sheared, spheres form chains along the flow direction. These chains may connect and form circular rings, which migrate outward at a velocity much higher than that for a single sphere. Rods interact with each other and aggregate in much the same way, but to a less extent than spheres. Particle interaction and aggregation can be explained by two fundamental mechanisms discovered in the numerical simulations of sedimentation.