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The Motion and Interaction of Solid Particles in Viscoelastic Liquids

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J. Feng, D. D. Joseph and P. Y. Huang

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*ASME-AMD* Vol. **217**, 123-133
(1996)

**Abstract** - In this paper we present numerical and
experimental results on the motion and interaction of solid particles in
polymeric fluids. The numerical work is done in two dimensions and is concerned
with 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 and
aggregate. 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.