## Direct simulation of the motion of solid particles in Couette and
Poiseuille flows of viscoelastic fluids

*P.Y. Huang, J. Feng, H.H. Hu, and D.D. Joseph*

ABSTRACT: This paper reports the results of direct numerical simulation of
the motion of a two- dimensional circular cylinder in Couette flow and
Poiseuille flow of an Oldroyd-B fluid. Both neutrally buoyant and non-neutrally
buoyant cylinders are considered. The cylinder's motion and the mechanisms
which cause the cylinders to migrate are studied. The stable equilibrium
position of neutrally buoyant particles varies with inertia, elasticity,
shear-thinning and the blockage ratio of the channel in both shear flows.
Shear-thinning promotes the migration of the cylinder to the wall while inertia
causes the cylinder to migrate away from the wall. The cylinder moves closer to
the wall in a narrower channel. In a Poiseuille flow, the effect of elastic
normal stresses is manifested by an attraction toward the nearby wall if the
blockage is strong. If the blockage is weak, the normal stresses act through
the curvature of the inflow velocity profile and generate a lateral force that
points to the centerline. In both cases, the migration of particles is
controlled by elastic normal stresses which in the limit of slow flow in two
dimensions are compressive and proportional to the square of the shear rate on
the body. A slightly buoyant cylinder in Couette flow migrates to an
equilibrium position nearer the centerline of the channel in a viscoelastic
fluid than in a Newtonian fluid; On the other hand, the same slightly buoyant
cylinder in Poiseuille flow moves to a stable position farther away from the
centerline of the channel in a viscoelastic fluid than in a Newtonian fluid.
Marked effects of shear thinning are documented and discussed.

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*Last updated October 16, 2000*