Dynamic Simulation of Sedimentation of Solid Particles in an Oldroyd-B Fluid

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

*J. Non-Newtonian Fluid Mech*.
**63**, 63-88 (1996)

**Abstract **- In this paper we present a two-dimensional numerical
study of the viscoelastic effects on the sedimentation of particles 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
with the EVSS formalism, and the particles are moved according to their equations
of motion. In a vertical channel filled with a viscoelastic fluid, a particle
settling very close to one side wall experiences a repulsion from the wall;
a particle farther away from the wall is attracted toward it. Thus a settling
particle will approach an eccentric equilibrium position, which depends on
the Reynolds and Deborah numbers. Two particles settling one on top of the
other 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
rotates till the line of centers is aligned with the direction of sedimentation.
The particle-particle interactions are in qualitative agreement with experimental
observations, while the wall repulsion has not been documented in experiments.
The driving force for lateral migrations is shown to correlate with the pressure
distribution on the particle's surface. As a rule, viscoelasticity affects
the motion of particles by modifying the pressure distribution on their surface.
The direct contribution of viscoelastic normal stresses to the force and
torque is not important.