DIRECT SIMULATION OF THE MOTION OF SOLID PARTICLES IN COUETTE AND POISEUILLE FLOWS OF VISCOELASTIC FLUIDS

This paper reports the results of direct numerical simulation of the m otion of a two-dimensional circular cylinder in Couette flow and in Po iseuille flow of an Oldroyd-B fluid. Both neutrally buoyant and non-ne utrally buoyant cylinders are considered. The cylinder's motion and th e mechanisms which cause the cylinders to migrate are studied. The sta ble equilibrium position of neutrally buoyant particles varies with in ertia, elasticity, shear thinning and the blockage ratio of the channe l in both shear flows. Shear thinning promotes the migration of the cy linder to the wall while inertia causes the cylinder to migrate away f rom the wall. The cylinder moves closer to the wall in a narrower chan nel. In a Poiseuille flow, the effect of elastic normal stresses is ma nifested by an attraction toward the nearby wall if the blockage is st rong. If the blockage is weak, the normal stresses act through the cur vature of the inflow velocity profile and generate a lateral force tha t points to the centreline. In both cases, the migration of particles is controlled by elastic normal stresses which in the limit of slow fl ow in two dimensions are compressive and proportional to the square of the shear rate on the body. A slightly buoyant cylinder in Couette fl ow migrates to an equilibrium position nearer the centreline of the ch annel 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 centreline of the channel in a viscoelastic fluid than in a Newtonian fluid. Marked effects of shear thinning are documented and discussed.