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 motion of a two-dimensional circular cylinder in Couette flow and in Poiseuille flow of an Oldroyd-B fluid. Both neutrally buoyant and nonneutrally 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 centreline. 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 centreline 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 centreline of the channel in a viscoelastic fluid than in a Newtonian fluid. Marked effects of shear thinning are documented and discussed. Disciplines Engineering | Mechanical Engineering Comments Suggested Citation: Huang, P.Y., James J. Feng, Howard H. Hu and Daniel D. Joseph. (1997). Direct simulation of the motion of solid particles in Couette and Poiseuille flows of viscoelastic fluids. Journal of Fluid Mechanics. Vol 343. p. 73-94. Copyright 1997 Cambridge University Press. http://dx.doi.org/10.1017/S0022112097005764 This journal article is available at ScholarlyCommons: http://repository.upenn.edu/meam_papers/210 J. Fluid Mech. (1997), Šol. 343, pp. 73–94. Printed in the United Kingdom # 1997 Cambridge University Press 73 Direct simulation of the motion of solid particles in Couette and Poiseuille flows of viscoelastic fluids By P. Y. HUANG, J. FENG, H. H. HU  D. D. JOSEPH "Department of Aerospace Engineering and Mechanics and the Minnesota Supercomputer Institute, University of Minnesota, Minneapolis, MN 55455, USA #Department of Chemical Engineering, University of California, Santa Barbara, CA 93106, USA $Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104, USA (Received 2 June 1996 and in revised form 4 February 1997) This paper reports the results of direct numerical simulation of the motion of a twodimensional circular cylinder in Couette flow and in 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 centreline. 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 centreline 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 centreline of the channel in a viscoelastic fluid than in a Newtonian fluid. Marked effects of shear thinning are documented and discussed.