Direct Simulation of the Sedimentation of Elliptic Particles in Oldroyd-B Fluids

Cross stream migration and stable orientations of elliptic particles falling in an Oldroyd-B fluid in a channel are studied. We show that the normal component of the extra stress on a rigid body vanishes; lateral forces and torques are determined by the pressure. Inertia turns the longside of the ellipse across the stream and elasticity turns it along the stream; tilted off-center falling is unstable. There are two critical numbers; elasticity and Mach numbers. When the elasticity number is smaller than critical the fluid is essentially Newtonian with broadside-on falling at the centerline of the channel. For larger elasticity numbers the settling turns the longside of the particle along the stream in the channel center for all velocities below a critical one, identified with a critical Mach number of order one. For larger Mach numbers the ellipse flips into broadside-on falling again. The critical numbers are functions of the channel blockage ratio, the particle aspect ratio and the retardation/relaxation time ratio of the fluid. Two ellipses falling nearby, attract, line-up and straighten-out in a long chain of ellipses with longside vertical, all in a row. Stable, off-center tilting is found for ellipses falling in shear thinning fluids and for cylinders with flat ends in which particles tend align their longest diameter with gravity. Disciplines Engineering | Mechanical Engineering Comments Suggested Citation: Huang, P.Y., Howard H. Hu and Daniel D. Joseph. (1997) Direct simulation of the sedimentation of elliptic particles in Oldroyd-B fluids. Journal of Fluid Mechanics. Vol. 362. p. 95-134. Copyright 1997 Cambridge University Press. http://dx.doi.org/10.1017/S0022112094000285 This journal article is available at ScholarlyCommons: http://repository.upenn.edu/meam_papers/211 1 Direct Simulation of the Sedimentation of Elliptic Particles in Oldroyd-B Fluids by P. Y. Huang1, H. H. Hu2 and D. D. Joseph1 1Department of Aerospace Engineering and Mechanics and the Minnesota Supercomputer Institute, University of Minnesota, Minneapolis, MN 55455-0153, USA 2Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104-6315, USA