DIRECT SIMULATION OF THE SEDIMENTATION OF ELLIPTIC PARTICLES IN OLDROYD-B FLUIDS

Cross-stream migration and stable orientations of elliptic particles f alling in an Oldroyd-B fluid in a channel are studied. We show that th e normal component of the extra stress on a rigid body vanishes; later al forces and torques are determined by the pressure. Inertia turns th e long side of the ellipse across the stream and elasticity turns it a long the stream; tilted off-centre falling is unstable. There are two critical numbers: the elasticity and Mach numbers. When the elasticity number is smaller than critical the fluid is essentially Newtonian wi th broadside-on falling at the centreline of the channel. For larger e lasticity numbers the settling turns the long side of the particle alo ng the stream in the channel centre for all velocities below a critica l one, identified with a critical Mach number of order one. For larger Mach numbers the ellipse flips into broadside-on falling again. The c ritical numbers are functions of the channel blockage ratio, the parti cle aspect ratio and the retardation/relaxation time ratio of the flui d. Two ellipses falling near to each other, attract, line-up verticall y and straighten-out with long sides vertical. Stable, off-centre tilt ing is found for ellipses falling in sheer-thinning fluids and for cyl inders with flat ends in which particles tend to align their longest d iameter with gravity.