Numerical simulations of the motion of ellipsoids in planar Couette flow of Giesekus viscoelastic fluids

The motion of neutrally buoyant ellipsoids in a planar Couette flow of Giesekus viscoelastic fluids between two narrowly set plates is numerically simulated with a fictitious domain method. The aspect ratio of the ellipsoid is 4 (i.e., prolate spheroids) and the Deborah number (De) ranges from 0 to 4.0. For a single ellipsoid initially placed in the mid-plane between the two plates, the ellipsoid major axis rotates around the vorticity axis in a kayaking mode at relatively low Deborah numbers, and is tilted in the flow-vorticity plane when the Deborah number exceeds a critical value, with the orientation being closer to the flow direction for a larger De. For a single ellipsoid initially not placed in the mid-plane, the ellipsoid undergoes lateral migration toward the nearby wall, and it is interesting that the ellipsoid turns its orientation to the vorticity axis at relatively small De and a direction close to the vorticity axis at large De (above 3.0), in contrast to the ellipsoid placed in the mid-plane without lateral migration, whose terminal orientation exhibits a kayaking motion at relatively small De and is close to the flow direction for De > 3. As a result, for the multiple-ellipsoid case, there exists a transient stage where the average orientation of the ellipsoids turns toward the vorticity axis for all nonzero Deborah numbers studied, and the orientation close to the vorticity axis can be often observed for the isolated ellipsoids. Both the particle interactions and the wall effect promote the ellipsoids to align with the flow direction. Particle aggregation and the dynamic aligning structures are observed at large Deborah numbers.