CLOSED-FORM SOLUTION FOR THE ORIENTATION FIELD IN A CENTER-GATED DISK

The orientation field induced by the steady, radially diverging, Newtonian flow between flat, parallel disks is studied. Exact solution for the three-dimensional rotation of a rigid, hydrodynamicatly isolated, neutrally buoyant, non-Brownian, slender particle is developed throughout the flow domain from an Eulerian viewpoint. Hence, a closed-form expression is obtained for the orientation distribution, which represents the accurate spatial characterization of the orientation field. In addition, the accuracy of the closure approximations used in complex suspension flow simulations is investigated. Both hybrid and quadratic closure approximations are found to yield considerably inaccurate results, including incorrect asymptotic behavior. The exact solution indicates a stable skin-core orientation structure at large distances from the inlet, which is also confirmed by the available experimental data. © 1995, The Society of Rheology. All rights reserved.