Three-Dimensional Orientation Structure in a Radially Diverging Suspension Flow Between Parallel Plates

The orientation structure of slender fibers induced by a steady, radially diverging flow between two flat, parallel disks is investigated. The suspending fluid is Newtonian and the rotational dynamics of individual fibers is assumed to be governed by Jeffery’s theory (1922). The orientation field is characterized by three-dimensional orientation tensors and the exact solution for the rotation of rigid, slender fibers is obtained throughout the flow domain from an Eulerian viewpoint. In addition, the effect of inlet conditions on the final orientation structure is explicitly incorporated into the orientation formulation. For comparison purposes, approximate solutions to the orientation field are obtained from the commonly used tensorial orientation evolution equations. The results show that, although both hybrid and quadratic closure approximations may predict the preferred orientation accurately, the orientation components are considerably inaccurate. Furthermore, the exact results clearly depict a stable skin-core orientation structure through the thickness at large radial distances from the inlet which, to some extent, is found to be dependent on the inlet orientation conditions.