Sink flows of a suspension of rigid rods: the failure of a similarity solution

Abstract

The flow of a suspension of rigid rods into a sink of finite size which may be either planar or axisymmetric is considered. For low rod concentrations the flow at large distances from the sink is well described by similarity solutions derived by Evans. For larger concentrations, however, these similarity solutions predict unrealistic flows with many regions of inflow and outflow. We show that the flow field far upstream of the sink is then dominated by an eigensolution involving zero net volume flux. This eigensolution is determined. The prediction is compared with the results of a full numerical solution for the flow of a suspension of rods from an infinite reservoir into a finite sink. It is also used to estimate the extent of the vortex enhancement generated by flow through a large but finite contraction. The results are compared with the numerical solutions and experiments of Lipscomb et al. This example shows that the parameter range for which a self-similar flow field is appropriate can be substantially smaller for a non-Newtonian fluid than is the corresponding range in the Newtonian case.