On the non-linear instability of fiber suspensions in a Poiseuille flow

The non-linear instability characteristics of fiber suspensions in a plane Poiseuille flow are investigated. The evolution equation of the perturbation amplitude analogous to Landau equation is formulated and solved numerically for different fiber parameters. It is found that the equilibrium amplitude decreases with the increase of the fiber aspect ratio and volume fraction, i.e. the addition of the fibers reduces the amplitude of the perturbation, and leads to the reduction of the flow instability. This phenomenon becomes significant for large volume concentration and aspect ratio. The mechanism of the reduction of the flow instability is also analyzed by taking into account of the modification of the mean flow and the energy transfer from the mean flow to the perturbation flow.