Non-linear instability of periodic orbits of suspensions of thin fibers in fluids

This paper is concerned with difficulties encountered by engineers when they attempt to predict the orientation of fibers in creation injection molded plastic parts. It known that Jeffery’s equation, which was designed model a single fiber an infinite fluid, breaks down very badly applied, no modifications, this situation. In previous paper, author described how interactions between and viscosity suspension might cause instability, could result simple predictions from equation being wrong. we give some rigorous proofs instability using Floquet Theory. We also show obtain exponential it insufficient consider only two dimensions, although linear still possible.