On the fiber orientation in steady recirculating flows involving short fibers suspensions

In this work we present a new numerical strategy to treat the 3D Fokker–Planck equation in steady recirculating flows. This strategy combines some ideas of the method of particles, with a more original treatment of the periodicity condition, which characterizes the steady solution of the FP equation in steady recirculating flows, as usually encountered in some rheometric devices. Using this numerical technique the fiber orientation distribution can be computed accurately in any steady recirculating flow. The simulation results can be used to identify some rheological parameters of the suspension, using an inverse technique, as well as to analyze the validity of some simplified models widely used, which require a closure relation. Thus, in this paper several closure relations of the fourth-order orientation tensor will be discussed in the context of a numerical example involving a steady recirculating flow.