On the Fiber Orientation in Steady Recirculating Flows Involving Short Fibers Suspensions
Résumé
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 Fokker-Planck 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.
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