Fiber suspension in 2D nonhomogeneous flow: The effects of flow/fiber coupling for Newtonian and power-law suspending fluids

A numerical study is presented for fiber suspension flows through a parallel plate channel and a planar 4:1 contraction. Besides examining a Newtonian suspending fluid, a non-Newtonian matrix exhibiting a pseudoplastic behavior and describing a power-law model is also investigated. Furthermore, instead of using orientation tensors for the macroscopic constitutive modeling, the proposed approach addresses the macroscopic scale by describing the fiber orientation state with the probability distribution function (PDF). It enables us to eliminate the error introduced due to the closure approximation when using orientation tensor description as our numerical scheme solves the PDF in both the spatial and configurational spaces. This allows us to correctly implement expressions for both the fiber extra stress, especially for the suspending matrix displaying a pseudoplastic behavior, and the fiber orientation state, describing the configuration. Hence, these two constitutive relations for suspensions are used to perform simulations in which flow and fiber orientation are fully coupled. Results are presented in planar geometries involving channel and 4:1 contraction flows. It is found that the coupling effect flattens the velocity profile for both suspending fluids but has a small impact on the fiber orientation distributions at the geometry outlets. However, in the corner region where a vortex is observed, its magnitude increases with the coupling and this enhancement is more pronounced for the Newtonian suspending fluid. The Newtonian viscosity model is replaced with the Carreau model and results are compared to a bi-viscosity model. It gives qualitatively correct results if no rapid fiber orientation change occurs along the streamlines.