Fiber orientation in hyperbolic channel flow of a semidilute short-fiber suspension

We investigate the orientation of non-Brownian, short, rigid, infinitely slender cylindrical fibers suspended in a Newtonian fluid by analyzing their behavior in the flow through a symmetric hyperbolic planar channel. The fiber orientation is described using the second-order tensor formulation developed by Advani and Tucker [J. Rheol. 31, 751–784 (1987)], which allows one to account for fiber–fiber interactions. A hybrid closure is used to approximate the fourth-order orientation tensor. For a semidilute fiber suspension, we neglect the contribution of the fibers to the stress tensor, decoupling the orientation from the flow problem. For the latter, the Newtonian solution is derived based on the extended lubrication theory by Sialmas and Housiadas [Eur. J. Mech. B Fluids 108, 272–285, (2024)]. First, it is shown that the orientation tensor equations decouple from those in the bulk along the wall and the midplane, leading to the same solutions as for simple shear and transient extensional flow, respectively. Second, the orientation tensor is evaluated in rotated components, developed following a boundary-fit mapping, thereby removing the jump discontinuity of the original components at the inlet of the hyperbolic section of the channel. The final equations are solved numerically using pseudospectral and finite-difference methods. The results indicate that the fiber orientation gradually reorients from its initial state to a more aligned state at the channel exit. This alignment is more pronounced at the midplane due to the strong extensional nature of the flow in that plane. The dependence of fiber orientation on the channel's aspect ratio, contraction ratio, and interaction diffusion coefficient is also investigated and presented parametrically.