Fiber orientation of a short-fiber suspension in hyperbolic pipe flow including wall slip

We investigate the orientation of non-Brownian, short, rigid, high-aspect-ratio cylindrical fibers suspended in a Newtonian fluid flowing through a three-dimensional axisymmetric hyperbolic pipe. Fiber orientation is described using a second-order orientation-tensor formulation that accounts for fiber–fiber interactions and employs a hybrid closure to approximate the fourth-order tensor, while the extra-stress contribution of the fibers to the total stress tensor is neglected. The flow kinematics are described using an analytical, high-order asymptotic solution in terms of the pipe's aspect ratio that incorporates Navier slip at the wall, developed by Sialmas and Housiadas [Eur. J. Mech. B 108, 272–285 (2024)]. As the slip coefficient increases, the magnitude of the rate-of-deformation tensor in the flow domain decreases overall, leading to significant modifications in the fiber-orientation dynamics. Based on this velocity field, the evolution equations for the orientation tensor are solved numerically. The results show that the fiber orientation gradually evolves from its initial Poiseuille-type distribution at the inlet toward a more aligned configuration as the flow approaches the pipe exit. The region of higher fiber alignment, most pronounced along the symmetry axis where the flow is purely extensional, extends progressively toward the walls with increasing slip. The investigation of the influence of the inlet conditions further demonstrates the ability of the hyperbolic geometry to erase upstream orientation history. The dependence of the fiber orientation on the dimensionless parameters is also examined and discussed.