Wall slip effects on the fiber orientation of a short-fiber suspension in hyperbolic channel flow

TL;DR

This study examines how wall slip influences fiber orientation in hyperbolic channel flow, revealing increased fiber alignment near walls with higher slip coefficients using advanced tensor modeling and numerical methods.

Contribution

It introduces a novel analysis of wall slip effects on fiber orientation in hyperbolic flows, extending previous no-slip models with new analytical and numerical approaches.

Findings

Fiber orientation shifts from shear to alignment as flow progresses.

Higher slip coefficients lead to more pronounced fiber alignment near walls.

Flow near the midplane becomes more extensional with increased slip.

Abstract

We investigate the effect of wall fluid slip on the orientation of non-Brownian, short, rigid, and high aspect ratio cylindrical fibers suspended in a Newtonian fluid in flow through a symmetric hyperbolic planar channel. The fiber orientation is described using a second-order tensor formulation that accounts for fiber-fiber interactions and employs a hybrid closure to approximate the fourth-order orientation tensor, while neglecting the extra-stress contribution of the fibers to the total stress tensor. Building on our previous work on the no-slip case (Housiadas, Beris and Advani, J. Rheol., 2025), the analytical Newtonian velocity field that has been obtained via the extended lubrication theory is utilized (Sialmas and Housiadas, Eur. J. Mech. B Fluids, 2024). Corresponding to this velocity field, the magnitude of the rate-of-deformation decreases as the slip coefficient increases. The resulting equations for the orientation tensor are solved numerically using a fully implicit finite difference method.The results show that the fiber orientation gradually evolves from its initial pure-shear state at the inlet toward a more aligned configuration as the channel exit is approached.The region of higher fiber alignment, that is most pronounced at the midplane where the flow is purely extensional, extends further toward the walls as the slip increases.