Rigid fiber motion in slightly non-Newtonian viscoelastic fluids

Abstract

The perturbation technique based on the retardation-motion expansion is a simple method to obtain flow solutions at low Weissenberg number. In this context, this perturbation analysis is used to develop simple expressions for the motion of fibers suspended in viscoelastic fluids. In particular, the suspending fluid is characterized by a second-order fluid, Giesekus and PPT (Phan–Thien–Tanner) models, and their derivatives, such as the upper and lower convected Maxwell models. The first-order perturbation results in a similar effective velocity gradient that is exploited to express the translation and rotational motion of a single fiber and the associated extra stress tensor. In terms of a parameter related to the various viscoelastic fluid models, it is found that a fiber aligns along the vorticity direction when subjected to a shear flow. However, when a lower convected Maxwell model is considered, the elongated particle orients in the flow direction, as basically predicted by the Jeffery solution for a Newtonian suspending fluid. Furthermore, the conservation equation for particle concentration leads to particle migration in a pressure-driven flow channel and good agreement is observed with experimental data.