Jeffery orbits in shear-thinning fluids

TL;DR

This study analyzes how shear-thinning fluids influence the motion of elongated particles, revealing modifications in rotation dynamics and orbit periods without lifting degeneracy of Jeffery orbits.

Contribution

It provides an analytical and numerical investigation of Jeffery orbits in shear-thinning fluids, highlighting effects on rotation rates and orbit periods.

Findings

Shear thinning modifies particle rotation trajectories.

Orbit periods depend on initial orientation in shear-thinning fluids.

Shear thinning effects resemble elongation in Newtonian fluids.

Abstract

We investigate the dynamics of a prolate spheroid in a shear flow of a shear-thinning Carreau fluid. The motion of a prolate particle is developed analytically for asymptotically weak shear thinning and then integrated numerically. We find that shear-thinning rheology does not lift the degeneracy of Jeffery orbits observed in Newtonian fluids but the instantaneous rate of rotation and trajectories of the orbits are modified. Qualitatively, shear thinning has a similar effect to elongating the particle in a Newtonian fluid. The period of rotation increases as the particle slows down more when aligned with the flow due to a reduction of shear stresses. Unlike Jeffery orbits in Newtonian fluids, in shear-thinning fluids the period of orbits depends on the specific trajectory (or initial orientation of the particle).