Orientation dynamics and stress of spheroids in weakly viscoelastic fluids

The development of particle orientation in suspensions has a multitude of applications in micro-rheology, active matter, and material science. In Newtonian fluids, spheroids in shear flow undergo periodic tumbling motion along paths called Jeffery Orbits. In the presence of viscoelasticity, normal stresses tend to dampen these oscillations, forcing the particle to attain a steady orientation with respect to the background flow. The orientation dynamics thus exhibits oscillating and decaying components in shear flow. In our study, we employ a multiple time-scale method to predict the viscoelastic correction to Jeffery Orbits at long timescales. We inspect the long-time, i.e., t ~ O(Wi^-1) orientation behavior and establish stability of steady states for different regimes of particle aspect ratio and fluid viscoelasticity. We determine the average stress of the suspension at these long-time orientations.