Orientation dynamics of spheroids in weakly viscoelastic fluids with inertia

Spheroids immersed in fluids with comparable inertia and elasticity are ubiquitous in numerous applications like food technology and polymer processing. In such applications, it is often important to characterize the orientation distribution of particles during flow processing. In this talk, we theoretically examine the motion of a single spheroid under steady shear flow when the suspending fluid has weak inertia (Reynolds number Re << 1) and weak viscoelasticity (Weissenberg number Wi << 1). In Stokes flow (Re = Wi = 0), elongated particles trace periodic Jeffery orbits that depend on the particle’s initial orientation. When weak viscoelasticity or fluid inertia is present, these orbits are no longer degenerate and the orientation drifts slowly to a preferred direction. In viscoelastic fluids, normal stresses make needle-shaped particle take a log-rolling orientation in the vorticity direction, whereas fluid inertia forces the particle towards a tumbling state in the shear-flow plane. Currently, not much is understood about the orientation dynamics when both effects are present – whether one of the two aforementioned behaviors are favored, or something intermediate occurs. We employ a multiple time-scale analysis to predict the drift of Jeffery Orbits at long times, i.e., t ∼ Ο(Wi^-1). We characterize several steady state regimes and comment on their stability for different particle aspect ratios, Reynolds numbers, and Weissenberg numbers.