(600j) Orientation Dynamics and Stress of Spheroids in Weakly Viscoelastic Fluids

Viscoelastic suspensions are polymeric fluids containing particulate matter. These systems are common in our daily lives, found in foods, consumer products, and pharmaceuticals, as well as biological fluids in our body (e.g., mucous, blood, bacterial suspensions). In this talk, we discuss the orientation dynamics of non-spherical particles in viscoelastic fluids, and the consequence of this behavior on suspension rheology. In Stokes flow, spheroids under shear flow undergo Jeffrey Orbits – i.e., periodic tumbling along a specified path depending on the particle’s initial orientation. When weak fluid viscoelasticity is present, normal stresses alter the long-time orientation behavior, giving rise to log-rolling (alignment along the vorticity direction) for prolate spheroids and tumbling in the flow/gradient plane for oblate spheroids. In this study, we employ a multiple time-scale analysis to predict the viscoelastic correction to Jeffery Orbits at long timescales (times comparable to the polymer relaxation time). We inspect the long-time orientation behavior and establish their stability for different regimes of particle aspect ratio and fluid viscoelasticity. We then determine the average stress of the suspension, determining the O(φ) correction to the long-time effective shear viscosity, extensional viscosity, and normal stress differences in the suspension in shear flow, uniaxial extensional flow, and planar extensional flow (where φ is the particle volume fraction) for different aspect ratios for prolate (needle shaped) and oblate (disk-like) spheroids. Lastly, we discuss effects of fluid inertia on the orientation dynamics and suspension rheology, examining situations where the fluid inertia (Reynolds number) is comparable to fluid viscoelasticity (Weissenberg number).