Effect of viscoelasticity on the orientational dynamics of a prolate spheroidal particle in simple shear flow: Slender body theory and fully resolved simulations*

Particle-laden viscoelastic/ polymeric flows undergo shearing motion in many processing applications such as injection molding, spin casting, or flow casting. The orientation of prolate spheroidal particles in Newtonian Stokes flow follows one of the degenerate orbits, dependent on the initial condition, known as Jeffery orbits. Using a regular perturbation in low polymer concentration, we develop a slender body theory to characterize the effect of viscoelasticity on the orientational motion of a large aspect ratio particle. Depending on the polymer relaxation time and particle aspect ratio, the theory predicts four qualitatively different behaviors to arrive at a fixed orientation. The particle orientation either spirals across Jeffery orbits or aligns near the flow-vorticity plane and eventually aligns at either the vorticity axis or near the flow axis. We test our theory and investigate higher polymer concentration effects using a novel finite-difference numerical solver written in prolate spheroidal coordinates, which exactly models the particle surface as one of the coordinate surfaces. This code allows us to simulate large aspect ratio particles with fewer mesh points and less computation time than a solver written in Cartesian coordinates.