(416c) Cross-Stream Migration of Non-Spherical Particles in a Second Order Fluid – Theories of Particle Dynamics in Arbitrary Quadratic Flows (i.e., Pressure Driven Flows)

Particle migration in viscoelastic suspensions is vital in many applications in the biomedical community and the chemical/oil industries. Previous studies in viscoelastic media provided insight on the dynamics of spherical particles in simple shear viscoelastic flows, yet the combined effect of more complex flow profiles and particle shapes on the particle motion is underexplored. We study the dynamics of arbitrary-shaped particles in a second-order fluid, in a flow profile up to quadratic order. For the two model constants ψ₁ and ψ₂ (first and second normal stress coefficient) we assume the relationship ψ₁ = -2 ψ₂ so that the flow dynamics will behave as a Stokes flow with modified fluid pressure. The assumption greatly simplifies the mathematical procedure and allows us to qualitatively capture the fundamental physics in any slow, viscoelastic flow. We apply multipole expansion approximation to derive the analytical expressions for the polymeric force and torque on an arbitrary-shaped particle. The solutions compared well to previous studies on spheres as well as to our boundary element method (BEM) simulation for arbitrary shaped particles. We apply the derived solutions to study the dynamics of sphere, spheroids (prolate & oblate) and ellipsoid in a quadratic flow of second-order fluid. We examine the particle migration behavior at different positions in a pressure driven flow, as well as the translational and rotational trajectories of the particles. We find that particles tend to migrate towards the flow center and orient themselves along the flow direction when under the influence of polymeric force and torque. We also find that particle position, shape and orientation post significant effects on their migration behaviors. Their influences are examined in this work. We summarize by discussing the future directions for experimental studies on particle dynamics as well as for extending current theory towards more complicated systems.