Cross-stream migration of non-spherical particles in a second-order fluid

Particle migration in viscoelastic suspensions is vital in many applications in the biomedical community and the energy industries. Previous studies have provided insight on the motion of spherical particles in simple viscoelastic flows, yet the combined effect of more complex flow profiles and particle shapes is underexplored. Here, we develop approximate, analytical expressions for the polymeric force and torque on an arbitrary-shaped particle in a second-order fluid, subject to a general quadratic flow field. This model is exact for the case when the first and second normal stress coefficients satisfy ψ₁ = -2ψ₂. In shear driven flows, we observe that spheroidal particles adjust their orientation to align their longer axis along the vorticity direction, although significant deviations from slender body theories occur for finite aspect ratios. In pressure driven flows, we identify scaling theories to quantify how the particle lift depends on shape for a wide variety of shapes. We find that prolate particles slowly transition to a log-rolling state as they approach the flow center, with the lift initially being larger than that of an equal-volume sphere, but then becoming smaller as log-rolling emerges. Lastly, we extend our analysis towards more complicated systems (ψ₁ ≠ -2ψ₂).