Experimental and theoretical studies of cross-stream migration of non-spherical particles in a quadratic flow of viscoelastic fluid

Particulate suspension in a viscoelastic fluid is common in industrial applications and in the fields of microbiology and microrheology. When in a quadratic flow, particles migrate in the lateral direction due to the imbalance of normal stress over the particle surface. A detailed understanding on the migration and rotation behavior of non-spherical particles within such system will be vital to developing precise particle manipulation and separation techniques.

In the first part of this work, we developed a theory based on the general second-order fluid model under the limit of weak viscoelasticity (Wi <<1) and solve the polymer force and torque on a non-spherical particle when subject to an arbitrary flow up to quadratic order. For spheroidal particles, we further investigate the combined effect of fluid normal stress ratio (α = ψ2/ψ1), particle geometry and orientation behavior on the overall particle migration trajectory in a quadratic flow. Particles in general gain faster migration speed with the increasing magnitude of α. In addition, the length the particle spans in the shear gradient direction dominates their migration speed. Prolate and oblate particle shows distinct orientation behavior, which leads to difference in overall migration speed towards the flow center.

In the second part of this work, we experimentally verify the theory in a microfluidic system. A suspension of spherical, prolate and oblate polystyrene particle in 8% polyvinylpyrrolidone solution is flowed in a straight glass capillary channel at the rate of vanishing inertia and weak viscoelasticity. We estimate the average particle migration speed by the particle distribution at various distances from the channel inlet. The results show a good agreement with the theory prediction at the corresponding conditions. We also comment on the particle orientation behavior in the microfluidic system.