No abstract

This work employs the second-order fluid model to investigate the effect of first and second normal stresses on the motion of spheroidal particles in unbound parabolic flows, where particles migrate toward the flow center. We specifically examine the effects of fluid Weissenberg number Wi and the ratio of normal stress coefficients α = ψ2/ψ1. Previous works have considered the motion of spheroidal particles in the co-rotational limit (α = −0.5), where the effect of fluid viscoelasticity is to modify the fluid pressure but not the shear stresses. Here, we examine all ranges of α that are found for functional complex fluids such as dilute polymer solutions, emulsions, and particulate suspensions and determine how viscoelastic shear stresses alter particle migration. We use perturbation theory and the Lorentz reciprocal theorem to derive the O(Wi) corrections to the translational and rotational velocities of a freely suspended spheroid in an unbound tube or slit flow. Our results show that for both prolate and oblate particles, the viscoelasticity characterized by α significantly affects the particle cross-stream migration, but does not qualitatively change the trends seen in the co-rotational limit (α = −0.5). For a range of α (−0.9 ≤ α ≤ 0) investigated in this work, particles possess the largest mobility when α = −0.9 and smallest mobility when α = 0. Although α does not alter particle rotation at a given shear rate, we observe significant changes in particle orientation during migration toward the flow center because changes in migration speed give rise to particles experiencing different shear histories.

We investigate the cross-stream migration of spheroidal particles in a weakly viscoelastic fluid under various unbound parabolic flows (circular and elliptic tube flow, as well as 2D slit flow). The viscoelastic fluid investigated is a second-order fluid under the co-rotational limit. Our theory finds that the different flow profiles do not significantly alter the migration speed of particles toward the flow centerline, but drastically alter their orientation dynamics. At long times, prolate particles align along the flow direction in a circular tube flow, but undergo log-rolling in a 2D slit flow. We explain the origin of these orientation dynamics, and explain why such behavior can give rise to a similar cross-stream migration velocity. We lastly examine particle motion in an unbound elliptic tube flow with unequal velocity curvature in the two lateral directions. We quantify the conditions under which the long-time particle orientation changes from log-rolling to flow-alignment.

We experimentally investigate the cross-stream migration of spherical, prolate, and oblate particles in a circular tube flow of a weakly viscoelastic fluid (De = O(10-2)) with negligible inertia (Re≈ 0)....

Suspensions of semi-transparent particles such as polystyrene microparticles are commonly used as model systems in the study of micro-rheology, biology, and microfluidics. Holography is a valuable tool that allows one...