# Dynamics of Particle Migration in Confined ViscoElastic Poiseuille Flows

## TL;DR

This study investigates particle migration in confined viscoelastic flows, confirming theoretical predictions that migration velocity scales with Weissenberg number and confinement, while highlighting slight overestimations by models.

## Contribution

It provides experimental validation of the scaling law for particle migration velocity in dilute polymer solutions using advanced 3D particle tracking.

## Key findings

- Migration velocity scales as Wi * β^2
- Viscoelastic properties characterized accurately
- Theoretical models slightly overestimate focusing efficiency

## Abstract

Particles migrate in the transverse direction of the flow due to the existence of normal stress anisotropy in weakly viscoelastic liquids. We test the ability of theoretical predictions to predict the transverse velocity migration of particles in a confined Poiseuille flow according to the viscoelastic constitutive parameters of dilute polymers solutions. Firstly, we carefully characterize the viscoelastic properties of two families of dilute polymer solutions at various concentrations using shear rheometry and capillary breakup experiments. Secondly, we develop a specific 3D particle tracking velocimetry method to measure with a high accuracy the dynamics of particles focusing in flow for Weissenberg numbers Wi ranging from $10^{-2}$ to $10^{-1}$ and particle confinement $\beta$ of 0.1 and 0.2. The results show unambiguously that the migration velocity scales as $\text{Wi}\beta^2$, as expected theoretically for weakly elastic flows of an Oldroyd-B liquid. We conclude that classic constitutive viscoelastic laws are relevant to predict particle migration in dilute polymer solutions whereas detailed analysis of our results reveals that theoretical models overestimate by a few tenth the efficiency of particle focusing.