  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.
