  The imbalance of normal stress around a particle induces its transverse
migration in pressure-driven viscoelastic flow, offering possibilities for
particle manipulation in microfluidic devices. Theoretical predictions align
with experimental evidence of particles migrating towards the center-line of
the flow. However, these arguments have been challenged by both experimental
and numerical investigations, revealing the potential for a reversal in the
direction of migration for viscoelastic shear-thinning fluids. Yet, a
significant property of viscoelastic liquids that remains largely unexplored is
the ratio of solvent viscosity to the sum of solvent and polymer viscosities,
denoted as $\beta$. We computed the lift coefficients of a freely flowing
cylinder in a bi-dimensional Poiseuille flow with Oldroyd-B constitutive
equations. A transition from a negative (center-line migration) to a positive
(wall migration) lift coefficient was demonstrated with increasing $\beta$
values. Analogous to inertial lift, the changes in the sign of the lift
coefficient were strongly correlated with abrupt (albeit small) variations in
the rotation velocity of the particle. We established a scaling law for the
lift coefficient that is proportional, as expected, to the Weissenberg number,
but also to the difference in rotation velocity between the viscoelastic and
Newtonian cases. If the particle rotates more rapidly than in the Newtonian
case, it migrates towards the wall; conversely, if the particle rotates more
slowly than in the Newtonian case, it migrates towards the center-line of the
channel. Finally, experiments in microfluidic slits confirmed migration towards
the wall for viscoelastic fluids with high viscosity ratio.
