Numerical simulations of particle migration in a viscoelastic fluid subjected to Poiseuille flow

In this work we present 2D numerical simulations on the migration of a particle suspended in a viscoelastic fluid under Poiseuille flow. A Giesekus model is chosen as constitutive equation of the suspending liquid. In order to study the sole effect of the fluid viscoelasticity, both fluid and particle inertia are neglected. The governing equations are solved through the finite element method with proper stabilization techniques to get convergent solutions at relatively large flow rates. An Arbitrary lagrangian-Eulerian (ALE) formulation is adopted to manage the particle motion. The mesh grid is moved along the flow so as to limit particle motion only in the gradient direction to substantially reduce mesh distortion and remeshing. Viscoelasticity of the suspending fluid induces particle cross-streamline migration. Both large Deborah number and shear thinning speed up the migration velocity. When the particle is small compared to the gap (small confinement), the particle migrates towards the channel centerline or the wall depending on its initial position. Above a critical confinement (large particles), the channel centerline is no longer attracting, and the particle is predicted to migrate towards the closest wall when its initial position is not on the channel centerline. As the particle approaches the wall, the translational velocity in the flow direction is found to become equal to the linear velocity corresponding to the rolling motion over the wall without slip.