Viscoelasticity-induced migration of a rigid sphere in confined shear flow

Suspensions of solid particles in liquids are often made to flow in devices with characteristic dimensions comparable to that of the suspended particles, the so-called confined situation, as in the case of several microfluidic applications. Combination of confinement with viscoelasticity of the suspending liquid can lead to peculiar effects. In this paper we present the first 3D simulation of the dynamics of a particle suspended in a viscoelastic liquid under imposed confined shear flow. The full system of equations is solved through the finite element method. A DEVSS/SUPG formulation with a log-representation of the conformation tensor is implemented, assuring stable and convergent results up to high flow rates. Particle motion is handled through an ALE formulation. To optimize the computational effort and to reduce the remeshing and pro jection steps required when the mesh becomes too distorted, a rigid motion of the grid in the flow direction is performed, so that, in fact, the particle moves along the cross-streamline direction only. Confinement and viscoelasticity are found to induce particle migration, i.e., transverse motion across the main flow direction, towards the closest wall. Under continuous shearing, three different dynamical regimes are recognized, related to the particle-wall distance. A simple heuristic argument is given to link the crossflow migration to normal stresses in the suspending liquid. The analysis is then extended to a time-dependent shear flow imposed by periodically inverting the direction of wall motion. A slower migration is found for higher forcing frequency. A peculiar effect arises if the inversion period is chosen close to the fluid relaxation time: the migration velocity oscillates around zero, and the overall migration is suppressed. Such novel prediction of a dynamic instability scenario, with the particle escaping the center plane of the channel, and many features of the computed results, are in nice agreement with recent experiments reported in the literature (B.M. Lormand and R.J. Phillips, J. Rheol. 48 (2004) 551-570).