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 suspendin
g 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 throu
gh the finite element method. A
DEVSS/SUPG
formulation with a lo
g-representation of the conformation tensor is implemented, assurin
g stable and conver
gent results up to hi
gh flow rates. Particle motion is handled throu
gh an ALE
formulation. To optimize the computational effort and to reduce the remeshin
g and projection steps required when the mesh becomes too distorted, a ri
gid motion of the
grid in the flow direction is performed, so that, in fact, the particle moves alon
g 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 cross-flow 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 [14].