Simulations of viscoelasticity-induced focusing of particles in pressure-driven micro-slit flow

The cross-streamline migration of a spherical particle in a viscoelastic fluid flowing in a wide slit microdevice is here investigated through 3D finite element simulations. The study is performed by neglecting both fluid and particle inertia, which is a common assumption in microfluidic systems. In order to highlight the role of the suspending liquid rheology, two viscoelastic constitutive equations were chosen, i.e. the Giesekus and the Phan Thien-Tanner models. Because of the large cross-section aspect ratio, the influence of the lateral walls can be neglected, and the migration is unidirectional, along the gap (small) height. For small confinement ratios, i.e. for small particle-gap dimensions ratios, a multistable dynamics is found whereby the particle is driven towards the channel centerplane or the closest wall depending on its initial position through the gap, thus leading to the existence of an unstable separatrix. The position of such a separatrix is strongly influenced by the fluid rheology. For the Giesekus suspending liquid, the centerplane attractive region is always found to be wider than the wall attractive zone, independently of the flow rate. On the other hand, for the Phan Thien-Tanner liquid, large flow rates drastically move the separatrix towards the channel center. Beyond a critical particle size, the multistable behavior disappears and the separatrix collapses on the centerplane or the wall depending on the second normal stress difference. Finally, the calculated particle distributions along the channel gap at different distances from the inlet show that the migration is faster for large particles, higher flow rates, and more shear thinning fluids.