Elasto-Inertial Focusing and Separation Mechanisms of Particles in Shear-Thinning Viscoelastic Fluid in Rectangular Microchannels*

The focusing and separation of particles in rectangular channel flow of shear-thinning viscoelastic fluid is investigated. Flow parameters are chosen to fix the elasticity number to El = 18 in order to ensure the elasto-inertial regime. Experiments and 3D finite element simulations are performed to study the effects of flowrate, particle size, and the extent of shear-thinning property of the fluid on the focusing position of particles. The Giesekus constitutive equation is used in the simulations to capture the shear-thinning and viscoelastic behaviors of the PEO solution. The general focusing pattern is due to the interplay between the elastic and shear-gradient lift forces, as well as the secondary flow transversal drag force that is caused by the non-zero second normal stress difference (N₂₎. At low flowrate with the Weissenberg number Wi = 3.6, both the elastic force and secondary flow effects push the particles towards the channel center. However, at high flowrate, Wi = 18, the elastic force direction is reversed in the central regions. This remarkable behavior of the elastic force, combined with the enhanced shear-gradient lift at high flowrate, will push the particles away from the channel center. The competition between the aforementioned forces causes the bifurcation of the focusing position into two streams that equilibrate in the intermediate region between the channel center and the walls. Owing to the different scaling of these competing forces with the particle diameter, smaller sized particles focus closer to the channel center, and hence, particle separation can be achieved at the channel outlet. Additionally, precise prediction of the focusing position is found to be strongly related to the correct estimation of the shear-thinning extent of the carrying medium in the simulations. The shear-thinning will also gives rise to the unique behavior of the inertial forces near the channel walls which is linked to the ‘warped’ velocity profile in such fluid.