Particle migration induced by hydrodynamic interparticle interaction in the Poiseuille flow of a Giesekus fluid

Abstract

Particle migration induced by hydrodynamic interparticle interaction in a Poiseuille flow of Giesekus viscoelastic fluid is studied numerically using the direct forcing/fictitious domain method with Weissenberg number 0.1 ≤ Wi ≤ 1.5, mobility parameter 0.1 ≤ α ≤ 0.7, viscosity ratio 0.1 ≤ β ≤ 0.7, block ratio 0.2 ≤ e ≤ 0.4, initial interparticle spacing 0.1 ≤ s ≤ 2.0, and initial vertical position 0.1 ≤ y0 ≤ 0.2. The method is validated by comparing the present results with previous numerical results. The effects of Wi, α, β, e, s and y0 on the particle migration are analyzed. The results showed that a particle tends to move toward the wall with the increases of the elastic effect of the fluid, shear thinning effect, solvent viscosity and block ratio. For three particles in initial parallel arrangement, the trajectory of two particles on the edge is obviously different from that of a single particle. A single particle would move toward the centerline at a definite y0. However, for the case of three particles at a same y0, the upstream particle first migrates a distance toward the wall and then return toward the centerline, while downstream particle migrates quickly to the centerline. This is called abnormal migration. The phenomenon of abnormal migration disappears when the initial interparticle spacing is large enough, and is more obvious when the initial vertical position of particles is close to the wall. The phenomenon of abnormal migration tends to be obvious with the increases of the shear thinning effect, solvent viscosity and the block ratio, but with the decrease of elastic effect of the fluid.