Particle migration in bounded shear flow of Giesekus fluids

In this paper, the migrations of two interacting particles in a three-dimensional bounded shear flow of Giesekus fluids are numerically investigated using the direct forcing/fictitious domain method for the Weissenberg number ranging from 0.1 to 1.0, the mobility parameter a which quantifies the shear-thinning effect ranging from 0.01 to 0.7, and the ratio of the solvent viscosity to the total viscosity being 0.1. The model is first validated by comparing the numerical results with the available data in the literature. The effects of the Weissenberg number, the shear-thinning effect, and the initial vertical distance between two particles on the particle migrations are explored. Some of the results are in agreement with the experimental ones. The results show that the pattern of particle migrations can be roughly classified into "returning" and "passing". The variations of particle velocity and pressure field in the "returning" pattern are totally different from those in the "passing" pattern. The separatrix between "returning" and "passing" pattern is dependent on the initial vertical distance between two particles, the Weissenberg number and the shear-thinning effect. With other parameters fixed, the trajectories of particle change from the "returning" pattern to the "passing" pattern as the initial vertical distance between two particles and the Weissenberg number increase, but as the shear-thinning effect decreases.