Three-Dimensional DLM/FD Methods for Simulating the Motion of Spheres in Bounded Shear Flows of Oldroyd-B Fluids



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In this dissertation, we present a novel distributed Lagrange multiplier/fictitious domain (DLM/FD) method for simulating fluid-particle interaction in Newtonian and Oldroyd-B fluids under creeping conditions. The categories go as follows: terminal speed of single ball in Newtonian fluid, rotating speed of single ball for the Weissenberg number up to 5.5, trajectories migration and two ball encounters in a three dimensional (3D) bounded shear flow for the Weissenberg number up to 1. For rotating speed, two different methodologies have been considered and the results are consistent with the exponential results for the Weissenberg number up to 1. For trajectories migration, the ball in Oldroyd-B fluid migrates toward the moving wall and it moves faster under higher value of the Weissenberg number. For two ball encounters, the pass and return trajectories of the two ball mass centers are similar to those in a Newtonian fluid, but they lose the symmetry due to the effect of elastic force arising from viscoelastic fluids. A chain of two balls can be formed in a bounded shear flow driven by the upper wall, depending on the value of the Weissenberg number and the initial vertical displacement of the ball mass center to the middle plane between two walls, and then such chain tumbles and migrates.



Oldroyd-B fluids, Binary encounter