Finite element modeling of particle interactions in creeping flow of yield stress materials

Finite element numerical simulation is used to investigate the interactions of particles in creeping flow of a yield stress material. A continuous approximation of the Bingham plastic constitutive equation, characterized by a regularization parameter, is used. A novel method of determining the location and shape of yield surfaces by examining trends in the scaled strain rate with regularization parameter is developed. This method is applied to flow past a single rigid sphere, two rigid spheres translating co-linearly, and flow past a single spherical bubble.; The results for flow past a single rigid sphere show good agreement with results previously reported in the literature. The simulations for two rigid spheres falling in a line demonstrate the short-range interaction characteristic of yield stress materials. Moreover, the range of these interactions was found to be slightly greater than that which would be predicted by linear superposition. The drag force and yield surfaces were calculated for varying sphere separations. A characteristic reduction in drag (up to 30%) was observed at separations below 5.5 sphere radii; the yielded regions surrounding each sphere coalesced into a single yielded region in this regime. The shapes of the yield surfaces calculated for two rigid spheres approaching one another were qualitatively different from those calculated for two spheres falling in a line. The range of interaction was also found to be shorter than for two spheres falling in a line and a slight drag reduction was observed.; Simulations of flow past a spherical bubble showed a drag reduction of 60%–70% compared to rigid sphere calculations. The yield surface calculated for the spherical bubble was found to be qualitatively similar in shape to the rigid sphere result, though the yielded region was significantly smaller. Calculations were performed to examine the effect of isotropic volume expansions on the ability of a bubble to rise. Rise enhancement due to isotropic expansion/contractions was observed, but showed only qualitative agreement with experimental results.