## BUBBLE RISE AND DEFORMATION IN A NON-NEWTONIAN FLUID IN A SQUARE DUCT
## ResumoThe rise of a bubble in a stagnant liquid column of a Newtonian fluid such as water and various oils has been pursued for a large number of years. When the bubbles are small, their shapes are nearly spherical. However, when the bubbles are large, they deform considerably as a result of the local shear and pressure forces induced by the surrounding flow field. Several complex shapes such as ellipsoid, spheroid, spherical cap, and skirted spherical cap have been observed. The drag and dynamics of such drops are quite complex. However, when the surrounding liquid is non-Newtonian, the bubble deformation and rise velocity can be far more complex as the surrounding fluid viscosity is a function of the velocity field and highly nonlinear. In this work, we have developed a GPU based multiphase flow code that implements an accurate algorithm for treating the surface tension force. In this method the surface tension force is modeled as a gradient of a new pressure field, which is computed by solving an additional pressure Poisson equation (PPE). In this paper, we present numerical results of the motion of a bubble in shear-thinning and shear-thickening fluids. Calculations have been performed for different Bond and Morton numbers. Results of bubble rise-velocity and bubble deformation are presented for different values of the power law index. |

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