Stress Distribution in Creeping Flow of a Viscoelastic Fluid around a Single Bubble

The stress distribution in creeping flow of a viscoelastic fluid around a single bubble was measured by the transmitted light flow birefringence technique. Distributions of the primary normal stress difference r_zz-r_rr and the shear stress r_rz could be obtained in the flow field around a growing and rising bubble. Moreover, the difference between the principal value of stress directed in the tangential direction and that directed in the normal direction on the bubble surface could be obtained. Observed features of all the distributions were consistent with the viscoelastic behavior of the fluid. The measured stress distribution around the freely rising bubble with a constant velocity was compared with the exact solution for a Newtonian fluid. In contrast with the theoretical result, the distribution of the absolute values of stress is not symmetrical with respect to the horizontal cross-sectional plane of the bubble. The measured values were larger downstream than upstream, especially at the region close to the bubble. This asymmetry is probably due to the viscoelastic property of the fluid. It was also found that the stress distributions for the rising bubble and for the falling rigid sphere were similar to each other except in the region close to the surfaces. The values of r_rz on the side of the bubble were smaller than that of the rigid sphere because the shear stress at the gas-liquid interface was so small that it could be disregarded.