Creeping flow of a wormlike micelle solution past a falling sphere: Role of boundary conditions

Creeping flow of a wormlike micelle solution past a falling sphere with varying surface roughness is considered. A combination of particle tracking velocimetry, particle image velocimetry and microscopy is used to obtain detailed information on the flow of the wormlike micelle solution based on CTAB/NaSal (9 mM/9 mM) around the falling spheres. We find that the surface roughness strongly affects the dynamics of the sphere motion in wormlike micelles such that roughened spheres fall with higher terminal velocities than smooth spheres. In addition, for the roughened spheres the stagnation point is closer to the sphere center of mass, and the magnitude of the negative wake is stronger. We also report, for the first time, formation of micron-size air bubbles at the surface of roughened spheres that are responsible for these unusual results. When these microbubbles are removed, roughened spheres fall with similar velocities as smooth spheres. The latter result may be considered as indirect evidence for no-slip boundary conditions in this CTAB/NaSal system. This hypothesis is further validated with local velocity profile measurements for the wormlike micelle solution sheared in a custom built Taylor-Couette geometry.