A study of velocity discontinuity for single air bubbles rising in an associative polymer

The motion of air bubbles in aqueous solutions of a hydrophobic alkali-swellable associative polymer is studied in this work. The associative nature of these polymer systems dictates their rheological properties: for moderate values of the shear rate, the formation of structure can lead to a shear-thickening behavior and to the appearance of first normal stress difference. For larger shear rates, the polymer associations can be broken, leading to shear thinning. In general, these fluids show a Newtonian behavior for small values of the shear rate, but behave as viscoelastic liquids for large shear rates. Experimental results show the appearance of a critical bubble volume at which a discontinuity in the relation velocity-volume occurs; however, the velocity increase found in this case is not as large as that previously reported for the case of shear-thinning viscoelastic fluids. The discontinuity is associated with a significant change of the bubble shape: before the critical volume, the bubbles are convex spheroids, while past the critical volume a sharp cusped end appears. The appearance of the tail is also associated with the appearance of an inflection point (change of curvature) on the bubble surface. Moreover, since the rheology of the liquids is measured it was found that the discontinuity, and hence the change of shape, occurs when the elastic nature of the liquid first manifests itself (appearance of a first normal stress difference). A comparison of the measured velocities for small bubbles with predictions from a Stokes-Hadamard law shows a discrepancy. The Newtonian viscosity measured in a viscometric flow was smaller than that determined from a falling-ball arrangement. Considering the viscosity measured under this nonviscometric flow, the comparison between theory and experiments was very good for bubbles having volumes lower than the critical one. Moreover, due to the importance of the elasticity, and due to the change of the shape of the bubble, a dimensionless number formed as the ratio of elastic to surface tension forces clearly defines the change of the behavior for the bubbles rising in these fluids. Finally, a photographic study of the peculiar shapes of the bubble tails, tip-, and edge-streaming phenomena is presented. To our knowledge, experiments in this class of fluids have not been reported to date. (c) 2006 American Institute of Physics.