On the abrupt change of velocity of bubbles rising in non-newtonian liquids

Abstract

The transition from the Stokes to the Hadamard—Rybczynski regime for bubbles rising in non-Newtonian liquids is analyzed in this work, first by using three earlier published analyses of flows of shear-thinning liquids past Newtonian fluid particles and then by considering the possible influence of viscoelasticity. A new approach is then offered which rests on the interaction between the variable viscosity and the surface tension gradient. It is shown that this model predicts accurately the magnitude of the transition, as well as the trend of this transition with respect to the flow index, bubble size, and density difference. It does not, however, offer any insight into why this transition is, in some cases, so abrupt or even discontinuous. It is conjectured that this phenomenon might be due to the elasticity of the ambient liquid.