On the velocity discontinuity of a bubble rising in a viscoelastic fluid

What is it about?

We examine the abrupt increase in the rise velocity of an isolated bubble in a viscoelastic fluid occurring at a critical value of its volume. This “velocity discontinuity”, in most of the experiments involving shear-thinning fluids, has been somehow associated with the change of the shape of the bubble to an inverted teardrop with a tip at its pole and/or the formation of the “negative wake” structure behind it. The interconnection of these phenomena is not fully understood yet, keeping the mechanism of the “velocity jump” unclear. By means of steady-state analysis, we study the impact of the increase of bubble volume on its steady rise velocity and with the aid of pseudo arc-length continuation, we are able to predict the stationary solutions, which lie even in the discontinuous area in the diagrams of velocity vs. bubble volume. The critical area of missing experimental results is attributed to a hysteresis loop. The use of a boundary-fitted finite element mesh and the open boundary condition are essential for, respectively, the correct prediction of the sharply-deformed bubble shapes caused by the large extensional stresses at the rear pole of the bubble and the accurate application of boundary conditions far from the bubble. The change of shape of the rear pole into a tip favors the formation of an intense shear layer, which facilitates the bubble translation. At a critical volume, the shear strain developed at the front region of the bubble sharply decreases the shear viscosity. This change results in the decrease of the resistance to fluid displacement, allowing the developed shear stresses to act more effectively on bubble motion. These coupled effects are the reason for the abrupt increase of the rise velocity. The flow field for stationary solutions after the velocity jump changes drastically and intense recirculation downstream of the bubble is developed. Our predictions are in quantitative agreement with published experimental results on the velocity jump in fluids with well-characterized rheology.

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Why is it important?

This is a phenomenon first reported in 1965 by Astarita and Apuzzo. Many papers have been published trying to explain it in various ways. We attribute it to a hysteresis loop generated by the combination of fluid elasticity and shear thinning with bubble deformability. Having achieved perfect agreement with experiments, we believe that we have finally resolved it.