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Figure. The trace of the configuration tensor A around a rising bubble, trA, from direct numerical simulations, showing that the trace is maximum at the trailing end of the bubble (left illustration). Also notice that the trailing end of the bubble is cup-shaped and the wake is negative as the velocity vectors in the wake point away from the bubble (right illustration).
A bubble released from rest in a liquid accelerates and, as its velocity increases, deforms because of the stresses acting on its surface. The shape of the deformed bubble after it reaches a steady velocity depends on many factors, including its volume which, together with the properties of the ambient liquid, determines the rise velocity. In a Newtonian liquid, at large Reynolds numbers (attained when the bubble volume is relatively large), the bubble assumes a mushroom-like shape.
In a viscoelastic liquid, on the other hand, a small bubble remains approximately spherical, but as the bubble volume is increased it deforms into a prolate shape. Furthermore, there is a critical volume above which the bubble develops a cusp-shaped trailing end due to the extensional nature of the viscoelastic stresses in the region near the trailing end.
Another interesting feature lies in the fact that the flow pattern in the wake of a bubble rising in a viscoelastic liquid is quite different from that in a Newtonian liquid. Specifically, in the former case for certain parameter values, there is an additional vortex ring in the surrounding flow corresponding to the existence of a negative wake.
This, in a way, is similar to the case of a jet engine where the thrust in the forward direction is generated by ejecting gases at a fast speed in the reverse direction (Newton’s third law); the difference being that in the present study the negative wake arises simply due to the viscoelasticity of the fluid. We are using direct numerical simulations and experiments to understand this process.