Global linear stability of a bubble rising in the presence of a soluble surfactant

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Abstract
We study the stability of the bubble rising in the presence of a soluble surfactant numerically and experimentally. For the range of surfactant concentrations considered, the Marangoni stress almost immobilises the interface. However, the non-zero surface velocity is crucial to understanding the surfactant behaviour. Global linear stability analysis predicts the transition to an oblique path above the threshold of the Galilei number (the bubble radius). This transition is followed by the coexistence of stationary and oscillatory instabilities as the Galilei number increases. These predictions agree with the experimental observations without any fitting parameters. We evaluate the bubble deformation, hydrostatic pressure variation and perturbed viscous stress. The perturbation of the velocity field causes a destabilising vortex in the rear of the bubble, while the perturbed viscous stress produces a torque opposing this vortex. We found that the torque significantly decreases above the critical Galilei number, which may constitute the origin of instability. The linear stability analysis and the experiments were conducted for Surfynol, which can be regarded as a fast (fast-kinetics) surfactant. Our experiments show the considerable differences between the rising of bubbles in the presence of a fast and a non-fast surfactant.

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