When, how, and why the path of an air bubble rising in pure water becomes unstable.

Recently, [Herrada, M. A. and Eggers, J. G., Proc. Natl. Acad. Sci. U.S.A. 120, e2216830120 (2023)] reported predictions for the onset of the path instability of an air bubble rising in water and put forward a physical scenario to explain this intriguing phenomenon. In this Brief Report, we review a series of previously established results, some of which were overlooked or misinterpreted by the authors. We show that this set of findings provides an accurate prediction and a consistent explanation of the phenomenon that invalidates the suggested scenario. The instability mechanism actually at play results from the hydrodynamic fluid-body coupling made possible by the unconstrained motion of the bubble which behaves essentially, in the relevant size range, as a rigid, nearly spheroidal body on the surface of which water slips freely.

Spontaneous spinning of a dichloromethane drop on an aqueous surfactant solution.

We report a series of experiments carried out with a dichloromethane drop deposited on the surface of an aqueous solution containing a surfactant, cetyltrimethylammonium bromide. After an induction stage during which the drop stays axisymmetric, oscillations occur along the contact line. These oscillations are succeeded by a spectacular spontaneous spinning of the drop. The latter quickly takes the form of a two-tip 'rotor' and the spinning rate stabilizes at a constant value, no longer varying despite the gradual changes of the drop shape and size. The drop eventually disappears due to the continual dissolution and evaporation of dichloromethane. Schlieren visualizations and particle image velocimetry are used to establish a consistent scenario capable of explaining the evolution of the system. The Marangoni effect induced by the dissolution of dichloromethane in the drop vicinity is shown to be responsible for the observed dynamics. Arguments borrowed from dynamical systems theory and from an existing low-order model allow us to explain qualitatively why the system selects the spinning configuration. The geometry of the immersed part of the drop is shown to play a crucial role in this selection process, as well as in the regulation of the spinning rate.

Weakly nonlinear model with exact coefficients for the fluttering and spiraling motion of buoyancy-driven bodies.

Gravity- or buoyancy-driven bodies moving in a slightly viscous fluid frequently follow fluttering or helical paths. Current models of such systems are largely empirical and fail to predict several of the key features of their evolution, especially close to the onset of path instability. Here, using a weakly nonlinear expansion of the full set of governing equations, we present a new generic reduced-order model based on a pair of amplitude equations with exact coefficients that drive the evolution of the first pair of unstable modes. We show that the predictions of this model for the style (e.g., fluttering or spiraling) and characteristics (e.g., frequency and maximum inclination angle) of path oscillations compare well with various recent data for both solid disks and air bubbles.

Dynamical model for the buoyancy-driven zigzag motion of oblate bodies.

We describe a dynamical model that predicts the zigzag motion of disks and oblate spheroids moving freely in a viscous liquid over a continuous range of aspect ratios and Reynolds numbers. This model combines the generalized Kirchhoff equations to describe the linear and angular momentum balances for the fluid-body system with a dynamical model for the wake-induced force and torque that incorporates the main characteristics of the wake dynamics deduced from previous experimental observations. The resulting model is shown to be able to reproduce quantitatively the oscillatory paths measured experimentally.

Path instability of a rising bubble.

We model the problem of path instability of a rising bubble by considering the bubble as a spheroidal body of fixed shape, and we solve numerically the coupled fluid-body problem. Numerical results show that this model exhibits path instability for large enough values of the control parameters. The corresponding characteristics of the zigzag and spiral paths are in good agreement with experimental observations. Analysis of the vorticity field behind the bubble reveals that a wake instability leading to a double threaded wake is the primary cause of the path instability.