Shapes and paths of an air bubble rising inside a liquid are investigated experimentally. About three hundred experiments are conducted in order to generate a phase plot in the Galilei and Eötvös numbers plane, which separates distinct regimes in terms of bubble behaviour. A wide range of the Galilei and Eötvös numbers are obtained by using aqueous glycerol solutions of different concentrations as the surrounding fluid, and by varying the bubble size. The dynamics is investigated in terms of shapes, topological changes and trajectories of the bubbles. Direct numerical simulations are conducted to study the bubble dynamics, which show excellent agreement with the experiments. To the best of our knowledge, this is the first time an experimentally obtained phase plot showing the distinct behaviour of an air bubble rising in a quiescent medium is reported for such a large range of Galilei and Eötvös numbers.
We study the motion of a bubble driven by buoyancy and thermocapillarity in a tube with a non-uniformly-heated walls, containing a so-called "self-rewetting fluid"; the surface tension of the latter exhibits a parabolic dependence on temperature with a well-defined minimum. In the Stokes flow limit, we derive the conditions under which a spherical bubble can come to rest in a self-rewetting fluid whose temperature varies linearly in the vertical direction, and demonstrate that this is possible for both positive and negative temperature gradients. This is in contrast to the case of simple fluids whose surface tension decreases linearly with temperature for which bubble motion is arrested for negative temperature gradients only. In the case of self-rewetting fluids, we propose an analytical expression for the position of bubble arrestment as a function of other dimensionless numbers. We also perform direct numerical simulation of axisymmetric bubble motion in a fluid whose temperature increases linearly with vertical distance from the bottom of the tube; this is done for a range of Bond and Gallileo numbers, and for various parameters that govern the functional dependence of surface tension on temperature. We demonstrate that bubble motion can be reversed and then arrested in self-rewetting fluids only, and not in linear ones, for sufficiently small Bond numbers. We also demonstrate that considerable bubble elongation is possible under significant wall confinement, and for strongly self-rewetting fluids and large Bond numbers. The mechanisms underlying the phenomena observed are elucidated by considering how the surface tension dependence on temperature affects the thermocapillary stresses in the flow.
Is a settling drop equivalent to a rising bubble? The answer is known to be in general a no, but we show that when the density of the drop is less than 1.2 times that of the surrounding fluid, an equivalent bubble can be designed for small inertia and large surface tension. Hadamard's exact solution is shown to be better for this than making the Boussinesq approximation. Scaling relationships and numerical simulations show a bubble-drop equivalence for moderate inertia and surface tension, so long as the density ratio of the drop to its surroundings is close to unity. When this ratio is far from unity, the drop and the bubble are very different. We show that this is due to the tendency for vorticity to be concentrated in the lighter fluid, i.e. within the bubble but outside the drop. As the Galilei and Bond numbers are increased, a bubble displays underdamped shape oscillations, whereas beyond critical values of these numbers, over-damped behavior resulting in break-up takes place. The different circulation patterns result in thin and cup-like drops but bubbles thick at their base. These shapes are then prone to break-up at the sides and centre, respectively.
The axisymmetric dynamics of a bubble rising in a Bingham fluid under the action of buoyancy is studied. The Volume-of-Fluid (VOF) method is used to solve the equations of mass and momentum conservation, coupled to an equation for the volume fraction of the Bingham fluid. A regularised constitutive model is used for the description of the viscoplastic behaviour of the material. The numerical results demonstrate that the rise dynamics are complex for large yield stresses, and for weak surface tension. Under these conditions, for which the bubble is highly deformable, the rise is unsteady and is punctuated by periods of rapid acceleration which separate stages of quasi-steady motion. During the acceleration periods, the bubble aspect ratio exhibits oscillations about unity, whose amplitude and wavelength increase with increasing yield stress and decreasing surface tension. These oscillations are accompanied by the alternating formation and destruction of unyielded
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