# Sinking Bubbles Physik | Technik

## Ophélie Rivière, 2002 | Binz, ZH

This paper aims to explain the motion of sinking bubbles in a vertically oscillating liquid. The conditions under which the formulas of earlier studies accurately describe the motion of the sinking bubbles have been determined experimentally. In the first part of the paper, it is shown that the static theory applies and in the second part, the regime for which the equation of motion is applicable is determined. In addition, an alternate equation of motion that can be used under different conditions is provided.

#### Fragestellung

Usually, bubbles in a liquid rise due to density difference. It is very counterintuitive to imagine a bubble of air sinking in water. Nevertheless, it is possible to achieve such a motion by creating a pressure inversion. Bubbles always go where the pressure is lowest. Hence, if the pressure at the bottom of the column of liquid becomes lower than ambient pressure, at the surface, the bubble will start moving downwards.
The original task says: “When a container of liquid (e.g. water) oscillates vertically, it is possible that bubbles in the liquid move downwards instead of rising. Investigate the phenomenon.”

#### Methodik

A cylindrical liquid column is driven harmonically by a shaker. At the bottom of the column an opening provides a controlled inlet of air bubbles. A small hole in the top cap ensures ambient pressure.
Due to the driven oscillation induced by the excitor, the bubble’s volume will periodically change size. One differentiates between two states of the bubble, the upwards and downwards acceleration. For high accelerations of the oscillator the bubble volume is significantly greater during the downwards acceleration, a net downward motion is thus observed.
Two types of experiments have been conducted. Firstly, for different frequencies and constant bubble position, the critical amplitude at which the bubbles would remain at the given depth (static motion) was measured. Secondly, the bubbles’ motions were filmed with a high-speed camera and tracked. The experimental data have then been compared with the theory.

#### Ergebnisse

The equation of the static state, which predicts the equilibrium position, has been validated experimentally.
The validity of the equation of motion given in literature has been discussed both experimentally and theoretically. The model was found to be in good agreement with the data for an intermediate Reynolds number range.
As the system is more stable in oil, a modified equation of motion was found to provide a better agreement with experimental data.
A wider parameter range could be investigated in oil, as this system exhibits better stability.

#### Diskussion

Combining theory and experiments, it is visible that the Reynolds number is a good scale of stability of the system, hence, it shows approximately when the respective equations of motions are applicable. Overall, one can achieve the best correspondence at low amplitudes and high bubble depths

#### Schlussfolgerungen

The formula giving the critical values of sinking for bubbles in a given liquid has been validated for the first time. Experiments were conducted in water to verify the existing equation of motion. It was confirmed that the equation only works in a limited range, which was later on determined. To be able to predict more cases of sinking bubbles, experiments were conducted in oil. A modified equation of motion was established and from the experimental results one was able to confirm its accuracy for a broader range. The case in oil offers the advantage of greater stability, hence the use of simpler physics. To sum up, this paper gives an overview of the previous publications, accompanied by thorough qualitative results as well as an additional simple quantitative explanation to the non-trivial problem of sinking bubbles.

#### Würdigung durch den Experten

Prof. Dr. Daniel Weiss

The behavior of bubbles in a surrounding liquid column is investigated experimentally, where the liquid is oscillating along the axis of gravity. It had been known from theoretical work in literature that bubbles can in certain cases sink rather than rise. For the first time this effect has been demonstrated here. The bubble behavior has been investigated quantitatively, their dynamics has been modelled and calculated numerically by solving an ode, good agreement has been found. The report is written in a pleasant way. Overall, the level of the work is comparable to university students’ works.

#### Prädikat:

hervorragend

Sonderpreis Aldo e Cele Daccò – European Union Contest for Young Scientists (EUCYS)

Rämibühl-MNG, Zürich
Lehrer: Dipl. Phys. ETH Daniel Keller