[Paper Review] Antibubbles: evidences of a critical pressure

S. Dorbolo, Nicolas Vandewalle|arXiv (Cornell University)|May 7, 2003

Fluid Dynamics and Heat Transfer1 references3 citations

TL;DR

This study investigates antibubbles—thin air shells enclosing liquid globules—by demonstrating that their stability is governed by a critical pressure threshold. Using a modified Laplace law and accounting for surfactant layer interactions, the authors show that increasing hydrostatic pressure reduces the air shell thickness until van der Waals forces dominate, causing collapse at a critical depth of approximately 120 cm, with variations linked to atmospheric pressure changes.

ABSTRACT

We present experimental investigations of antibubbles. Such an unusual fluid object is a thin spherical air shell surrounding a liquid globule. We explain how to produce them and we study their stability. By overweighting antibubbles with a small amount of salt, they sink and pop at a definite depth. A critical depth related to a critical pressure has been found. A modified Laplace law describes the air shell thickness evolution with respect to pressure. This law combined with surfactant layers interaction allows to explain the critical depth for antibubble stability.

Motivation & Objective

• To experimentally investigate the stability of antibubbles, which are rare fluid entities consisting of a thin air shell enclosing a liquid globule.
• To determine the physical mechanisms behind antibubble popping, particularly the role of pressure and intermolecular forces.
• To establish a critical depth threshold related to a critical pressure that triggers antibubble collapse.
• To explore the influence of surfactant layers and disjoining pressure on the stability of the air shell.
• To validate a modified Laplace law for predicting air shell thickness evolution under pressure.

Proposed method

• Antibubbles were produced by dripping liquid streams into a 200 cm tall, 30 L water-detergent mixture column, forming stable antibubbles via Rayleigh-Plateau instabilities.
• A copper wire connected the liquid source to the cell to prevent electrical potential differences, enhancing air film stability.
• Heavy antibubbles were created by adding salt, enabling controlled free-fall motion and depth-dependent observation of popping.
• Interference fringes (Newton ring-like) were used to estimate the air shell thickness at ~3 μm via optical imaging.
• The modified Laplace law, $ \varepsilon = \frac{2\gamma}{\Delta p_2} - R $, was applied to relate air shell thickness $ \varepsilon $ to pressure difference $ \Delta p_2 $, incorporating hydrostatic and surfactant contributions.
• Disjoining pressure from surfactant layer interactions (Van der Waals attraction and electrostatic repulsion) was modeled to explain the critical thickness $ \varepsilon_c $ at which collapse occurs.

Experimental results

Research questions

• RQ1 What causes the sudden popping of antibubbles at a specific depth in a liquid column?
• RQ2 How does hydrostatic pressure affect the thickness of the air shell in an antibubble?
• RQ3 What role do surfactant layer interactions play in determining the critical thickness for antibubble stability?
• RQ4 Why does the critical depth for popping vary slightly between experimental sessions?
• RQ5 Can a modified Laplace law accurately describe the thickness evolution of the air shell under increasing pressure?

Key findings

• Antibubbles consistently pop at a critical depth of approximately 120 cm, with slight variations (116–148 cm) attributed to daily atmospheric pressure fluctuations.
• A 10% change in air shell thickness $ \varepsilon $ is predicted when antibubbles sink to 150 cm depth, sufficient to cause observable interference fringe shifts.
• The modified Laplace law $ \varepsilon = \frac{2\gamma}{\Delta p_2} - R $ accurately describes the inverse relationship between pressure difference and air shell thickness.
• The critical thickness $ \varepsilon_c $ corresponds to the point where Van der Waals attraction between surfactant layers overcomes electrostatic repulsion, leading to film collapse.
• Electrostatic screening is negligible in the air shell due to the low dielectric constant of air, making antibubbles highly sensitive to interfacial potential differences.
• The presence of a copper wire connection between the liquid source and cell significantly stabilizes the air film, indicating the importance of eliminating electrical potential differences.