What is the maximum wall pressure developed at the time of bubble burst?

Bulk modulus relates the change of volume to change in pressure

B=(v/dv)*dp

dp=B*dv/v

https://www.theleeco.com/support-resources/engineering-tools/fluid-mechanics-for-liquids/bulk-modulus/

Because the initial volume of the bubble remains constant greater the change in volume of the bubble greater the pressure developed at the wall.

Bubble is basically a liquid film enclosing gas within it. When it bursts it's actually the liquid film that fractures. The amount of pressure developed at this time depends upon the volumetric strain stored within the film.

At the time of formation of the bubble the liquid film has to stretch. It's volume increases as it expands. This expansion is stored in the film as volumetric strain. So more the expansion of bubble ,more the strain that will be developed and thus greater the pressure at the time of collapse.

However there are limitations. Maximum strain that can be sustained by the liquid film depends upon intermolecular forces.For water it is hydrogen bonding.

These hydrogen bonds provide cohesive forces that result in high surface tension of water. Meaning water molecules prefer to stick close to each other and occupy a minimum surface area. Expansion of film means that molecules have to be pushed aside overcoming attractive forces. Compression means molecules have to be brought closer together overcoming electronic repulsion. Both need considerable energy input.

As the film expands, limits reach on intermolecular bonds and they start to break and the bubble will collapse. So the liquid film can expand to a maximum value sustained by its intermolecular bonds.

Notes

Giant soap bubbles have been reported that can grow upto 3 meters in length

https://pmc.ncbi.nlm.nih.gov/articles/PMC5347548/

When pressure on a material approaches it's bulk modulus and exceeds it , it will start to deform and eventually fracture.

Expansion occurs not just in fluids but also in solids. Glass expands when its heated. Too much of it can cause cracking. When it cracks it means that volumetric strain induced by thermal stress has exceeded the bulk modulus which is 36gPa for glass.

Certain high pressure experiments use laser to vaporise solid films resulting in shockwaves that generate pressure in hundreds of gigapascals range. If volume expansion during transformation to vapor phase is known pressure can be calculated using bulk modulus equation.

Liquid that have entrained air generally have lower bulk modulus as the air molecules interfere with the intermolecular forces in the liquid that resist compression or expansion.

For example pure water has a very high bulk modulus of 2.2 Gpa. However dissolved air or suspended particles in water lowers this significantly. Air being more hydrophobic causes water film to encapsulate it and form a bubble around it. Because some air is always trapped in water nano bubbles are always found which act as seeds for formation of larger bubbles. In this case it is the hydrophobic force that provides the pressure to cause deformation of liquid film.

Burst areas of bubbles are typically in nm range leading to high pressures in GPA range at the wall. Bubble twall thickness is an important parameter that determines how high the pressure will be. Thinner films represent highly expanded bubbles storing large volumetric strain compared to thick films.

Comments

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Notes by Akshat Jiwan Sharma

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