What is the pressure on the bubble wall as it explodes? At what velocity does the bubble wall collapse?

Bubble collapse is actually 2 things

1.Rupture/spalling of the outer water film leading to shockwaves inside gas.

2. Implosion/compression of the inner gas leading to sonoluminescence

To calculate the pressure at the bubble wall we can plug in numbers in the expression for bulk modulus

K=v*dp/dv

dp is the change in pressure

dv is the change in volume

v is the initial volume

At 1% change in volume with K=2.22*10^9 pa for water

2.22*10^9=V*dp/(1.01v-v)

2.22*10^9*.01=dp

2.2*10^7 pa

or 22 Mpa

To calculate the velocity at which the film ruptres we need to derive an expression that relates stress at fracture to known parameters like volume and mass.

Work done to fracture the film,W=F*d*a/a

Where a is the area d is the distance , f is the force applied and w is the work done.

This can be rewritten as

W=stress*volume

The work done will be equal to kinetic energy acquired by the ruptured film

.5mv2=stress*volume

V=√2*stress*volume/m

Rewriting this expression in terms of density

V=√2*stress/p

Plugging in values

V=√2*2.2*10^7/10^3

V=209.76m/s

Some notes and questions

Bulk modulus is defined as resistance of a material to compression. It is the increase in pressure required to cause the decrease in volume.

How does bulk modulus relates to atomic bonds?

What is the max energy that can be released as a material breaks?

If all the bonds in water film broke and it converted to steam what would be the resultant pressure?

Given that expansion is just the opposite of compression does bulk modulus hold true for increase in volume of the material as a result of internal pressure? As opposed to decrease in volume due to external pressure?

Is bulk modulus the same as the pressure developed inside a material as it forms?

Expansion during explosion of bubble means breaking of hydrogen bonds in water film.

When the bubble explodes all of the compressed energy in the fluid film is released resulting in a large pressure at the wall.

Bubbles are ideal impactors as they release most of the energy within them upon the substrate on which they impact resulting in localised fractures and spalling.

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