Balloon inflated by external vacuum: why won't it burst?

[Swamp Thing]

Why doesn't the balloon burst in this video? To me it seems that the differential (guage) pressure between inside and outside the balloon is what matters, and I would think it would be the same as a balloon inflated in the usual way.

https://youtube.com/shorts/3HZ0JkgtpDU?feature=share

 

[Chestermiller]

Maybe the pressure difference is not large enough for the tensile strength of the balloon material to be exceeded?

 

[Swamp Thing]

Isn't it the case that the inflated surface area of the balloon is a measure of the pressure differential? And the area seems to be such that the balloon would normally burst?

 

[jbriggs444]

Isn't it the case that the inflated surface area of the balloon is a measure of the pressure differential? And the area seems to be such that the balloon would normally burst?

There are competing effects at work. But no, the surface area is not a good gauge of the pressure differential. Paradoxically, increasing surface area is compatible with decreasing pressure differential.

If you've ever blown up a balloon by mouth, you may note that it is hard at first and easy after.

Rubber makes things more interesting. Rubber extends elastically only so far. Then it stops. A typical balloon is inflated approximately to this limit and has high tension as a result. One assumes that the balloon in the bell jar is not inflated that full. It has low tension as a result.

 

[hutchphd]

The curvature and tensile strength matter.
For a curved surface the Young-Laplace equation $$\Delta P=-\gamma (\frac 1 R_1 +\frac 1 R_2)$$ gives Pressure differential in terms the principal radii of curvature and the surface tension

Edit: I put in the minus sign

 

[Bandersnatch]

I think this calls for a bit lower-level approach:

 

[Swamp Thing]

I think this calls for a bit lower-level approach:

So the vacuum setup is just a misleading distraction?

 

[Bandersnatch]

I'd say so, yes. The problem is with the assumption that all balloons burst when pierced.

 

[Chestermiller]

The curvature and tensile strength matter.
For a curved surface the Young-Laplace equation $$\Delta P=-\gamma (\frac 1 R_1 +\frac 1 R_2)$$ gives Pressure differential in terms the principal radii of curvature and the surface tension

Edit: I put in the minus sign

For a spherical balloon, the tensile stress in the rubber is $$\sigma=\frac{R}{2h}\Delta P$$where h is the present thickness of rubber. For incompressible rubber, h is related to the initial thickness and radius at low pressure by: $$h=\left(\frac{R_0}{R}\right)^2h_0$$

 

[kuruman]

I think @Chestermiller's answer to the original question is the correct one. I have done this demonstration using what I called a "funny balloon" which the class quickly recognized as a condom. The darn thing filled the entire available volume without bursting until it was constrained from further expansion by the bell jar wall.

 

[sophiecentaur]

the differential (guage) pressure between inside and outside the balloon is what matters

It is and the maximum exterior 'suck' you can get is when ambient pressure is 0Bar. At that stage, the internal air will have expanded somewhat and what started as 1Bar will have reduced considerably so the pressure difference will be a lot less than -1Bar. Simple Boyle's Law would suggest that an increase in internal volume of 4 would produce a pressure difference of 0.25Bar - and so on. At some stage the envelope will be stressed but not enough to rupture it.
This is very different from the situation where you can use a pump to increase the internal pressure to however much the pump can provide (even your lungs) and that can easily (if you have the nerve) burst the balloon.
It's quite hard to measure the difference between a Good Vacuum and a Deep Vacuum.

The darn thing filled the entire available volume without bursting until

The embarrassing question is why a condom should ever be required to stretch that far! Not by me, your honour.

 

[Chestermiller]

For additional information, see this thread: https://www.physicsforums.com/threads/estimating-balloon-internal-pressure.867908/#post-5449479