Surface tension, negative pressure and air bubbles

[IndigoBerry]

Hello you all.

Well, I think the title speaks pretty much for itself.

I'm having some troubles understanding how can surface tension affect pressure. I know there's a rule:

P = -2(T) / r

with P = pressure
T = surface tensione
r = radius of meniscus formed (because of surface tension) at air-water interface

...according to which, surface tension is directly proportional to P. Actually, I should write to |P|, since actually as surface tension gets greater, pressure becomes more negative. Negative pressure may also be called "depression", or "tension", as far as I know.

Now that we know what we're talking about, I've got two problems.

(1) Why on the earth does surface tension affect P? It just looks a parameter relative to the air-water interaction surface, but I don't really get how it can develop a negative pressure.

(2) This one is tricky. Do you remember about an experiment dealing with a syringe, its tip capped, containing some water with tiny air bubbles inside? Well, while pulling the plunger upwards (and so, offering a negative pressure), the air bubbles get bigger and bigger, and eventually unite - forming a very big, single air bubble. I believe that this effect is always relalated to the P = -2(T) / r equation, but I can't really get what's going on.

Could someone help me understanding, please?

Many thanks in advance!

EDIT

I thought this image could be helpful. Have a look at it:

http://www.chem1.com/acad/webtext/states/state-images/bubble_pressures.png

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[IndigoBerry]

I'm going for a little "up".

I've a feeling that I won't be receiving any answer, this topic has puzzled me for so long and I've never been able to find anyone who could help me understanding the whole thing. But hey, hopes do not die that easily!

 

[amy_k]

Here is a good website for you:
http://hyperphysics.phy-astr.gsu.edu/hbase/surten2.html

But I don't like it when someone doesn't get a response so here is mine
We really should be talking about the pressure difference inside and outside the meniscus and its relation to surface tension.

There is a difference in pressure inside and outside the meniscus. As we know, pressure is a force exerted over an area. So at the interface there is a force due to the internal pressure pushing outwards on the surface of the bubble. There is also a force due to the external pressure pushing inwards on the bubble. The surface tension is an additional force which acts parallel to the surface of the bubble and is dependent on the radius of the bubble, which determines its surface area. In order for this system to exist in equilibrium, all these forces must balance, so:

Pi - Po = 2T/r (it will be 4T/r if it is a sphere)

or ∆P = 2T/r

Pressure inside will be greater than outside, so it depends how you calculated ∆P as to whether we get a positive or negative pressure difference. It seems that this equation with P = -2T/r is specifically referring to the pressure difference in terms of the outside on the top surface of the bubble? I have actually never seen the equation with a negative sign.

 

[amy_k]

In terms of the experiment, this is fairly straightforwards.

Pi - Po = 4T/r for the bubble

Po is decreasing when you pull back the syringe, causing the air bubbles to expand (Pi also decreases) to maintain the equilibrium.

 

[IndigoBerry]

Many thanks for your answer.

Well, I'm pretty sure the negative sign is correct, my teacher mentioned it - and it's even on my book. I guess that, considering the bubble example, the "minus" is there because surface tension actually acts 'against' the pressure inside the bubble.

Think of soap bubbles: you use soap to LOWER surface tension, in order to keep a balance from the pressure acting from the inside and the surface tension - preventing an "implosion".

I'm still not really convinced about the negative pressure matter, but at least I got an answer.
_
As for bubbles expanding in syringe, it's okay: by lowering hydrostatic pressure around the bubble, the air inside the bubble is not suffering an as big compression as before, and so may expand.

I also recalled something about cavitation and water passing from liquid to solid at very low pressures: do you think it may be involved as well?