Understanding Negative Pressure: Myth or Reality in Gases and Liquids?

[the4thamigo_uk]

Wikipedia suggests it is possible for some gases to exert negative pressure?

'Most often, gases and liquids are not capable of negative absolute pressure, or even zero pressure...'

Is this an error or can some gases exert negative pressure?

 

[stewartcs]

Wikipedia suggests it is possible for some gases to exert negative pressure?

'Most often, gases and liquids are not capable of negative absolute pressure, or even zero pressure...'

Is this an error or can some gases exert negative pressure?

There is no such thing as negative absolute pressure. Maybe it was referring to negative gauge pressure instead. Wikipedia isn't a reputable source by the way.

CS

 

[the4thamigo_uk]

Searching for absolute pressure comes up with the following.

* When attractive forces (e.g., van der Waals forces) between the particles of a fluid exceed repulsive forces. Such scenarios are generally unstable since the particles will move closer together until repulsive forces balance attractive forces. Negative pressure exists in the transpiration pull of plants, and is used to suction water even higher than the ten metres that it rises in a pure vacuum.
* The Casimir effect can create a small attractive force due to interactions with vacuum energy; this force is sometimes termed 'vacuum pressure' (not to be confused with the negative gauge pressure of a vacuum).So, assuming this scenario, i.e. a gas in a perfectly elastic container with particles that are attracted to each other, could it be true to say that they can exert negative pressure? At all moments we have particles that are in motion and they will exert forces on the container walls. Even when they coalesce they still will be in motion and will exert forces on the walls? Can anyone suggest what is the basis for these Wikipedia comments? Could there be any chance of some truth in this?

 

[cesiumfrog]

There is no such thing as negative absolute pressure. Maybe it was referring to negative gauge pressure instead. Wikipedia isn't a reputable source by the way.

CS

You're mistaken. There is such a thing as negative absolute pressure. In a solid, you normally call it tension. In some trees, it is the mechanism thought to be responsible for lifting water higher than the 10m limit.

I don't see why it should be impossible in principle, but I don't know of any gases exhibiting it.

 

[Andy Resnick]

Wikipedia suggests it is possible for some gases to exert negative pressure?

'Most often, gases and liquids are not capable of negative absolute pressure, or even zero pressure...'

Is this an error or can some gases exert negative pressure?

I'm not sure about gases, but liquids can support tension (which IIRC is negative absolute pressure).

http://web.pdx.edu/~d4eb/tensile/index.htm
http://www.nature.com/nature/journal/v278/n5700/abs/278148a0.html

I don't think gases can support tension, because there are no intermolecular bonds.

 

[stewartcs]

You're mistaken. There is such a thing as negative absolute pressure. In a solid, you normally call it tension. In some trees, it is the mechanism thought to be responsible for lifting water higher than the 10m limit.

I don't see why it should be impossible in principle, but I don't know of any gases exhibiting it.

No I'm not, you are mistaken.

Since a partial vacuum will be below atmospheric pressure, the phrase "negative pressure" is often used. Certainly there is no such thing as a negative absolute pressure, but small decreases in pressure are commonly used to entrain fluids in sprayers, in carburetors for automobiles, and many other applications. In the case of respiration, we say that the lungs produce a negative pressure of about -4 mmHg to take in air, which of course means a 4 mmHg decrease from the surrounding atmospheric pressure.

Source: http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/idegas.html

In a solid, "pressure" is referred to as stress. If it is negative, it is called compression. If it is positive it is called tension. With respect to fluids, by definition they cannot be negative since a fluid cannot support a shear stress. In other words, it cannot be "pulled apart" or placed in tension.

They only exception I know of is with Surface Tension but that is a special phenomenon that only occurs at the surface of a liquid.

CS

 

[cesiumfrog]

No I'm not, you are mistaken.

Source: http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/idegas.html"

In a solid, "pressure" is referred to as stress. If it is negative, it is called compression. If it is positive it is called tension. With respect to fluids, by definition they cannot be negative since a fluid cannot support a shear stress. In other words, it cannot be "pulled apart" or placed in tension.

They only exception I know of is with Surface Tension but that is a special phenomenon that only occurs at the surface of a liquid.

CS

Heh. Look, for starters, compression relates to positive pressure. And of course I'll concede that an ideal gas cannot exert negative pressure! Now have you thought about how surface tension works at the molecular level?

 

[DrDu]

If you consider e.g. the van der Waals isothermal curves. There are regions where the curve really drops below 0 of p. These regions which assume a homogeneous system are unstable against a separation into a liquid and gaseous phase. The question arises whether they are at least meta-stable. However, they correspond to a super-heated liquid rather than a gaseous phase.

 

[Andy Resnick]

I'm not sure about gases, but liquids can support tension (which IIRC is negative absolute pressure).

http://web.pdx.edu/~d4eb/tensile/index.htm
http://www.nature.com/nature/journal/v278/n5700/abs/278148a0.html

I don't think gases can support tension, because there are no intermolecular bonds.

I'm going to change my answer- tension is not a negative absolute pressure- that would correspond to negative absolute energy density and is not physical.

But fluids can indeed support tension- it's related to the onset of cavitation.

 

[stewartcs]

Heh. Look, for starters, compression relates to positive pressure. And of course I'll concede that an ideal gas cannot exert negative pressure! Now have you thought about how surface tension works at the molecular level?

Sorry, I believe I misread what you wrote with respect to tension being equated to negative pressure. That part is true. However, it is normally accepted in Fluid Mechanics that negative absolute pressures do not exist since that implies fluids could sustain a tensile force.

Axial stress (i.e. mechanical pressure) in Mechanics is the equivalent to fluid pressure. There are two types of axial stress; tensile and compressive. The standard convention in Statics or Strength of Materials is for the tension to be positive and compression negative. I misread what you wrote and thought you had implied the opposite. Which you did not.

Liquids normally cannot sustain a tensile (or pulling apart) stress since the liquid would vaporize. Therefore, absolute pressures used in this book are never negative, since this would imply that the fluid is sustaining a tensile stress.

Source: Fluid Mechanics, 9th Edition - Streeter, Wylie, Bedford. 1998, McGraw-Hill Companies.

This excerpt from one of my Fluid Mechanics books shows the common ruling on tensile stress in liquids (we all seem to agree that fluids in a gas phase cannot be negative).

Honestly, I'm not sure what conditions constitutes "abnormal" (other than Surface Tension which I've already pointed out) so I'll concede that there may, emphasis on may, be some situation that would allow one to say a fluid can sustain a tensile stress other than through Surface Tension. I'd appreciate any reputable and properly vetted sources for further reading if anyone has them.

CS

 

[kcdodd]

If water can not sustain tension, then how can water drops form on the bottom of a/c vents on the ceiling?

 

[cmos]

Not to add more confusions to the mix, but in engineering practice, we will often say something is "under negative pressure" if it's pressure is lower than atmosphere. For example, an arsenic-containing apparatus might be kept "under negative pressure" so that, in the event of an interlock failure, arsenic is not seeped out into the air. Obviously, the "negative" here refers more to the pressure gradient than the actual pressure.

 

[Studiot]

Not to add more confusions to the mix, but in engineering practice, we will often say something is "under negative pressure" if it's pressure is lower than atmosphere. For example, an arsenic-containing apparatus might be kept "under negative pressure" so that, in the event of an interlock failure, arsenic is not seeped out into the air. Obviously, the "negative" here refers more to the pressure gradient than the actual pressure.

This has already been discussed. It is referred to as gauge pressure.

I wonder if the original poster's reference was referring to the "hydrostatic pressure" that appears in the decomposition of stress at a point into a hydrostatic stress matrix and a deviator stress matrix.

This "hydrostatic stress" can be positive or negative and is sometimes called hydrostatic pressure.

 

[stewartcs]

If water can not sustain tension, then how can water drops form on the bottom of a/c vents on the ceiling?

As previously discussed, a phenomenon called Surface Tension is responsible for the water droplets.

CS

 

[kcdodd]

And what is the surface of water made out of?

 

[Andy Resnick]

Honestly, I'm not sure what conditions constitutes "abnormal" (other than Surface Tension which I've already pointed out) so I'll concede that there may, emphasis on may, be some situation that would allow one to say a fluid can sustain a tensile stress other than through Surface Tension. I'd appreciate any reputable and properly vetted sources for further reading if anyone has them.

CS

What's wrong with the Nature article I posted?

 

[kcdodd]

Yes, Andy, clearly intermolecular bonds can support tension, otherwise surface tension would be impossible to begin with. These bonds are also present throughout the bulk liquid, which means there could be tension in bulk liquid as well, not just at the surface. Any surface which can make a similar bond to the water can clearly "pull" on the water in such a case. Otherwise water droplets could not stick to the ceiling.

Also, negative energy is valid. Just not negative kinetic energy. You can set zero anywhere. Say you have two separate water droplets. If they join into one droplet the energy in the bonds will drop. Otherwise they would not join. If you set the binding energy to zero before, then it becomes negative. I think the best place to put zero is when all water molecules are separate, which would mean any droplet has negative binding energy.

 

[stewartcs]

What's wrong with the Nature article I posted?

How about we start with why, other than surface tension, you think a liquid supports a tensile stress?

CS

 

[stewartcs]

Yes, Andy, clearly intermolecular bonds can support tension, otherwise surface tension would be impossible to begin with. These bonds are also present throughout the bulk liquid, which means there could be tension in bulk liquid as well, not just at the surface. Any surface which can make a similar bond to the water can clearly "pull" on the water in such a case. Otherwise water droplets could not stick to the ceiling.

Clearly, that only applies to the surface of a liquid. Otherwise they wouldn't call it Surface Tension, it would be called Fluid Tension or something similar. Those special bonds are not present other than at the surface, which means that a liquid will generally not support a tensile stress as stated clearly in most all Fluid Mechanics books.

CS

 

[Studiot]

Those special bonds are not present other than at the surface, which means that a liquid will generally not support a tensile stress as stated clearly in most all Fluid Mechanics books.

Not quite accurate here.
The bonds are indeed present throughout the liquid. That's the whole point.

There are none outside the liquid so there is a net attraction into the liquid on the particles at the surface, unbalanced by any force from the outside.

this doesn't mean I'm suggesting a fluid can support internal tension, just that your proposed mechanism for surface tension need adjusting.

 

[stewartcs]

Not quite accurate here.
The bonds are indeed present throughout the liquid. That's the whole point.

There are none outside the liquid so there is a net attraction into the liquid on the particles at the surface, unbalanced by any force from the outside.

this doesn't mean I'm suggesting a fluid can support internal tension, just that your proposed mechanism for surface tension need adjusting.

Yes that was probably a poor choice of words. Let's try the book definition of why surface tension exists only at the surface.

At the interface between a liquid and a gas, a film or special layer seems to form on the liquid, apparently owing to attraction of liquid molecules below the surface. The formation of this film can be visualized on the basis of surface energy or work per unit area required to bring the molecules to the surface. The surface tension is then the stretching force required to form the film, obtained by dividing the surface-energy term by unit length of the film in equilibrium.

Source: Fluid Mechanics, 9th Edition - Streeter, Wylie, Bedford. 1998, McGraw-Hill Companies.

CS

 

[Studiot]

Surface energy?
Why make things complicated?

A picture is woth 1k words.

In my 2D attachment
The white surface molecule at 'A' experiences a net force into the liquid.
The black interior molecule at 'B' experiences a zero net resultant.

What did you think about my comment from continuum mechanics?

 

[stewartcs]

What did you think about my comment from continuum mechanics?

That seems like a possible explanation. It fits with what is asserted in the links by Andy as well (at least to me anyway).

What that link (the one Andy gave - actually one inside of the one he gave, given just below) seem to indicate, especially by the analogies they gave with the cylinder and water, is that they are calling "negative pressure" the pressure in the liquid that exists due to surface tension.

How does a liquid break?
Measuring the tensile strength of a solid involves applying an increasing stress until the solid breaks. The study of cavitation in liquids follows a similar path. Suppose that some water is put into a cylinder that is sealed with a piston. If the piston is above the water and has a weight placed on top of it, the water will be under a positive pressure. The pressure will be equal to the weight divided by the cross-sectional area of the cylinder. But if the apparatus is turned upside down and a weight hung from the piston, what happens? The correct answer depends critically on some details of the situation that we have not yet specified. If there is an air bubble in the water above the piston, then when the weight pulls on the piston, the bubble will grow and the piston will fall. If there is no air bubble and the weight is small, the piston will move down a short distance but soon come to rest. In that equilibrium position, the force exerted by the weight is balanced by a force that the water exerts. The water is thus under negative pressure—that is, under positive stress. If there is no air bubble and the weight is heavy enough, then the piston will move down, the water will be stretched, and eventually a bubble will spontaneously appear within the liquid or possibly on the wall of the container.

Source: http://www.aip.org/pt/feb00/maris.htm

The bolded section is describing what happens with surface tension. So I guess with that respect one could think of that as "negative pressure" so to speak. But that's a really loose definition IMO. But I still have issues with this analogy.

My point all along was that there is no such thing, at least in Fluid Mechanics, as negative absolute pressure since that implies liquids can support a tensile stress. The only time that I know of that happening is with surface tension and that stress is really low (for water it is like 0.074 N/m I think).

CS

 

[Studiot]

If you want a demonstration of a liquid supporting tension, get a beaker 1/2 full of polyethylene oxide solution.

edit not polyethelene glycol as first stated.

Stand it in a tray and tip some out and stand it back.
Watch the rest of the solution pour itself up over the edge and out of the beaker.

Not sure if this open air syphon qualifies?

 

[the4thamigo_uk]

http://th-www.if.uj.edu.pl/acta/vol21/pdf/v21p0177.pdf

 

[Andy Resnick]

How about we start with why, other than surface tension, you think a liquid supports a tensile stress?

CS

Cavitation.

Edit- in case that's too cryptic: Cavitation occurs when there is low pressure in the bulk phase. Getting pure water to rip apart under low pressure is very difficult- see, for example, single-bubble sonoluminescence.

Your number of 72 erg/cm^2 is the interfacial energy of pure water an vacuum, and is not germaine to caviation.

 

[cesiumfrog]

Here's a measurement of water pressures lower than vacuum, in the xylem of plants:
http://www.springerlink.com/content/v3r3umv36567l172/"

The basic idea is that, the same way Laplace found the pressure that surface tension causes inside a bubble, evaporation at a stoma on the plant's leaf also carves out a half-bubble shape, reduces the water pressure, siphoning water up from the roots. However, one atmosphere of pressure can only lift the weight of water for 10m. Normally you cannot siphon higher, because cavitation occurs so shortly after the absolute pressures become negative, but evidently cavitation can be suppressed. So in tall trees the water is literally sucked or pulled upward by tensile forces between water molecules, rather than being pushed by the atmospheric pressure from below.

Do you know how to derive from first principles the height that liquid rises in a capilliary tube?

If water can not sustain tension, then how can water drops form on the bottom of a/c vents on the ceiling?

If you want a demonstration of a liquid supporting tension[...] Not sure if this open air syphon qualifies?

CS already believes in surface tension, and both those examples are typically negative gauge pressure but positive absolute pressure.

it is normally accepted in Fluid Mechanics that negative absolute pressures do not exist since that implies fluids could sustain a tensile force.
[...]

Liquids normally cannot sustain a tensile (or pulling apart) stress

[..] (we all seem to agree that fluids in a gas phase cannot be negative).

[...]which means that a liquid will generally not support a tensile stress as stated clearly in most all Fluid Mechanics books.

What that link (the one Andy gave - actually one inside of the one he gave, given just below) seem to indicate, especially by the analogies they gave with the cylinder and water, is that they are calling "negative pressure" the pressure in the liquid that exists due to surface tension.[..]The bolded section is describing what happens with surface tension. So I guess with that respect one could think of that as "negative pressure" so to speak. But that's a really loose definition IMO.

Even though negative absolute pressure is so unusual, your textbooks do not deny it exists. By the way, interpreting what happens to the liquid bulk inside a piston-cylinder as wholly a surface tension effect is just weird.

 

[Studiot]

Originally Posted by Studiot
If you want a demonstration of a liquid supporting tension[...] Not sure if this open air syphon qualifies?

CS already believes in surface tension, and both those examples are typically negative gauge pressure but positive absolute pressure

How so?

 

[stewartcs]

Cavitation.

Edit- in case that's too cryptic: Cavitation occurs when there is low pressure in the bulk phase. Getting pure water to rip apart under low pressure is very difficult- see, for example, single-bubble sonoluminescence.

Your number of 72 erg/cm^2 is the interfacial energy of pure water an vacuum, and is not germaine to caviation.

Cavitation doesn't explain it. In fact, it would contradict it since when the pressure of the liquid drops below the vapor pressure, boiling of the liquid would occur. If the liquid is now vaporized you certainly can't say it supporting a tensile stress.

CS

 

[stewartcs]

Even though negative absolute pressure is so unusual, your textbooks do not deny it exists. By the way, interpreting what happens to the liquid bulk inside a piston-cylinder as wholly a surface tension effect is just weird.

I agree that they don't deny it exists. Which is why I posted the excerpt - to point out what is generally accepted in Fluid Mechanics.

However, after reviewing a few of the resources and consulting a few more books, apparently there are certain fluids under certain conditions that can support tensile stresses. However, they are the exception to the rule. Nevertheless I'll concede that my statement was technically incorrect by saying there is no such thing as negative absolute pressure since it implies that all liquids cannot support tensile stresses.

CS

 

[Andy Resnick]

Cavitation doesn't explain it. In fact, it would contradict it since when the pressure of the liquid drops below the vapor pressure, boiling of the liquid would occur. If the liquid is now vaporized you certainly can't say it supporting a tensile stress.

CS

I could have been unclear- I am referring to the *nucleation* of a bubble, not it's growth. Nucleation occurs via tunneling through a high-energy barrier (which is significantly lowered when there is dissolved gas or contaminants), and that energy barrier represents the tensile strength.

http://pof.aip.org/resource/1/pfldas/v12/i9/p1775_s1?isAuthorized=no
http://www.agu.org/pubs/crossref/2002/2001WR000282.shtml
http://pubs.acs.org/doi/abs/10.1021/la100268q