Back to basics: bubbles in a syringe

[rwooduk]

Please could someone give me some idea of what is happening when you pull back on a syringe filled with fluid and the bubbles in the fluid (in the syring) expand?

Let's assume it's water. How do the bubbles grow? I am assuming it is a rectified diffusion process where gas in the fluid is drawn into the bubbles due to the change in pressure. But I want to understand in more detail. Why does the pressure change cause gas in solution to enter the bubbles? Does the volatility of the water play any role i.e. does the pressure change cause any vapourisation of water into the bubbles? I'm trying to visualise the whole situation rather than just say, it's due to the pressure change(!).

I'd appreciate any viewpoints on this, thanks in advance!

 

[Nugatory]

I'm trying to visualise the whole situation rather than just say, it's due to the pressure change(!).

Well, maybe it is due to the pressure change.

Start by calculating the amount of expansion you get just because any volume of gas will expand when the pressure is reduced, using the ideal gas law $PV=nRT$ and the known force required to pull back on the plunger. Does this match the observed expansion of the bubbles? If so, the pressure change is a sufficient explanation and there's no need to explore more elaborate hypotheses like vaporization of the water.

Now if you want to know why gases expand when the pressure is reduced, you'll want to look at how the ideal gas law is explained. That's a different question; googling for "ideal gas law derivation" will get you started.

 

[pbuk]

The volume of the bubbles is given by $PV = kRT$. If P changes, R does not have to change in order for V to change.

Edit: Nugatory beat me to it.

 

[rwooduk]

Well, maybe it is due to the pressure change.

Start by calculating the amount of expansion you get just because any volume of gas will expand when the pressure is reduced, using the ideal gas law $PV=nRT$ and the known force required to pull back on the plunger. Does this match the observed expansion of the bubbles? If so, the pressure change is a sufficient explanation and there's no need to explore more elaborate hypotheses like vaporization of the water.

Now if you want to know why gases expand when the pressure is reduced, you'll want to look at how the ideal gas law is explained. That's a different question; googling for "ideal gas law derivation" will get you started.

Many thanks for the reply, it was more of a visualisation question and I had not considered a calculative element. It's not for any particular given physics question, thus, I do not have numerical values to insert. However, yes, good point, as the pressure is reduced the volume of gas (at constant temperature), according to the ideal gas law, will increase. This explains the growth, but it does not explain how it happens, the actual mechanics of what is happening, hence the visualisation aspect.

So you are saying the gas inside the bubbles expands when the pressure is reduced and it is not caused by rectified diffusion?

Thanks again.

 

[Chestermiller]

When you move the plunger to increase the volume, and the volume of liquid in the syringe is roughly constant, the volume of gas in the bubbles must increase. Even if there were negligible air dissolved in the liquid, the bubbles would still get larger. This would be the result of water evaporation into the bubbles so that the bubbles equilibrated with the new lower pressure in the syringe and the increase in volume of bubbles matched the additional volume created by the plunger motion (assuming no air is allowed to enter through the needle). Given the amount of water in the syringe and the initial volume of bubbles, you can precisely calculate the new pressure when the system equilibrates. So, a combination of both mechanisms contribute.

 

[pbuk]

For a visualisation consider a weather balloon which expands as it rises through the atmosphere, or search 'Cartesian Diver'

 

[jbriggs444]

It is fairly easy to pull a syringe strongly enough for a vacuum. Bubbles full of vacuum can then spontaneously form (also known as "boiling"). Due to surface tension, this can require either significant negative pressure or the existence of nuclei where bubbles can form.

One might think of the bubbles as tears in the fluid fabric. It is easier to extend an existing tear than to pull the fabric strongly enough to create a new one.

 

[rwooduk]

When you move the plunger to increase the volume, and the volume of liquid in the syringe is roughly constant, the volume of gas in the bubbles must increase. Even if there were negligible air dissolved in the liquid, the bubbles would still get larger. This would be the result of water evaporation into the bubbles so that the bubbles equilibrated with the new lower pressure in the syringe and the increase in volume of bubbles matched the additional volume created by the plunger motion (assuming no air is allowed to enter through the needle). Given the amount of water in the syringe and the initial volume of bubbles, you can precisely calculate the new pressure when the system equilibrates. So, a combination of both mechanisms contribute.

Interesting, thanks, this is along the lines of what I was thinking. Could you explain a little more? The evaporation of water, how is this caused and is it dependant on the vapour pressure of the water? When you say evaporation inside the bubbles, do you mean that the air content of solution increases (due to vaporisation) throughout solution such that diffusion into the bubbles can occur more readily? What causes the diffusion? Is the diffusion caused by attempting to reach equilibrium between the bubbles and solution?

 

[rwooduk]

It is fairly easy to pull a syringe strongly enough for a vacuum. Bubbles full of vacuum can then spontaneously form (also known as "boiling"). Due to surface tension, this can require either significant negative pressure or the existence of nuclei where bubbles can form.

One might think of the bubbles as tears in the fluid fabric. It is easier to extend an existing tear than to pull the fabric strongly enough to create a new one.

So in this case the ease of formation / expansion of bubbles would depend on the solutions volatility?

 

[jbriggs444]

So in this case the ease of formation / expansion of bubbles would depend on the solutions volatility?

The mass of zero pressure vapor needed to fill a vacuum is how much?

 

[rwooduk]

The mass of zero pressure vapor needed to fill a vacuum is how much?

Hmm, sorry you've lost me with the terminology, how can a bubble be full of vacuum? I understand the need for a greater amount of negative pressure to "create" bubbles, some argue that impurities in water always exist (except with extensive degassing) and provide sites for nucleation. But you lost me with the vacuum part.

 

[jbriggs444]

Why should a bubble need to contain a gas? If absolute pressure is zero, a hole in the liquid counts as a "bubble".

One might well ask whether such a hole is stable against small disturbances. I would argue that surface tension makes for stability. If the hole deviates from a spherical shape, surface tension will act to restore it.

Possibly we are talking at cross-purposes. I have in my mind's eye a syringe completely full of liquid. All bubbles having been expelled previously. The tip is plugged and the plunger is pulled back. The volume of the syringe now exceeds the volume of the contained liquid. Voids must form.

 

[rwooduk]

Why should a bubble need to contain a gas? If absolute pressure is zero, a hole in the liquid counts as a "bubble".

One might well ask whether such a hole is stable against small disturbances. I would argue that surface tension makes for stability. If the hole deviates from a spherical shape, surface tension will act to restore it.

I see, but I thought very small bubbles which you refer to would not be stable and dissolve due to Laplace pressure?

 

[jbriggs444]

I see, but I thought very small bubbles which you refer to would not be stable and dissolve due to Laplace pressure?

The pressure inside a bubble of vacuum is zero. The Laplace pressure difference means that the absolute pressure of the fluid must go negative in order to allow vacuum bubbles of a particular size to grow.

 

[rwooduk]

The pressure inside a bubble of vacuum is zero. The Laplace pressure difference means that the absolute pressure of the fluid must go negative in order to allow vacuum bubbles of a particular size to grow.

Hah good point! I see now, a vacuum environment certainly changes things. Thanks for the interesting discussion!

 

[jbriggs444]

As I think more on this, there is a particular form of instability that is present in a syringe containing more than one vacuum bubble.

Suppose there are two [spherical] bubbles that differ in size. The smaller tends to shrink while the larger tends to grow. So the only stable state is with one consolidated bubble.

Once you manage to pull the plunger strongly enough to get some nucleate boiling started, it suddenly gets easier to draw it the rest of the way out. [That matches with my experience the last time I tried it]

 

[rwooduk]

As I think more on this, there is a particular form of instability that is present in a syringe containing more than one vacuum bubble.

Suppose there are two [spherical] bubbles that differ in size. The smaller tends to shrink while the larger tends to grow. So the only stable state is with one consolidated bubble.

Once you manage to pull the plunger strongly enough to get some nucleate boiling started, it suddenly gets easier to draw it the rest of the way out. [That matches with my experience the last time I tried it]

The reason for this thread was to apply some of this theory to an ultrasonic cavitation environment (my field of research), where growth of bubbles occurs due to rectified diffusion and cycles of oscillation (more vapour goes in on expansion than goes out during compression). I had not considered the aspect of more vacuum conditions for the syringe, but what you are saying makes sense.

 

[Chestermiller]

Interesting, thanks, this is along the lines of what I was thinking. Could you explain a little more? The evaporation of water, how is this caused and is it dependant on the vapour pressure of the water? When you say evaporation inside the bubbles, do you mean that the air content of solution increases (due to vaporisation) throughout solution such that diffusion into the bubbles can occur more readily? What causes the diffusion? Is the diffusion caused by attempting to reach equilibrium between the bubbles and solution?

I think the dominant mechanism is going to be PV=nRT mechanism discussed by others. But, there will also be some evaporation of water into the bubbles, such that the partial pressure of water within the bubbles always equilibrates to the (typically small) equilibrium vapor pressure. Any additional air present in the bubbles is caused by air diffusing into them from the overall liquid. Google Henry's Law. At equilibrium, of course, there will be no further diffusion. The diffusion during the transient part of the process is due to lower air concentrations within the liquid adjacent to the bubble.

 

[Bystander]

Grad school many years ago, degassing aqueous solutions, I used this technique, plugging a syringe containing the solution, pull, shake, repeat, until it "rattled," or "cavitated." Water vapor collapse is quite noisy, hence the scene in Hunt for Red October in which Jonesy mouths off to his captain. Collapse of bubbles when air is present is "cushioned" by the solution process.

 

[rwooduk]

The diffusion during the transient part of the process is due to lower air concentrations within the liquid adjacent to the bubble.

Yes indeed, this is Crum's shell effect! Where do you think the evaporation would take place? Throughout solution due to the pressure changes? This would cause a greater amount of gas to become concentrated around the 'shell' of the bubble upon its expansion increasing the amount of rectified diffusion taking place.

edit Sorry I misread, I was talking about the ultrasonic cavitation system here.

 

[Chestermiller]

Yes indeed, this is Crum's shell effect! Where do you think the evaporation would take place? Throughout solution due to the pressure changes? This would cause a greater amount of gas to become concentrated around the 'shell' of the bubble upon its expansion increasing the amount of rectified diffusion taking place.

If there are already bubbles present, the air coming out of solution will go into the existing bubbles. Because of Henry's Law, the concentration of air in the solution immediately adjacent to the bubble will become lower than throughout the bulk of the solution. This will provide the driving force for air diffusion toward the bubble.

 

[rwooduk]

If there are already bubbles present, the air coming out of solution will go into the existing bubbles. Because of Henry's Law, the concentration of air in the solution immediately adjacent to the bubble will become lower than throughout the bulk of the solution. This will provide the driving force for air diffusion toward the bubble.

Unless the bubble is expanding (see my last post), but that's another situation, thanks for your help!

 

[Chestermiller]

Unless the bubble is expanding (see my last post), but that's another situation, thanks for your help!

Even if the bubble is expanding this will happen.

 

[rwooduk]

Even if the bubble is expanding this will happen.

Hmm, we may be saying the same thing, but what I was getting at is that on expansion of the bubble the "solution immediately adjacent to the bubble" (I'm assuming you mean surrounding the bubble here) will become more concentrated allowing increased diffusion into the bubble due to the greater concentration gradient.

 

[Chestermiller]

On what basis do you think that the solution next to the bubble will become more concentrated?

 

[rwooduk]

On what basis do you think that the solution next to the bubble will become more concentrated?

It's a theory from Crum, widely accepted in the ultrasonics community. Here's an excerpt from my literature review and the associated reference for your interest.

On expansion, a liquid shell surrounding the bubble may be envisaged that becomes thinner and gas will be concentrated in this region. At the same time, inside the bubble the concentration decreases due to expansion. This change in concentration gradient causes the rate of diffusion from the shell into the
bubble to occur more readily. On contraction, the shell becomes thicker and less concentrated, whilst the concentration in the bubble increases, therefore the diffusion does not readily occur. Hence the pressure induced oscillation cycles cause an overall growth in bubble size, generally known as growth by rectified diffusion.

L. Crum, Acoustic cavitation series: part five rectified diffusion, Ultrasonics, 22 (1984) 215-223.

 

[Chestermiller]

It's a theory from Crum, widely accepted in the ultrasonics community. Here's an excerpt from my literature review and the associated reference for your interest.
L. Crum, Acoustic cavitation series: part five rectified diffusion, Ultrasonics, 22 (1984) 215-223.

With all due respect to Crum, this makes absolutely no sense to me.

 

[rwooduk]

With all due respect to Crum, this makes absolutely no sense to me.

Hah, maybe that's why I'm struggling with the diffusion concepts. But it is difficult to explain the growth of bubbles during multiple oscillations otherwise. When the bubbles collapse during the contraction phase the contents reach very high temperatures (~ 5000 K), there is also an associated bubble surface temperature (~ 1900K) although this is disputed. I was thinking along the lines of vaporisation at the surface causing an increase in diffusion into the bubble, but I'm not sure that could account for the oscillatory growth.

Do you have any other opinions on why growth may occur? I'd be interested to hear them, this is also good practice for my upcoming viva!

 

[rwooduk]

Don't forget that the bubble is oscillating very, very quickly (extremely fast bubble "wall" velocity). It makes more sense this way.

 

[Chestermiller]

This started out as a model in which the system is close to thermodynamic equilibrium and gradually changing within a syringe. Now it turns out that the desired idealized model should be something like a bubble in an infinite ocean of water containing dissolved air in which the dissolved air concentration at infinity is a fixed value and the pressure at infinity is being oscillated. We would be looking for the oscillatory steady state (in which velocities, concentrations, and pressures are varying sinusoidally). This is quite a stretch from a system close to thermodynamic equilibrium.

 

[rwooduk]

This started out as a model in which the system is close to thermodynamic equilibrium and gradually changing within a syringe. Now it turns out that the desired idealized model should be something like a bubble in an infinite ocean of water containing dissolved air in which the dissolved air concentration at infinity is a fixed value and the pressure at infinity is being oscillated. We would be looking for the oscillatory steady state (in which velocities, concentrations, and pressures are varying sinusoidally). This is quite a stretch from a system close to thermodynamic equilibrium.

I agree, you are quite right, I was trying to compare the two, taking the syringe as a simplified version of the ultrasonic system, which I now realize is inaccurate. But I first needed to understand the syringe system. Basically I was trying to assess if any vaporisation could occur for the syringe system with a view to understanding more the effects of vaporisation for the ultrasonic system.

 

[Chestermiller]

I agree, you are quite right, I was trying to compare the two, taking the syringe as a simplified version of the ultrasonic system, which I now realize is inaccurate. But I first needed to understand the syringe system. Basically I was trying to assess if any vaporisation could occur for the syringe system with a view to understanding more the effects of vaporisation for the ultrasonic system.

The amount of water vapor in the bubbles is going to be changing, although it is not clear (until the problem is fully modeled) how important this effect will be.

 

[rwooduk]

The amount of water vapor in the bubbles is going to be changing, although it is not clear (until the problem is fully modeled) how important this effect will be.

It does change and is often related to the structural stability of the bubbles (which adds another element to the situation). A more unstable bubble such as would be seen at high acoutic pressures or with increased acoustic streaming can increase rectified diffusion. It's important for sonolytic process where polyatomic vapours can act to reduce the bubble temperature due to their higher heat capacity. But I'll stop there in an effort to not move further away from the OP. Thanks again.