The great nitrogen bubble debate

[ajdelange]

actually both CO2 and N2 solubility depends on temperature similarly - with a drop of 2.5-3 from 0C to 40C. Overall CO2 is about 100 times more soluble than N2 (3g/L for CO2 and 0.03 g/L for N2).

I borrowed that wording from Carroll. In fact in terms of percentage change in Henry coefficient with temperature nitrogen is more sensitive but because nitrogen is so much less soluble than CO2 the change in level of dissolved N2 changes much less which is clearly what he meant as he has a graph illustrating this. Between 0 and 15 °C the dissolved level of CO2 under 1 bar partial pressure changes by 1.307 grams. The level of N2, conversely, under 1 bar partial pressure of nitrogen, changes by only 5.7 mg between 0 and 15 °C.

This means that bubbles in your beer are almost entirely CO2 (99% or maybe 97% - depending on gas composition and level of saturation reached).

So we take some ungassed beer and put it under 3 atm (to make the math easy) beer mix with PaCO2 = 1 atm (abs) and PaN2 = 2 atm (Guiness is served with a 25% mix). Things come to equilibrium at, lets say, 5° C and we have 1*44000*CO2KHy(5) = 3041.54 mg/L dissolved CO2 and 2*28000*N2KHY(5) = 47.8879 mg/L N2. Now we very carefully (reversibly, if you speak the language of thermodynamics), without disturbing it in any way draw some of the equilibrated beer into a syringe. Next we seal the inlet to the syringe and allow the plunger to come back a bit but a very small bit. What happens here? Gas, a very small amount, leaves the beer to push the plunger back thus creating a very small head space. What is the pressure of the gas in the head space? Since it is in equilibrium with beer that was in equilibrium with 3 bar in the keg, the head space pressure will be close to 3 bar in the syringe. And what will be the partial pressure of N2 in that head space? One percent of 3 bar? No, clearly it will be 66% of 3 bar i.e. the original 2 bar. Were it less than this the nitrogen would have had to stay preferentially in the beer but that, as we haven't allowed enough time for the temperature to change much, would require the Henry coefficient to have changed by some other mechanism.

I doubt that 1% Nitrogen content inside the bubbles contributes to significant reduction of carbonic bite.

I'd doubt it too but as the nitrogen content in the bubbles is 66% (in our example) and 75% in an actual Guiness serving set up the picture is far different. But, you may say, the mg of CO2 in a bubble of a given size aren't very different between pure CO2 and CO2 diluted 2:1 or 3:1 with nitrogen and that's true but you must remember that the ability of the CO2 to form carbonic acid (which is responsible for the bite) depends on the fugacity of the gas which is a function of its partial pressure. The partial pressure is reduced to 25% of what it is with pure CO2 and the fugacity will be down to something close to 25%. Less bite.

I believe Nitrogen contribution in bubbles is irrelevant to the taste -

I thought that too for a long time but if you taste beer drawn on nitrogen carefully I think you will change your mind. I did.

you just need to create small bubbles by applying high pressure and forcing lightly carbed beer through an aperture.

I have done this (out of N2 and who wants to run all the way out to Roberts just for a glass of stout) and have suggested people do this for years claiming you will get 95% of the effect. I'm not backing away from that position but I think I might revise the 95% number downward.

The "smooth" taste is simply result of those small bubbles.

The fact of the bubbles being smaller does have an effect as part of the prick is mechanical (with the rest being carbonic acid).

You can push lightly carbed beer with other gases, or mechanical devices and get the precisely same effect.

Guiness originally got into this because they wanted to be able to draw draught beer with relatively uniform head properties from the beginning of the cask to the end and they wanted the head to resemble that from a hand pump. They started with air and then moved to nitrogen which is Carroll's words led to the 'dramatic' difference a small amount of dissolved nitrogen makes. Thus while you can get a similar effect with just a hand pump you cannot get precisely the same effect. From the physics it is clear that any gas which dilutes (lowers the partial pressure of) CO2 should work in the same way. Clearly an inert gas such as argon (but not radon) would seem to be a reasonable choice for experimentation.

 

[55x11]

Regarding your example of a plunger and diffusion of gases back into the extra headspace volume - this is what happens in the headspace of the keg.
The beer coming out of the faucet will still have 1:30 ratio of N to CO2 (assuming 1:3 in beer gas ratio) dissolved in it though.

But, the crucial thing that I am missing is the mechanism of foaming / bubble nucleation. I always assumed that as you open the faucet (say stout faucet), the beer (at this point say 3% nitrogen and 97% CO2 dissolved in it) flows through the constrictor plate and turbulence forces for the gases dissolved in beer to come out of the solution, forming the foam. Due to turbulence, its rapid enough process that its precipitation/nucleation driven, and not diffusion limited. In other words, it's highly non-equilibrium process, and I assumed that most if not all gas dissolved will be knocked out of the solution and into he foam - and that both gases will be knocked out at the same relative rate.

 

[ajdelange]

Regarding your example of a plunger and diffusion of gases back into the extra headspace volume - this is what happens in the headspace of the keg.

Yes, and what happens anywhere else is the same as long as the pressure and temperature remain the same.

The beer coming out of the faucet will still have 1:30 ratio of N to CO2 (assuming 1:3 in beer gas ratio) dissolved in it though.

Beer that is in equilibrium with 1 bar CO2 at 5 °C contains 3.04 grams of CO2 (aq) per liter. Beer that is in equilibrium with 3 bar N2 contains 23.9 mg/L N2(aq). In the syringe, you'll have the same mix in the beer and in the headspace.

But, the crucial thing that I am missing is the mechanism of foaming / bubble nucleation. I always assumed that as you open the faucet (say stout faucet), the beer (at this point say 3% nitrogen and 97% CO2 dissolved in it)...

Behind the restricter plate an when the valve is closed the beer still contains N2:CO2::3:1

... flows through the constrictor plate and turbulence forces for the gases dissolved in beer to come out of the solution, forming the foam.

Yes and this may start behind the restricter plate as when you open up the valve the pressure behind the restriter plate drops.

Due to turbulence, its rapid enough process that its precipitation/nucleation driven, and not diffusion limited. In other words, it's highly non-equilibrium process, and I assumed that most if not all gas dissolved will be knocked out of the solution and into he foam - and that both gases will be knocked out at the same relative rate.

Yes, I think so. There may be nuances that are well beyond me but by the time the beer is in the glass lots (but not all) of the gas is out of solution. The rate at which this happens is some power of the concentration of the aqueous species (in mols) and of the activation energy. I have no idea what the rates might be. One the beer is in the glass we know it is moving towards 0.0003 atm CO2 and 0.8 atm N2 and we all know it takes hours for the the CO2 in a beer to establish equilibrium. My recall from scuba diving days that N2 moved into and out of blood pretty quickly but took much longer for bone and cartilage isn't helping me much here. What I do have is some data from that same paper that says that the duration of the surge (bubble show) depends on the ratio of Nitrogen to CO2 in the driving gas and that heads stand much longer if N2 is included in the mix.

 

[55x11]

Beer that is in equilibrium with 1 bar CO2 at 5 °C contains 3.04 grams of CO2 (aq) per liter. Beer that is in equilibrium with 3 bar N2 contains 23.9 mg/L N2(aq). In the syringe, you'll have the same mix in the beer and in the headspace.

Behind the restricter plate an when the valve is closed the beer still contains N2:CO2::3:1

Hmm... I am sorry for being so obtuse, but I am just trying to understand this part.

So let's say that beer in the keg contains 3g/L of CO2 and 24 mg/L of N2, both dissolved in the liquid. That's a ratio of 100 to 1 or so (I think it should be 30:1 but whatever the ratio is).

When I open the tap, and say empty 1L of beer into a container, I will be knocking both those gases out of the solution, correct? (by providing nucleation site in a form of restrictor plate and a lot of turbulence).

So the foam should contain a ratio of CO2 to N2, of about 100:1 (or whatever it was in the dissolved beer, I think more like 30:1). If not, why not? If the ratio in the foam bubbles is predominantly N2, where does this extra N2 come from? Nitrogen from headspace, where it's indeed at 3:1 ratio over CO2, will have no chance to get to the bottom of the keg through all the beer and make it out of the faucet.

Note: I am not super-competent to talk about fine details of the design of the stout valves, but I don't think it's relevant - I could imagine a valve before or after restrictor plate, and the volume of beer contained there is negligible there. Besides, if the valve is closed, that beer should be in thermodynamic equilibrium with the rest of the keg (same pressure and lets assume the same temperature).

By the way, don't forget about "Guiness" gadget that Guiness people themselves use - basically a syringe that sucks up lightly carbed beer from the glass and reinfects it back into the glass creating a creamy Guiness foam of cascading bubbles - this uses no nitrogen whatsoever and creates the same "nitro" effect, purely mechanically? I did some experiments with the same technique at home and the effect is quite dramatically similar to nitro foam.

Someone with access to residual gas analyzer should take a bunch of foam from nitro beer and analyze it for CO2 to N2 ratio.

 

[ajdelange]

So let's say that beer in the keg contains 3g/L of CO2 and 24 mg/L of N2, both dissolved in the liquid. That's a ratio of 100 to 1 or so (I think it should be 30:1 but whatever the ratio is).

That's by weight and were we discussing how N2(aq) and CO2(aq) reacted in solution those numbers (the concentrations) would be what we would use. But we are not talking about the solution phase but a gas phase that arises when bubbles form. In gasses the fugacity takes the role of concentration (activity really) and the fugacity of a gas depends on its partial pressure (and an activity coefficient). Thus we are concerned with the partial pressures of CO2 and nitrogen.

When I open the tap, and say empty 1L of beer into a container, I will be knocking both those gases out of the solution, correct? (by providing nucleation site in a form of restrictor plate and a lot of turbulence).

Not all of it perhaps but certainly an appreciable part of it.

So the foam should contain a ratio of CO2 to N2, of about 100:1 (or whatever it was in the dissolved beer, I think more like 30:1). If not, why not?

If the ratio in the foam bubbles is predominantly N2, where does this extra N2 come from?

We have noted that it takes a lot of pressure to force a little nitrogen into beer. The converse is that a little nitrogen dissolved in beer produces a high nitrogen pressure in any gas in equilibrium with it.

There is no extra gas. The gas that dissolves in the beer was at 3:1 and the gas that comes back out is at 3:1.

Nitrogen from headspace, where it's indeed at 3:1 ratio over CO2, will have no chance to get to the bottom of the keg through all the beer and make it out of the faucet.

If nitrogen has no chance to make it to the bottom of the keg neither does CO2 but in fact CO2 does make it to the bottom of the keg as does N2 if the keg has been properly carbonated i.e. left under adequate partial pressures of both gasses for long enough.

Note: I am not super-competent to talk about fine details of the design of the stout valves, but I don't think it's relevant

Carroll's paper shows curves of surge duration for both 5 hole and 9 hole restrictor plates. The differences are dramatic.

I could imagine a valve before or after restrictor plate,

In the traditional Guiness faucet it is before. I don't believe the ones made today have any valve.

It is clear that the bubbles that first break out of beer carbonated with gas in a 3:1 mix are going to be in a 3:1 mix in my syringe model. But those first bubbles are at 4 bar pressure (assuming the beer was 'carbonated' with 3 atm N2 and 1 of CO2. But those are not the bubbles in the foam. The bubbles in the foam have been released into beer at 1 bar absolute pressure and while the ratio of partial pressures for bubbles in equilibrium with 3:1 carbonated beer is 3:1 at 4 bar it is 0.2:1 but then the pressure inside the foam bubbles is higher than 1 bar because of the surface tension (without which the bubbles would not be tiny). If the internal pressure were as much as 2 bar the N2 to CO2 ratio would be about 1:1.

That's about as far as my limited knowledge will allow me to take it. I think we conclude that the nitrogen content of the bubbles is at least 17% and as much as 15% if we ignore diffusion through the bubble film. If we consider that then we would recognize that N2 is trying to get into equilibrium at 0.8 bar and CO2 is heading for 0.0003 bar

 

[55x11]

That's by weight and were we discussing how N2(aq) and CO2(aq) reacted in solution those numbers (the concentrations) would be what we would use. But we are not talking about the solution phase but a gas phase that arises when bubbles form. In gasses the fugacity takes the role of concentration (activity really) and the fugacity of a gas depends on its partial pressure (and an activity coefficient). Thus we are concerned with the partial pressures of CO2 and nitrogen.

Not all of it perhaps but certainly an appreciable part of it.




We have noted that it takes a lot of pressure to force a little nitrogen into beer. The converse is that a little nitrogen dissolved in beer produces a high nitrogen pressure in any gas in equilibrium with it.

There is no extra gas. The gas that dissolves in the beer was at 3:1 and the gas that comes back out is at 3:1.
...
That's about as far as my limited knowledge will allow me to take it. I think we conclude that the nitrogen content of the bubbles is at least 17% and as much as 15% if we ignore diffusion through the bubble film. If we consider that then we would recognize that N2 is trying to get into equilibrium at 0.8 bar and CO2 is heading for 0.0003 bar

Now I understand you better. And the chemistry says this is just wrong - the pressure ratio of gases coming out of solution should generally NOT be the same as the pressure ratio of gases that got them in there.

If you dilute a beer gas, say with 1:1 ratio of N2 to CO2, you will end up with 100:1 ratio of CO2 to N2 at 0C (and very similar ratio at room temperature).
If you take out some arbitrary volume of liquid (gently) and agitate it till you get gases out of solution, or boil the liquid or freeze it, whatever, and analyze, the amount of gases that will come out will be whatever is "stored" in liquid. So still 100:1 ratio in this scenario. You are correct, this is by mass. By volume it will be 48/28 (atomic weights of CO2 and N2 respectively) smaller, so 1.7 times smaller, or 58:1. And if you use 3:1 N2:CO2 gas ratio pressure, you will end up with about 20:1 ratio - by volume. Still, that's about 95% CO2 and 5% N2 - by volume, not mass - inside the bubbles.

Perhaps 5% Nitrogen inside the bubbles makes such a dramatic difference in taste or bubble formation process, but somehow I really doubt it. I will bet the exact same effect can be obtained with any other inert gases with very low solubility, and the same effect can be obtained by mechanically pushing on the liquid at the right pressure, through small aperture, at low carbonation level, to agitate and precipitate gases (basically CO2) out of solution and into the foam.

Something fro Brulosophers to test.

 

[ajdelange]

Now I understand you better. And the chemistry says this is just wrong - the pressure ratio of gases coming out of solution should generally NOT be the same as the pressure ratio of gases that got them in there.

I'm not sure whose chemistry you are using but the rest of the world's chemistry describes what I have been posting.

The chemical potential of a gas dissolved in a liquid is

mul = mul0 + R*T*ln(c)

where R is the gas constant, T the absolute temperature and c the concentration of the species in the liquid. mug0 is a constant representing the potential when the concentration is 1.

The chemical potential of the gas in the gas phase is

mug = mug0 + R*T*ln(P)

where R and T are the same but mug0 represents the potential when the partial pressure P = 1.

When gas and liquid are in equilibrium the chemical potentials are equal and there is no net exchange of gas between solution and head space

mug0 + R*T*ln(P) = mul0 + R*T*ln(c)

so ln(c) - ln(P) = (mul0 - mug0)/(R*T)

and the ratio of concentration to pressure is

c/P = exp((mul0 - mug0)/(R*T))

which is clearly the Henry coefficient.


If you dilute a beer gas, say with 1:1 ratio of N2 to CO2, you will end up with 100:1 ratio of CO2 to N2 at 0C (and very similar ratio at room temperature).

If you equilibrate water or beer with a 1:1 mix of N2 and CO2 the concentration ratio , cCO2/cNO2 , in mg/L will be approximately 100 to 1 but if you draw some of that liquid out of keg with a syringe keeping it under pressure (if we used 1 bar each N2 and CO2 that would be 2 bar) and then reversibly (that is a thermodynamics term which you should really understand the meaning of if you are to grasp this) decrease that pressure a tiny bubble will form. The partial pressures of CO2 and Nitrogen within that bubble will be 1:1 (to within an infinitesimal tolerance) because only an infinitesimal mass of either gas has moved to the bubble and Raoult's law still applies. mul0 and mug0 are still the same constants and so is R. For purposes of this discussion we'll assume T is the same.

If you take out some arbitrary volume of liquid (gently) and agitate it till you get gases out of solution, or boil the liquid or freeze it, whatever, and analyze, the amount of gases that will come out will be whatever is "stored" in liquid. So still 100:1 ratio in this scenario.

What you find in the gas depends on the volume to which you have expanded in the syringe or, invoking the gas law, the pressure within it. I put some numbers in a previous post for a 3:1 N2/CO2 ratio. When the gas (no bubbles here - we assume at this point we've put some hexanol or octanol in the beer) volume is 4% of the liquid volume (I started with 100 cc of beer at 4 atm and eased the plunger back to an extra 4 cc) the pressure (ignoring water vapour) over the liquid would be about 2 atm and the ratio of partial pressures 1:1. If I ease back another 4 cc so the volume of the gas is now 8% of the volume of the beer the pressure in that gas is (sans water vapor again) about 1.5 atm and the ratio of N2 to CO2 pressure is now 0.61. And it continues to drop until the volume of the gas is about 10 times the volume of the liquid at which point PaN2/PaCO2 is clearly leveling off at about 0.04 (not 0.01 ~ 100:1) By weight the ratio is 0.027.

You can do these calculations yourself. To get you started for CO2 the Henry coefficient is
0.03875*exp( 2400*( (1/T) -(1/298.15) ) )

and for N2 it is

0.000625*exp( 1300*( (1/T) -(1/298.15) ) )

with T in Kelvins.

R = 0.08206 // atm•L/mol•K

What you have to do is start with a volume of beer with x mol/L dissolved gas with no head space under some pressure. Now you start to add in head space incrementally. When the head space is Vh the moles of gas in it are P*Vh/(R*T) and the concentration of the gas dissolved in the beer is Vb*P*KHy. The sum of these two is Vb (volume of beer) times the initial concentration. Solve for P. It is then a simple matter to get the partial pressures and the ratio.

You are correct, this is by mass. By volume it will be 48/28 (atomic weights of CO2 and N2 respectively) smaller, so 1.7 times smaller, or 58:1. And if you use 3:1 N2:CO2 gas ratio pressure, you will end up with about 20:1 ratio - by volume. Still, that's about 95% CO2 and 5% N2 - by volume, not mass - inside the bubbles.

What you seem to be failing to take into account is the pressure of the released gas i.e. the volume to which the gas which escapes from the beer expands. What controls that is the surface tension of the beer. The bubbles are tiny and their internal pressure is inversely proportional to the radius. Thus the expansion is to only a small fraction of the beer volume and we are pretty high up on the N2/CO2 curve. I don't know what the radius of the bubbles is nor what the surface tension of Guiness is (but I'll bet the lab guys at Guiness do). It's quite plain from the physics alone that the ratio of N2 to CO2 is pretty high (not as high as 3:1 or maybe not even as high as 1:1). From the physics. Now let's take into consideration that there is a huge drop in CO2 chemical potential across the membrane of the bubble. The atmosphere is at 0.0003 bar CO2. But it as at 0.8 bar N2. I don't know what the diffusion properties of a Guiness bubble are WRT either of these gasses but it's pretty obvious the CO2 wants to get out much more than the N2 does. So I'm guessing that when you take this into account the ratio of N2 to CO2 is pretty high. Given the evidence (that the CO2 prick is reduced noticeably) we have further support for that notion.

I will bet the exact same effect can be obtained with any other inert gases with very low solubility,

I don't see why that shouldn't be the case.[/QUOTE]

and the same effect can be obtained by mechanically pushing on the liquid at the right pressure, through small aperture, at low carbonation level, to agitate and precipitate gases (basically CO2) out of solution and into the foam.

You'd lose that one for reasons given above. I used to say you could get 95% of the nitrogen effect that way but I'm lowering that now that I understand the process better.

 

[ajdelange]

I'm putting up a plot for the syringe gedanken experiment. In this experiment we put a beer under 3 atm nitrogen and 1 atm CO2 and wait for equilibrium to be reached. We then equip our lab daemon with a syringe and lower him into the tank through a gas lock. He fills the syringe, caps it and locks the plunger in place, and returns to the lab with the syringe which is full of beer and is at pressure 4 atm (absolute). We now start to release the plunger lock such as to allow the plunger to come back a bit relieving some of the pressure. Bubbles form in the beer and rise to the top. There is no foam as he syringe was wetted with a miniscule drop of octanol. We measure the partial pressures of N2 and CO2 in the head space of the syringe and compute their sum and their ratio. These are plotted in, respectively, red and blue, against the ratio of the gas volume to the beer volume.

It is obvious that when the gas volume is tiny its composition will be the same as the head space gas in the keg: 3 atm N2 and 1 atm CO2 for a total pressure of 4 atm and a 3:1::N2:CO2 partial pressure ratio. It is also obvious when the plunger is drawn way back such that the gas volume is many times the beer sample volume that the total partial pressures will be very low and that their ratio will be ratio of the dissolved gasses molar concentrations in the beer:

3*N2Khy(5)/CO2Khy(5) = 0.0371124

The curves show what happens between these two extremes. Note that the pressure curve does not include the partial pressure of water vapour.

The mistake 55x11 is making is in assuming that the conditions in a stout bubble are represented by this low pressure region.

 

[55x11]

I'm not sure whose chemistry you are using but the rest of the world's chemistry describes what I have been posting.

The chemical potential of a gas dissolved in a liquid is

mul = mul0 + R*T*ln(c)

where R is the gas constant, T the absolute temperature and c the concentration of the species in the liquid. mug0 is a constant representing the potential when the concentration is 1.

The chemical potential of the gas in the gas phase is

mug = mug0 + R*T*ln(P)

where R and T are the same but mug0 represents the potential when the partial pressure P = 1.

When gas and liquid are in equilibrium the chemical potentials are equal and there is no net exchange of gas between solution and head space

mug0 + R*T*ln(P) = mul0 + R*T*ln(c)

so ln(c) - ln(P) = (mul0 - mug0)/(R*T)

and the ratio of concentration to pressure is

c/P = exp((mul0 - mug0)/(R*T))

which is clearly the Henry coefficient.


If you dilute a beer gas, say with 1:1 ratio of N2 to CO2, you will end up with 100:1 ratio of CO2 to N2 at 0C (and very similar ratio at room temperature).

If you equilibrate water or beer with a 1:1 mix of N2 and CO2 the concentration ratio , cCO2/cNO2 , in mg/L will be approximately 100 to 1 but if you draw some of that liquid out of keg with a syringe keeping it under pressure (if we used 1 bar each N2 and CO2 that would be 2 bar) and then reversibly (that is a thermodynamics term which you should really understand the meaning of if you are to grasp this) decrease that pressure a tiny bubble will form. The partial pressures of CO2 and Nitrogen within that bubble will be 1:1 (to within an infinitesimal tolerance) because only an infinitesimal mass of either gas has moved to the bubble and Raoult's law still applies. mul0 and mug0 are still the same constants and so is R. For purposes of this discussion we'll assume T is the same.


What you find in the gas depends on the volume to which you have expanded in the syringe or, invoking the gas law, the pressure within it. I put some numbers in a previous post for a 3:1 N2/CO2 ratio. When the gas (no bubbles here - we assume at this point we've put some hexanol or octanol in the beer) volume is 4% of the liquid volume (I started with 100 cc of beer at 4 atm and eased the plunger back to an extra 4 cc) the pressure (ignoring water vapour) over the liquid would be about 2 atm and the ratio of partial pressures 1:1. If I ease back another 4 cc so the volume of the gas is now 8% of the volume of the beer the pressure in that gas is (sans water vapor again) about 1.5 atm and the ratio of N2 to CO2 pressure is now 0.61. And it continues to drop until the volume of the gas is about 10 times the volume of the liquid at which point PaN2/PaCO2 is clearly leveling off at about 0.04 (not 0.01 ~ 100:1) By weight the ratio is 0.027.

You can do these calculations yourself. To get you started for CO2 the Henry coefficient is
0.03875*exp( 2400*( (1/T) -(1/298.15) ) )

and for N2 it is

0.000625*exp( 1300*( (1/T) -(1/298.15) ) )

with T in Kelvins.

R = 0.08206 // atm•L/mol•K

What you have to do is start with a volume of beer with x mol/L dissolved gas with no head space under some pressure. Now you start to add in head space incrementally. When the head space is Vh the moles of gas in it are P*Vh/(R*T) and the concentration of the gas dissolved in the beer is Vb*P*KHy. The sum of these two is Vb (volume of beer) times the initial concentration. Solve for P. It is then a simple matter to get the partial pressures and the ratio.



What you seem to be failing to take into account is the pressure of the released gas i.e. the volume to which the gas which escapes from the beer expands. What controls that is the surface tension of the beer. The bubbles are tiny and their internal pressure is inversely proportional to the radius. Thus the expansion is to only a small fraction of the beer volume and we are pretty high up on the N2/CO2 curve. I don't know what the radius of the bubbles is nor what the surface tension of Guiness is (but I'll bet the lab guys at Guiness do). It's quite plain from the physics alone that the ratio of N2 to CO2 is pretty high (not as high as 3:1 or maybe not even as high as 1:1). From the physics. Now let's take into consideration that there is a huge drop in CO2 chemical potential across the membrane of the bubble. The atmosphere is at 0.0003 bar CO2. But it as at 0.8 bar N2. I don't know what the diffusion properties of a Guiness bubble are WRT either of these gasses but it's pretty obvious the CO2 wants to get out much more than the N2 does. So I'm guessing that when you take this into account the ratio of N2 to CO2 is pretty high. Given the evidence (that the CO2 prick is reduced noticeably) we have further support for that notion.


I don't see why that shouldn't be the case.

You'd lose that one for reasons given above. I used to say you could get 95% of the nitrogen effect that way but I'm lowering that now that I understand the process better.[/QUOTE]

I appreciate the response, and the explanation, I now understand it fully I think. I can double-check calculations but it looks about right.

I wasn't arguing with Henry's Law, I was just saying that ratio of gases won't be 3:1 entire time because liquid will quickly run out of N2 and so there will still be more CO2 in the foam than N2 - at 1 volume of CO2, liquid only has something like 0.05 volumes of N2, assuming beer gas. But you are correct, it's not going to be 95% CO2, assuming it's equilibrium process (I assumed most gases will end up in the foam eventually).

But is it really an equilibrium process? My feeling is that because we are forcing beer through Guiness tap with small aperture, turbulence is "knocking out" or precipitating dissolved gases without much regard for equilibrium.

If foam was all about equilibrium, the glasses of beer (normally carbed only) would end up with the same amount of head, but we know that the pour, length of line, serving pressure, type of faucet, can change the amount of foam dramatically.

Furthermore, you can take any glass of beer where the foam appears to be settling, insert a syringe, pull some liquid back and reinject it back, forcefully - and this will foam the beer more.

So my assumption is that the faucet can precipitate most of N2 and CO2 out in non-equilibrium pathway of some sort, by agitating the liquid.

But let's assume it's equilibrium process that proceeds gradually. Then it would appear first bubbles to form will have highest amount of N2 (3:1), and the last ones will be essentially pure CO2. Is that a factor in foam stability at all? Would the N2 dominated bubbles that formed immediately during pour be on top of the foam and CO2 bubbles at the bottom?

I definitely agree about the disproportionate ratio of partial pressures of CO2 and N2 relative to atmosphere. But could it be that the top N2 layer of bubbles somehow prevents bottom bubbles from bursting, becoming a sort of "membrane" that CO2 must diffuse through?

Anyways, thanks for clarifying the physics/chemistry, I think it's a bit clearer now, even though I am still confused on how equilibrium or non-equilibrium this whole process is.

 

[55x11]

The mistake 55x11 is making is in assuming that the conditions in a stout bubble are represented by this low pressure region.

I admit it, I was wrong for me to think/assume the composition will be dominated by low-pressure ratio. I owe you a beer for this detailed explanation!

It's a beautiful (and informative curve) - I would guess most Guinness style stout pours will end up with head/volume ratio of about 0.1. Which seems to correspond to N2:CO2 partial pressure ratio of about 0.5.

Still blows my mind to think about how rapidly the composition of gases within nucleating bubbles shifts from 3:1 for early bubbles to something below 0.1-0.2 probably (so that the average is say 0.5).

 

[ajdelange]

You ask lots of reasonable questions about where we are WRT equilibrium none of which I can answer except to say that we aren't at equilibrium but then in brewing we never are. Thermodynamics is great at telling us whether something can happen but not so good at letting us know whether it will nor how long it might take. Nonetheless, its about all we have in many cases and it is clear in most of them which direction we are going in.

It may be helpful to look at the same data in the form of a ratio vs bubble pressure (remember it is not really bubble pressure but rather head pressure in the syringe experiment which we are assuming is a reasonable proxy for bubble pressure). I think it is reasonable to suppose that bubble pressure is somewhat above 1 atm as the bubbles are sitting under 1 atm when in the glass and there is the additional internal pressure from the surface tension. Based on that it looks as if the ratio is going to be 0.2 to 0.4 (Nitrogen/CO2). But then I have made the thermodynamic argument that CO2 wants out more than N2 because of a much larger CO2 chemical potential gradient across the bubble film. This suggests that the bubbles upon reaching the surface and becoming foam bubbles will shrink by preferential loss of CO2. But as it is a thermodynamic argument I can't say if this does happen nor how long it might take if it did.

 

[55x11]

You ask lots of reasonable questions about where we are WRT equilibrium none of which I can answer except to say that we aren't at equilibrium but then in brewing we never are. Thermodynamics is great at telling us whether something can happen but not so good at letting us know whether it will nor how long it might take. Nonetheless, its about all we have in many cases and it is clear in most of them which direction we are going in.

It may be helpful to look at the same data in the form of a ratio vs bubble pressure (remember it is not really bubble pressure but rather head pressure in the syringe experiment which we are assuming is a reasonable proxy for bubble pressure). I think it is reasonable to suppose that bubble pressure is somewhat above 1 atm as the bubbles are sitting under 1 atm when in the glass and there is the additional internal pressure from the surface tension. Based on that it looks as if the ratio is going to be 0.2 to 0.4 (Nitrogen/CO2). But then I have made the thermodynamic argument that CO2 wants out more than N2 because of a much larger CO2 chemical potential gradient across the bubble film. This suggests that the bubbles upon reaching the surface and becoming foam bubbles will shrink by preferential loss of CO2. But as it is a thermodynamic argument I can't say if this does happen nor how long it might take if it did.

assuming bubble size is about 100 microns (as reported by Guinness themselves) and surface tension of beer is about 40mN/m, the Laplace pressure should be on the order of 4*\gamma/R=1600 Pa, or about 1.6% of atmospheric pressure - small correction.

 

[ajdelange]

I never put any numbers in but recall that a 1u bubble in water was a little over an atmosphere (1.4 atm - checked it). Doubling that for two interfaces in a foam bubble and noting that beer's surface tension is about half that of water's gets us back to about 1.4 atmosphere for a 1 u bubble and about 1.4% of an atmosphere for a 100u bubble which is ROM what you got. Now how about the size? A human hair is about 100 u and while it seems that the bubbles in the beer are perhaps that size the bubbles in the foam seem smaller than that based on visual inspection (not that I see that well in this range of sizes). In any case I don't think we could expect more than 0.1 bar (14u bubble).

I set a dial caliper for 100 u and looked at it under a dissecting microscope then drew 100 mL of stout (75% N2, 25% CO2) and looked at the foam. This is very crude because my 'measurement' is by comparison of how wide the caliper gap looks to how big the bubbles appear to be but I'd say there were no bubbles as big as 100u with the average size perhaps 1/2 - 2/3 that and quite a few less than that. Doesn't really change the conclusion but interesting.


EDIT: Wait a minute! That's radius we're talking about. I was looking at the diameter of the bubbles! So radii 50u and less for internal pressures of 2.8 - 10% of an atmosphere but 10% of an atmosphere would correspond to a 28u diameter bubble. Sill not a game changer but might as well have it right.

 

[Littlestan]

You guys just scienced the **** out of this. Well done! Love chewing into a largely technical read about anything homebrewing.

 

[BitterSipper]

I'd doubt it too but as the nitrogen content in the bubbles is 66% (in our example) and 75% in an actual Guiness serving set up the picture is far different.

I'm still really confused as to how you can say there is almost no nitrogen dissolved in the beer, yet the bubbles will form mostly full of nitrogen.

 

[ajdelange]

Just the laws of physics at work. Nitrogen is not very soluble meaning that a lot of nitrogen pressure in a space over water (or beer) puts very little into solution. But the law works the other way too. It also says that very little nitrogen in solution puts lots of it into the space above the liquid.

 

[BitterSipper]

Just the laws of physics at work. Nitrogen is not very soluble meaning that a lot of nitrogen pressure in a space over water (or beer) puts very little into solution. But the law works the other way too. It also says that very little nitrogen in solution puts lots of it into the space above the liquid.

OK, but there's basically no nitrogen to make many bubbles. If you actually try to dissolve pure nitrogen in beer/water etc, you get basically no bubbles, you would barely get any observable head and the beer would taste completely flat. Knowing that, to say the bubbles will be mostly nitrogen goes against basic logic. Maybe the first bubble.... but the main composition of the head will be essentially void of nitrogen and everything that effects your perception should be irrelevant to the nitrogen.

 

[ajdelange]

All the physics have been set out with numerical examples in the previous postings in this thread. You just need to understand the physics to see how it works. See esp. the gedenken experiment with the syringe.

There is, in fact, quite a bit of nitrogen in a can of Guiness. Each can gets a couple of drops of liquid nitrogen just before it is sealed. That is enough to raise the pressure high enough in the pasturation tunnel to drive the beer into the widget and, expanded to atomospheric pressure would lead to quite a bit of gas.

Remember that Guiness does not have much head. A quarter inch is about right - at most, perhaps, a half. It is made up of tiny bubbles that are mostly nitrogen because of the laws of physics. Work the numbers given in the examples above and it should become clear. The fact that it is counter to your intuitions doesn't mean it runs counter to everyone elses. Yes, there are some nuances here involving surface tension and the Henry coefficient for the two gasses. You will have to understand those aspects of physical chemistry before you can understand how this works.

 

[BitterSipper]

The fact that it is counter to your intuitions doesn't mean it runs counter to everyone elses.

I am not speaking of intuition I am speaking of experimental results. Again, try dissolving nitrogen in beer, you will get effectively zero head, and that would be from beer with a greater content of dissolved nitrogen.

Repeating "physics says" is a response of no value, and a poor rebuttal.

That combined with zero response of the valid logic that since there's many times more CO2 dissolved than nitrogen, that it's impossible for there to always be more nitrogen, makes me wonder if you understand the physics.

"if you can't explain it simply, you don't understand it well enough"

 

[ajdelange]

I only repeat that you need to understand the p-chem because clearly you don't as you clearly demonstrate in your penultimate paragraph. I have dissolved nitrogen in beer with the result being just what the science predicts.

I am not so concerned about proper rebuttal as I am about helping you to understand this. You will not be able to do that unless you can follow the rather straightforward postings that precede this one. I can't explain it much more simply than I have already.

 

[ajdelange]

Can you accept that if beer is confined in a container and is at equilibrium with a headspace mixture that is 3:1::N2:CO2 (keg of Guiness ready to serve) that were you to disturb the keg to the point that a bubble formed in the beer its N2:CO2 ratio would be the same as in the headspace (3:1)? Were it otherwise Henry's law would have to be different for the interface between the headspace and the beer and the bubble interior and the beer. How could this be? There is only one Henry's law. If you can accept that this is the case we can go forward from there. If not read #67 until you understand it and then we can go forward. Perhaps you are not familiar with Henry's law or the concept of chemical potential. Any p-chem text should get you up to speed on those but there should be enough in #67 to explain things adequately. A couple of other posters here have seen the light. You should be able to as well.

 

[BitterSipper]

I only repeat that you need to understand the p-chem because clearly you don't as you clearly demonstrate in your penultimate paragraph.

No, I choose not to get into what is not relevant. It does not matter what the contents of a bubble under pressure inside of the keg or under pressure in a syringe are. I even conceded to you that possibly some bubbles might contain mostly nitrogen, but this is not relevant to the context. It matters how much of each gas is dissolved and the amount that they diffuse during the pour. On a cursory exam of your postings, you even contradict your own statement, even with best case equilibrium scenarios that don't even account for the complete circumstances of pouring a beer.



I saw an easy way to show this to you and I have posed to you fully valid logic that is completely contradictory to your statement but you refuse to address it.

but as the nitrogen content in the bubbles is 66% (in our example) and 75% in an actual Guiness serving set up the picture is far different

Again, I pose to you a simple logic argument;
Beer poured with only nitrogen dissolved in it forms next to no head
A beer with less nitrogen dissolved in it must have less of a head comprised of nitrogen than the beer with more nitrogen.
Beer poured with CO2 and nitrogen has less nitrogen dissolved than the 100%, but pours with a substantial head.
That head must be comprised of mostly Co2.


If you repeat Henrys law again, I will assume you simply have no supporting argument for your statement.

 

[ajdelange]

No, I choose not to get into what is not relevant. It does not matter what the contents of a bubble under pressure inside of the keg...

And in so saying declare with even louder voice that you don't know what you are talking about.

I saw an easy way to show this to you and I have posed to you fully valid logic that is completely contradictory to your statement but you refuse to address it.

It only contradicts what I say because it is wrong.

Again, I pose to you a simple logic argument;

Hardly

Beer poured with only nitrogen dissolved in it forms next to no head
A beer with less nitrogen dissolved in it must have less of a head comprised of nitrogen than the beer with more nitrogen. Beer poured with CO2 and nitrogen has less nitrogen dissolved than the 100%, but pours with a substantial head.
That head must be comprised of mostly Co2.

Except that it isn't. You can verify this for yourself fairly simply. Draw a beakerfull of beer with the spout below the surface of the beer. Equip a good sized syringe with a short length of tubing and have a pair of haemostats handy. Draw a goodly amount of beer into the syringe. As you do so it will foam. Draw it gradually so that no (or very little) air leaks in around the plunger. Hold the syringe vertically. Shake it. As you do so more gas will escape the beer displacing it. When you have recovered a good amount of gas depress the plunger until all the liquid is out of the syringe. You now have a syringe with nothing but gas from the beer in it.

Move the end of the tube to a container of a strong lye solution and carefully draw in 10 - 20 cc of it. Clamp the tube before withdrawing from the lye. Shake. The gas volume from a regular beer will change dramatically from say 35 to 5 ml (what I just got with a Pils amounting to an 86% reduction in volume). With a stout (or any beer drawn on mix) the gas volume will change less dramatically. I just got about a 50% reduction with the stout I have on tap. Clearly, as the theory (based on the Henry Law) predicts, the bubbles in my stout are about 50% nitrogen. And we note that work at the Guiness lab says theirs contain about 75% nitrogen.

If you repeat Henrys law again, I will assume you simply have no supporting argument for your statement.

You don't understand the theory. You have no experimental evidence. I have both. I think we have to give this one to science.

I am happy to discuss, explain, illuminate to the extent I can any of this but there comes a time when one realizes that he is trying to teach a pig to sing. As the old adage goes one shouldn't do that as he isn't going to succeed and it annoys the pig. I think we are at that point. If I see a logical question I will respond in turn. If not, I won't.

I do hope the other readers were interested by the little experiment I did tonight. Pretty neat and based on the ASBC MOA for determining the amount of carbon dioxide in a beer.

 

[timdillon36]

So if we look at the scientific method, in the few years of this post, we have steps one to three covered.

Its time to test, analyze, and report findings.

I am willing to help in the testing but currently lack the funds for a nitro or beer gas setup but i do have a simple way to test the one theory of carbing a beer and then dispensing at higher presure with a bladder.

Anyone in the Indy area willing to help with this please PM me.

My idea for this experiment:

Make a large batch of a clone of a commercially available stout. I have the equipment to makea 15g. I was also thinking a left hand millk stout clone because bloth reg and nitro versions are available for comparison.

Ferment beer in one or several FV.

Transerfer into 5 seperate 2.5g cornies and one bladder vessel which i can provide.

Keg 1 carb as normal and serve with co2 at high pressure.

Keg 2 carb as normal and push with nitro.

Keg 3 beer gas

Keg 4 remove all co2 from beer using vacuum or wine whip? and put on straight nitro.

Edit
Keg 5 carb as normal and serve with short large diameter line.

Assemble a group of 20-30 taste testers.

Collect data and report results.

 

[ajdelange]

Looking back over the thread it appears that there are many long standing misconceptions about pouring beer with mix. I used to believe, as many appear to, that the CO2 is there to make the bubbles and the N2 to push the undercarbonated (by usual standards) beer hard enough through the sparkler plate to produce the tiny bubbles which I, too, thought contained no nitrogen. I used to argue that one could get the same effect as beer gas by carbing to 1 vol, storing at 1 vol and then temporarily doubling or tripling the CO2 pressure while serving.

What I've gotten from this thread is that the CO2 for carbonation and N2 for pushing model is wrong. The goal is to have a bubble with about equal amounts (partial pressures) of CO2 and N2 in order to dilute the CO2 to the level where the carbonic 'prick' on the tongue is attenuated thus making for a smoother, milder, creamier head. I did not understand this until I did the sums in response to this thread. This, is I think, the most important aspect of the discussion here.

 

[passedpawn]

This is the Brew Science forum. If applying science (math, chemistry) to the properties of beer and brewing offends you, you're in the wrong place!

The entire rest of the forum is available for discussion based on anecdotal evidence and "logical arguments". Those things have value of course, as it's mainly how brewing progressed for millennia, and to a great extent it's how it still progresses.

 

[timdillon36]

This is the Brew Science forum. If applying science (math, chemistry) to the properties of beer and brewing offends you, you're in the wrong place!

The entire rest of the forum is available for discussion based on anecdotal evidence and "logical arguments". Those things have value of course, as it's mainly how brewing progressed for millennia, and to a great extent it's how it still progresses.

I dont know if this is directed at me or in general.

I agree that science and formulas based on theories and laws are very useful. But those theories and laws were not accepted as such without testing with results that back up those hypothesis.

I am in no way educated enough to understand most of the math that has been discussed but i do grasp the concept and would like to test the ideas that have been talked about. If anyone else has acces to equipment to measure results better or has a better plan on how to do this test please speak up.

I make my living working on a professional race car. I have seen time and again the guys at the desk have an idea that should work great on paper but when you take it to the track you find that they were so focused on one part rather then the whole the car is slower.

If we want more than anecdotal evidence maybe some people here that have access to lab grade equipment can test the beer and foam that is poured from different methods.

View this as you want but what i am saying is i am willing to be your lab tech in training. If anyone else that has a more ambitious plan or a better idea on how they plan to carry this to fermentation (or fruition) i believe this needs to get past talking shop.

With science and technology along with testing those ideas we continue to advance and build a better mouse trap.

How many times has palmer been quoted but then proven wrong in the past 20 years.

I do not dispute anything that was said earlier but am being redundent again that it should be tested.

If a bar uses beer gas to serve all beer does that mean the local ipa poured from a bottoms up will now be a nitro ipa?

 

[ajdelange]

While I cannot speak for passedpawn I am certain his remarks were not directed at you but out our resident Luddite.

I did post in #85 a simple method for estimating the relative nitrogen/CO2 content of your beer foam/bubbles using nothing more sophisticated than a syringe.

Based on my take on this thread the most important taste test you can do is a comparison (double blind triangle of course) of the heads on the same beer poured with straight CO2 against those poured with mix. Is there a statistically discernable difference in the 'creaminess' of those heads?

 

[BitterSipper]

And in so saying declare with even louder voice that you don't know what you are talking about.

Except that I do, you are equating keeping a discussion simple as ignorance, which is a flaw in your own character.

Again, the diffusion of gas under 3 atmospheres of beer gas is irrelevant to beer in a glass under 1 atmosphere of mostly nitrogen and oxygen, and essentially void of co2. That you keep claiming they are is astounding.

Not to mention that the conditions of pouring a beer are not that of undisturbed progression to to equilibrium, which all of your posts have basically used as a premise, and at least one of your posts has contradicted your own claim.

Draw a beakerfull of beer with the spout below the surface of the beer. Equip a good sized syringe with a short length of tubing and have a pair of haemostats handy. Draw a goodly amount of beer into the syringe. As you do so it will foam. Draw it gradually so that no (or very little) air leaks in around the plunger. Hold the syringe vertically. Shake it. As you do so more gas will escape the beer displacing it. When you have recovered a good amount of gas depress the plunger until all the liquid is out of the syringe. You now have a syringe with nothing but gas from the beer in it.

Move the end of the tube to a container of a strong lye solution and carefully draw in 10 - 20 cc of it. Clamp the tube before withdrawing from the lye. Shake. The gas volume from a regular beer will change dramatically from say 35 to 5 ml (what I just got with a Pils amounting to an 86% reduction in volume). With a stout (or any beer drawn on mix) the gas volume will change less dramatically. I just got about a 50% reduction with the stout I have on tap. Clearly, as the theory (based on the Henry Law) predicts, the bubbles in my stout are about 50% nitrogen. And we note that work at the Guiness lab says theirs contain about 75% nitrogen.

Great, you're actually moving your experiment towards the conditions of an actual pour of beer, that's good. However, you're still a long ways off. You still aren't diffusing in the proper conditions and you seem to have tried to recreate some of the disturbances of a pour, but I would be aghast if you claimed it was equivalent.

 

[BitterSipper]

This is the Brew Science forum. If applying science (math, chemistry) to the properties of beer and brewing offends you, you're in the wrong place!

I don't, I take issue with the misapplication of principles, and the poor control of variables.

The entire rest of the forum is available for discussion based on anecdotal evidence and "logical arguments". Those things have value of course, as it's mainly how brewing progressed for millennia, and to a great extent it's how it still progresses.

It's an easily understood equivalent. If I can explain to a person that their diatribe is contradicted by basic logic, they should immediately review their statements and address that logic directly. I chose a simple "anecdotal" (not technically, but whatever) route to point out the flaws in his reasoning. If you prefer a plain stating of facts;

There is much more CO2 than nitrogen dissolved in beer under beer gas.
Under 1 atmosphere of pressure of earths air, which is comprised mostly of nitrogen and effectively no CO2, effectively all the CO2 will diffuse out. In addition not all of the already much lower amount of dissolved nitrogen will. I already conceded to him that initially, nitrogen may (in his context) diffuse more quickly. However, there is very little of it and more importantly;

This is ignoring the fact that the beer is highly disturbed during the pouring process. The forcing of the liquid through such a small restriction causes immense conditions. Rapid pressurization and depressurization, high velocities, cavitation etc. What occurs during this process is not explained by simple gas principles (at least not the way they are being applied here), not that they agreed in the first place.