TL;DR: Don’t worry about headspace.
The common consensus among home brewers has been to keep headspace in the fermenters to a minimum. This is usually attributed to the need to reduce the amount of oxygen in the headspace from ruining the beer through Oxidation, Esters and Acetic Acid production etc.
However this usually requires us to buy two different sized fermenters. A large fermenter for primary with extra space for krausen, and one for secondary that minimizes headspace. Truth is, I don’t want to buy a bunch of different sized bottles, and I’m guessing you don’t either. So how big of a problem is headspace in secondary, and is it a problem to age/lager my beer in a fermenter that’s too big?
To answer this question we need to examine how O2 gets into the fermenter in the first place.
This happens in two ways:
1) Oxygen can permeate through the walls of the fermenter, bung, and airlock.
2) Temperature swings change the volume inside the fermenter and cause air to “suck back” through the airlock.
Let’s tackle the permeation problem first.
I am going to ignore permeation through the walls of the fermenter. If you are using glass this is not an issue. If you are using PET the Oxygen permeation is much lower than comes through the airlock, therefore this is also not an issue. http://www.better-bottle.com/pdf/ClosuresOxygenPassageStudy.pdf
So if we ignore the permeation through the walls we are only left with permeation through the bung/airlock setup. The Oxygen has a couple steps before it makes it to the beer. It needs to pass through the bung/airlock, diffuse through the gas mixture in the headspace, and finally dissolution into the beer. I will address these individually,
Diffusion through the bung/airlock:
Better bottle did a great study about this that can be found here. http://www.better-bottle.com/pdf/ClosuresOxygenPassageStudy.pdf
This experiment was set up to measure the MAXIMUM flow through the bung/airlock. Ficks law (ill discuss in the next part) says that if there is any O2 in the carboy, the flow will be slower than these results ( it comes from the Cs-C term). However I claim that these results are in fact valid for our purposes as we will find out.
Diffusion through the gas mixture in the headspace:
Diffusion can be modeled by Ficks First Law. https://en.wikipedia.org/wiki/Permeation
J = -D(Cs-C)/L
Where:
• J is the "diffusion flux" (how fast the gas is moving and in what direction)
• D is the diffusion coefficient or mass diffusivity (a number we find from experimentation)
• C is the concentration of the permeate (Cs is the same but at a different location)
• L is the thickness of the membrane (or position if the problem has no membrane)
STICK WITH ME. This is as bad as the math gets I promise. What we need to realize from this equation is that the form is the same for both diffusion in a gas and diffusion through a membrane. The geometry is a little different (which is why it’s represented as “flux” and not “flow”
But the real shocker is when we compare the diffusion coefficients D.
D Oxygen (g) – air (g) - 0.176 cm^2/s
https://en.wikipedia.org/wiki/Mass_diffusivity#cite_note-Cussler-3
D O2 Silicone = 1.6×10− 5 cm^2/s
https://imageserv5.team-logic.com/mediaLibrary/99/D116_20Haibing_20Zhang_20et_20al.pdf
Here we can see that the diffusivity in a gas-gas transfer is much much faster than the gas-solid transfer. Because we are 4 orders of magnitude off, we can safely ignore the time it takes for the Oxygen to diffuse through the gas mixture in the headspace.
Dissolution into the beer:
Ok, I am admittedly going to hand waive a bit. We can’t calculate the speed of this analytically because we don’t know the value of a constant called the “diffusion layer” which is measured experimentally. Diffusion layer would show up as L in the equation above. However I claim the gas-liquid interface also transfers Oxygen much faster than the gas-solid transfer.
A quote from Morebeer:
“The dissolved oxygen levels in wort drop from saturation to near zero very quickly after pitching yeast, usually within 30 minutes under ideal conditions, because yeast absorbs the oxygen for eventual membrane biosynthesis.”
https://www.morebeer.com/articles/how_yeast_use_oxygen
Michael Tonsmeire suggests in the American Sour beer book that this happens rather quickly as well. He said (paraphrase) that a dried up airlock almost guarantees a vinegary beer.
My explanation for this phenomenon is the diffusion layer is incredibly small because the yeast (or bugs) are consuming the dissolved oxygen very quickly. If the yeast consume the Oxygen then it cannot contribute to the partial pressure of Oxygen. We also need to remember that this doesn’t need to be that fast to be a lot faster than the first case. The rate through the bung is incredibly slow.
If anyone has any additional info on this that would be great.
But let’s move on. If the diffusion through the headspace and the dissolution into the beer happen much much faster than the permeation through the bung/airlock then we can conclude that the rate of Oxygen transfer is determined solely by the permeability of the bung/airlock! Not headspace!
Now let’s consider the case of a large temperature drop. In a temperature drop the air drops in volume. This volume drop sucks some bubbles back through the airlock. (I am assuming S-type airlock. The 3 piece airlock you might be sucking in fluid.)
The volume of air bubbles coming in through the airlock can be measured by the Ideal gas law under an Isobaric process.
In an isobaric process pressure is constant and:
V2 = V1(T2/T1) (Remember these temperatures are in Kelvin)
Let’s set up a sample problem set to measure a bad thing happening to your beer: 1 gal of headspace (5gal beer, 6 gal fermenter) and a 10 degree F temperature swing (pretty significant.)
1.02 = 1(297/291)
The change in volume is 0.02 gallons which is about 76ml (~1/3 cup! A whole lot of bubbles!)
But is that really an issue? Only about 20% of this air is O2 so we end up with 16ml (16cc’s) of O2.
If we compare this to the diffusion through a water-trap airlock (2.6 cc’s/day). A 10 degree F worth of bubbles equals about 6 days’ worth of O2 traveling through the bung. This is less than using a silicone bung for a single day, which many people do with no problems.
So even if this happened every day, we can safely ignore it.
Now there is one area where headspace is a huge concern. This is in sampling. When you take a sample from the fermenter you can pretty much count on the headspace being 20% Oxygen when you put the airlock back. If you can purge with CO2 then definitely do that. If you can’t, then keep sampling to an absolute minimum.
This is also the case when racking to secondary. The air in the headspace is 20% Oxygen and will be absorbed into the beer. This could be significant. Purge with CO2 if possible.
In conclusion the rate at which oxygen permeates into the fermenter is unchanged by headspace. And while the amount of bubbles sucked in through the airlock can look like a big problem, in reality it’s no big deal. Headspace is not a problem for homebrewers so long as you keep sampling to a minimum and only rack once. The racking and sampling are the main offenders here so keep them to a minimum.
In practice, this means that we can stop buying 5 gallon fermenters for aging/lagering, there’s no point.
Yes, I know I got a little crazy with this. It’s a sickness. I can’t help myself. Hopefully this was helpful.
Cheers
The common consensus among home brewers has been to keep headspace in the fermenters to a minimum. This is usually attributed to the need to reduce the amount of oxygen in the headspace from ruining the beer through Oxidation, Esters and Acetic Acid production etc.
However this usually requires us to buy two different sized fermenters. A large fermenter for primary with extra space for krausen, and one for secondary that minimizes headspace. Truth is, I don’t want to buy a bunch of different sized bottles, and I’m guessing you don’t either. So how big of a problem is headspace in secondary, and is it a problem to age/lager my beer in a fermenter that’s too big?
To answer this question we need to examine how O2 gets into the fermenter in the first place.
This happens in two ways:
1) Oxygen can permeate through the walls of the fermenter, bung, and airlock.
2) Temperature swings change the volume inside the fermenter and cause air to “suck back” through the airlock.
Let’s tackle the permeation problem first.
I am going to ignore permeation through the walls of the fermenter. If you are using glass this is not an issue. If you are using PET the Oxygen permeation is much lower than comes through the airlock, therefore this is also not an issue. http://www.better-bottle.com/pdf/ClosuresOxygenPassageStudy.pdf
So if we ignore the permeation through the walls we are only left with permeation through the bung/airlock setup. The Oxygen has a couple steps before it makes it to the beer. It needs to pass through the bung/airlock, diffuse through the gas mixture in the headspace, and finally dissolution into the beer. I will address these individually,
Diffusion through the bung/airlock:
Better bottle did a great study about this that can be found here. http://www.better-bottle.com/pdf/ClosuresOxygenPassageStudy.pdf
This experiment was set up to measure the MAXIMUM flow through the bung/airlock. Ficks law (ill discuss in the next part) says that if there is any O2 in the carboy, the flow will be slower than these results ( it comes from the Cs-C term). However I claim that these results are in fact valid for our purposes as we will find out.
Diffusion through the gas mixture in the headspace:
Diffusion can be modeled by Ficks First Law. https://en.wikipedia.org/wiki/Permeation
J = -D(Cs-C)/L
Where:
• J is the "diffusion flux" (how fast the gas is moving and in what direction)
• D is the diffusion coefficient or mass diffusivity (a number we find from experimentation)
• C is the concentration of the permeate (Cs is the same but at a different location)
• L is the thickness of the membrane (or position if the problem has no membrane)
STICK WITH ME. This is as bad as the math gets I promise. What we need to realize from this equation is that the form is the same for both diffusion in a gas and diffusion through a membrane. The geometry is a little different (which is why it’s represented as “flux” and not “flow”
But the real shocker is when we compare the diffusion coefficients D. D Oxygen (g) – air (g) - 0.176 cm^2/s
https://en.wikipedia.org/wiki/Mass_diffusivity#cite_note-Cussler-3
D O2 Silicone = 1.6×10− 5 cm^2/s
https://imageserv5.team-logic.com/mediaLibrary/99/D116_20Haibing_20Zhang_20et_20al.pdf
Here we can see that the diffusivity in a gas-gas transfer is much much faster than the gas-solid transfer. Because we are 4 orders of magnitude off, we can safely ignore the time it takes for the Oxygen to diffuse through the gas mixture in the headspace.
Dissolution into the beer:
Ok, I am admittedly going to hand waive a bit. We can’t calculate the speed of this analytically because we don’t know the value of a constant called the “diffusion layer” which is measured experimentally. Diffusion layer would show up as L in the equation above. However I claim the gas-liquid interface also transfers Oxygen much faster than the gas-solid transfer.
A quote from Morebeer:
“The dissolved oxygen levels in wort drop from saturation to near zero very quickly after pitching yeast, usually within 30 minutes under ideal conditions, because yeast absorbs the oxygen for eventual membrane biosynthesis.”
https://www.morebeer.com/articles/how_yeast_use_oxygen
Michael Tonsmeire suggests in the American Sour beer book that this happens rather quickly as well. He said (paraphrase) that a dried up airlock almost guarantees a vinegary beer.
My explanation for this phenomenon is the diffusion layer is incredibly small because the yeast (or bugs) are consuming the dissolved oxygen very quickly. If the yeast consume the Oxygen then it cannot contribute to the partial pressure of Oxygen. We also need to remember that this doesn’t need to be that fast to be a lot faster than the first case. The rate through the bung is incredibly slow.
If anyone has any additional info on this that would be great.
But let’s move on. If the diffusion through the headspace and the dissolution into the beer happen much much faster than the permeation through the bung/airlock then we can conclude that the rate of Oxygen transfer is determined solely by the permeability of the bung/airlock! Not headspace!
Now let’s consider the case of a large temperature drop. In a temperature drop the air drops in volume. This volume drop sucks some bubbles back through the airlock. (I am assuming S-type airlock. The 3 piece airlock you might be sucking in fluid.)
The volume of air bubbles coming in through the airlock can be measured by the Ideal gas law under an Isobaric process.
In an isobaric process pressure is constant and:
V2 = V1(T2/T1) (Remember these temperatures are in Kelvin)
Let’s set up a sample problem set to measure a bad thing happening to your beer: 1 gal of headspace (5gal beer, 6 gal fermenter) and a 10 degree F temperature swing (pretty significant.)
1.02 = 1(297/291)
The change in volume is 0.02 gallons which is about 76ml (~1/3 cup! A whole lot of bubbles!)
But is that really an issue? Only about 20% of this air is O2 so we end up with 16ml (16cc’s) of O2.
If we compare this to the diffusion through a water-trap airlock (2.6 cc’s/day). A 10 degree F worth of bubbles equals about 6 days’ worth of O2 traveling through the bung. This is less than using a silicone bung for a single day, which many people do with no problems.
So even if this happened every day, we can safely ignore it.
Now there is one area where headspace is a huge concern. This is in sampling. When you take a sample from the fermenter you can pretty much count on the headspace being 20% Oxygen when you put the airlock back. If you can purge with CO2 then definitely do that. If you can’t, then keep sampling to an absolute minimum.
This is also the case when racking to secondary. The air in the headspace is 20% Oxygen and will be absorbed into the beer. This could be significant. Purge with CO2 if possible.
In conclusion the rate at which oxygen permeates into the fermenter is unchanged by headspace. And while the amount of bubbles sucked in through the airlock can look like a big problem, in reality it’s no big deal. Headspace is not a problem for homebrewers so long as you keep sampling to a minimum and only rack once. The racking and sampling are the main offenders here so keep them to a minimum.
In practice, this means that we can stop buying 5 gallon fermenters for aging/lagering, there’s no point.
Yes, I know I got a little crazy with this. It’s a sickness. I can’t help myself. Hopefully this was helpful.
Cheers
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