Thread by @BucknellThermo

Hi! This is Cammie and Reagan, & over the next few hours, we're going to tell you all about the elusive concept of fugacity!

Before you scroll past & lose some pretty valuable information, ask yourself this: do you like beer?

If you answered no, don’t fret: this thread is for you! We’re taking a deep dive into two different camps of beer, comparing their taste & texture through the lens of fugacity. You don’t have to settle for draft beer any longer, & this is why!

Have you ever wondered why some beers are more rich than others? Or why a smooth head is a staple of certain breweries? It has to do with the tap! 3/

p.s.- forgot to add numbers to the last few, sorry

You’ve seen beer taps before. They bring beer to the customer from the cylinder or keg it’s stored in. Most taps use pressure-dispensing methods to make beer flow. That is, the beer is pushed out of the tap by a type of gas from the keg. (4/)

In brewing communities, people noticed that the “beer gas” used to create flow has an effect on the taste & texture of beer. Depending on the type of gas used, different styles of beer can be produced & served to the customer. (5/)

The draft beer you’re probably most familiar with is pumped from a 100% CO2 gas line. These beers are bubbly & slightly acidic, with frothy, light heads. (6/)

The other type of draft beer we’ll be talking about today is nicknamed a “nitro beer.” Nitro beers are pumped from a 70% nitrogen, 30% CO2 gas line. These beers are less acidic, rich in flavor, and have more of a dense head. (7/)

While it may not seem like a gas line would affect an alcoholic beverage a lot, you can actually see the difference, let alone taste it! (8/)

Don’t believe us? If you’ve ever had a Guinness brew, it was probably a nitro beer. How did it compare to a Budlight, or even a traditional lager from Miller? We’re going to try and explain these differences now. (9/)

We did some intense research on homebrewing and beer threads all over the internet. We’ve seen two explanations of why this is the case. The first has to do with pressure, and the second has to do with solubility. (10/)

The pressure camp says that the differences are due to varying tap pressures. Traditional draft beers are tapped at 12 psig, while nitro beers are tapped at 30 psig. The higher pressure could cause smaller bubbles, making nitro beers smoother. (11/)

On the other hand, the solubility camp says that the differences are due to the fact that nitrogen is a smaller molecule, so when it dissolves in the beer, smaller bubbles are produced. (12/)

So. Which explanation is correct? Before we can answer this question, we’ll need to introduce a few concepts. (13/)

First, we gotta talk about ideal behavior. Ideality in gases assumes that there are no interactions, & in liquids assumes that all interactions are identical. However, we know this isn’t true: molecules *do* interact, & their interactions are uneven. (14/)

This is fugacity comes into play. We can quantify how non-ideal something is behaving with the fugacity coefficient, ϕ. The closer ϕ is to 1, the more ideal the gas is behaving. For liquids, γ takes the place of ϕ, and γ = 1 for ideal behavior. (15/)

In a keg, there’s a mixture of liquid and gas, i.e. beer and beer gas, so we also have to talk about mixtures. (16/)

When the amounts of each component in each phase do not change, the system is said to reach equilibrium. Mathematically, this means that the component fugacity of each phase (ie, beer and beer gas) are the same. (17/)

We can use this equilibrium expression to find how ideal a pint of beer is behaving. While the homebrewing community feuds over the pressure v. absorption argument, we believe that the essence of each side has to do with ideality of draft v. nitro beer. (18/)

Now, let’s take a look at the math. For a traditional draft beer stored in a keg at 12 psig, we find that the fugacity coefficient at equilibrium is 0.995. Pretty close to ideal! (19/)

For a nitro tap at 12 psig, the fugacity coefficient at equilibrium is 0.9996. (20/)

The temperature is pretty cool for the kegs & the pressure is relatively low, so it makes sense that both gas lines would act ideally. But 12 psig isn’t the normal operating pressure of nitro taps! Nitro taps over double the pressure at about 30 psig. (21/)

When repeating the calculation, we find that a nitro tap has a fugacity coefficient of 0.8301. Admittedly, it’s still pretty ideal, but it’s a lot farther from 1 than the CO2! (22/)

A gas that acts less ideally will have stronger interactions between itself, making for smaller bubbles overall. The smaller the bubble, the more dense the beverage will be. So, it makes sense that a less ideal beer gas will create a rich, heavy beer. (23/)

Let’s compare even further, with the activity coefficients from the liquid phases. For a traditional draft beer, γ is 2.84 for carbon dioxide in solution. (24/)

For a nitro beer at 30 psig, γ ends up being 0.2056 for nitrogen in solution. (25/)

It’s pretty clear that both taps have some pretty non ideal interactions within the “solution” of beer and gas. However, these numbers help those who believe that the absorption of nitrogen causes the differences between the two beers as well! (26/)

We know that CO2 is more reactive & interactive than nitrogen. Because beer is basically water and ethanol, the absorption of CO2 will actually allow the gas to dissociate and create an acid. (27/)

This dissociation creates uneven interactions between H2O, CO2, and ethanol. In theory, a traditional draft beer should be *very* non ideal & we see that in our calculations! A γ of 1 indicates ideal solution behavior, & we calculate a γ of nearly 3 for draft beer. (28/)

With nitrogen, it is not easily absorbed, let alone dissociated into the beer. Even if we could absorb the same amount of nitrogen in beer (as seen in our example) the gas is equally unreactive in water and ethanol. (29/)

This means that the interactions in solution should be much more ideal & even in nitro beers than traditional beers. & we see this in our calculations! A γ of 0.2 is much closer to 1 comparatively, meaning that nitro beers are a more ideal solution. (30/)

In fact, with our gas line still containing 30% of CO2, it may even be possible to make nitro beers even more rich and dense by using a 100% nitrogen line! (31/)

So, in a message to both camps: yes, you’re correct! By acting more non-ideal in the gas line, and more ideal in the beer, the use of nitrogen actively makes the best environment for a rich, dense beer. (32/)

... and it all has to do with fugacity, a theoretical measurement of exactly how ideal a solution or gas is! Guess you never knew just how important thermodynamics could be when it comes to your beer! (33/)

For more insight on the benefits of using nitro beer, you can visit: homebrewtalk.com/forum/threads/… This is where we got some inspiration to look into the argument ourselves! (34/)

And if you want to learn more about fugacity, there is a GREAT comic book that explains it super well, along with more applications of the concept! northeastern.edu/landherr/wp-co… (35/)

Well that’s all we have! Hopefully you learned more than you previously knew, whether it be about fugacity, ideality, or beer! (36/36)