Applying the scientific method to fermentation

As a physics student, I always think of the microprocesses and what exactly is going on and am always predicting the future.

Now, I have a question about the rate of fermentation. The way I see it there are two possible trends at a given time frame. The rate could be either generally linear (until it starts to slow down) or it could be logarithmic.

Logarithmic:
If you look at fermentation strictly as a chemical process, you will see it as a first order reaction, where rate of change is dependent on the instantaneous concentration of the reactants. Being sugar as the reactant, you start of with a higher concentration that gets lower, hence a decreasing reaction rate and a logarithmic function.

Linear:
If you look at this from a biological standpoint, you might say the majority of fermentation occurs as a zeroth order reaction with a linear function independent of instantaneous concentration of reactants, since a single yeast cell has a maximum rate of production. Once this maximum is reached, it will continue at a linear rate until there is not enough sugar to allow every yeast cell to produce at maximum.

A combination:
Now here's where it gets really tricky and the concepts of entropy and quantum statistical mechanics comes into play (don't worry, I'm not actually going to go into this). Basically, realistically a fermentation must be looked at from a chemical, biological, ecological, and physical standpoint with both micro and macro level focuses. Ultimately we want to predict the ABV at any given time during the fermentation. Essentially the major things we would need to pay attention to (in a controlled environment) are as follows:

• Initial Sugar, nutrient, and yeast levels
• Type of yeast and it's qualities
• The rate at which the yeast will reproduce and when the active colony will cease to increase (more yeast means more fermentation)
• When and how much given concentrations of alcohol will affect yeast performance
• How big the container is (to consider surface area)

This is a lot of stuff to look at and really to the only way to get accurate trends is by extensively experimenting each variable using very accurate equipment to determine ABV at every time interval. With enough experimental data I would mathematically try to calculate a sort of rough algorithm using tedious integration (likely partial).

I think roughly the trend of (ABV vs. time) will be exponential for a short amount of time while the yeast gets acclimated and reproduces, roughly linear while the rate is at a maximum, and then logarithmic as sugar levels decrease and alcohol content rises giving it sort of a half life type behavior.

I see the process as being logarithmic. Just as in bacterial growth, the process starts to increase dramatically until slowing down as the sugars in solution begin to dwindle. Eventually, the lack of nutrients and the increase of alcohol cause the yeast to become inactive and flocculate. ABV is based on the initial simple sugar concentration and the ability of the yeast to survive higher alcohol levels. Time can vary based on these two variables and environmental factors, such as ambient temperature, liquid temperature, and initial yeast concentration. There are many ways you can experiment with these variables, have fun with it!

Logarithmic growth until it reaches steady state where the number of yeast cells is sustained by the amount of sugar available for digestion. When the amount of sugar available can no longer sustain the steady state population, there will be an asymptotic decay.

I think ABV vs. time is also logarithmic.

thechemister said:

This is a lot of stuff to look at and really to the only way to get accurate trends is by extensively experimenting each variable using very accurate equipment to determine ABV at every time interval. With enough experimental data I would mathematically try to calculate a sort of rough algorithm using tedious integration (likely partial).

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It would probably be a lot easier to capture and measure CO2 production as a function of time, rather than taking countless samples and ABV measurements.

I could imagine an airtight fitting out of the carboy with a hose running to a CO2 meter interfaced with a PC. With a fast enough scan rate, timer, and storage space, a nice graph of CO2 concentration vs. time could be generated rather easily with no external interference or sampling.

Just a thought.

Science, really?

Data leads to hypothesis, then testing and reformulation.

You seem to have started with conjecture.

Yeah, I guess that would be one way of doing it. But CO2 production doesn't necessarily tell you alcohol content does it? I would imagine different sugars yield different product ratios.

Yeast can only utilize a few simple sugars. There is also a potential for unwanted byproducts using other sugars.

Wow...to be honest, I could have fermented a batch of beer in the time it took me to read your post....lol!
What exactly are you trying to figure out? You would have to use the same type of yeast and temp and volume of liquid every single batch of beer that you brew to see a trend.
Each yeast has different temperature tolerances, different alcohol tolerances, not to mention if you are using a dry yeast vs. a liquid yeast that have a very different amount of viable cells, if you are making a yeast starter, using rehydration nutrients, yeast nutrient, and so on.
I'm not a chemistry student, but I think that there is much more to this than you may be thinking.
My suggestion is to brew a few dozen batches of beer, get familiar with the yeasts and their tolerances, I'm sure that you realize that we use many different yeasts with different outcomes, many variables, check out the manufacturer websites that will list all of the info that you need, and brew a kick ass batch of beer!!!!
RDWHAHB

There are simply too many variables to make it worth the effort.
Dissolved oxygen
Pitch rate
Fermentation temperature
Yeast strain
Yeast health
Original Gravity
Types of sugars
pH
More

You can keep as many variables constant as possible, but the data is only true for that specific system.

If the goal is just to determine if alcohol production tends to be more linear or more logarithmic at a constant temperature, 7 data points over a week should get a close enough qualitative indication.

I suspect the answer is more sigmoidal. Slow increases as metabolism is primarily aerobic, rapid gains as the large yeast mass transitions to anaerobic alcohol production, then diminishing as alcohol starts killing it off.

If you have a lab, set it up with a headspace GC sampler and small batches.

I think for most of us it's binary, done or not.

pelipen said:

Slow increases as metabolism is primarily aerobic

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Actually, the Pasteur effect does not apply when brewing yeast strains are pitched into normal worts because brewing yeast strains are Crabtree positive. Primary carbon source utilization occurs via the fermentative metabolic pathway because the glucose level exceeds the Crabtree threshold. In the presence of oxygen, a small amount of pyruvate is shunted towards the biosynthesis of sterols and unsaturated fatty via the respirative metabolic pathway; however, the cells never truly respire because the Crabtree effect shuts down the Krebs cycle (a.k.a. the TCA cycle).

Density change is roughly linear with respect to time during the most active fermentation period (day 2-4 generally). Most enzymatic reactions have a strict maximum rate due to the affinity of the enzyme for it's substrate and the phenomenon of active site saturation. These result in a turn-over limit. It is not a purely collision driven kinetics.

It becomes more logarithmic once the substrate concentration drops to a particular level and the collisions become more random. If you graph apparent extract (i.e. density) vs. time, you see a logarithmic-like function, with a short period of lag at the beginning, though the lag phase can vary greatly depending on the wort composition, pitch rate, and yeast health.

thechemister said:

Yeah, I guess that would be one way of doing it. But CO2 production doesn't necessarily tell you alcohol content does it? I would imagine different sugars yield different product ratios.

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During fermentation they are directly proportional. The products of fermenting a single hexose are 2 EtOH and 2 CO2. Plus electrons and junk and stuff. As the Zymurgist says, a very small portion of the carbon is diverted for membrane synthesis and other catabolic pathways, but this is very close to negligible.