Even making coffee is related to mathematics?

Produced by: Science Popularization China

Author: denovo

Producer: China Science Expo

Since it was introduced to China, coffee has gradually become a common drink in people's lives from a luxury drink. The modern young people's lifestyle of "I don't sleep until the moon comes" has made coffee and other refreshing drinks their "source of happiness".

People not only go to stores to buy coffee, but also choose to brew coffee at home if they have the conditions. However, brewing coffee and brewing good coffee are two different concepts. So how can you brew good coffee?

Drinking coffee at work

(Photo source: Veer Gallery)

Didn’t expect that coffee extraction also has a formula!

The taste of coffee is related to the variety, origin, roasting degree, brewing method of coffee beans, as well as the water quality, water temperature, grinding degree, dosage, and squeezing degree when brewing coffee. Coffee extraction is the most important part of brewing coffee and is the key step to get good coffee.

Extraction is a unit operation that uses the different solubility of components in the system in the solvent to separate the mixture. Simply put, it is the process of taking away the soluble substances from the coffee powder when brewing coffee with water. After extraction, the coffee we drink is a mixture of soluble substances and water. The extraction rate (%) is usually used to measure the degree of extraction. The calculation formula is:

Extraction rate (%) = the mass of coffee substance extracted ÷ the mass of coffee beans originally added

For example, if you use 20 grams of coffee powder to make coffee, and the final coffee residue is weighed to be 17 grams after drying, then the soluble component is 3 grams and the coffee extraction rate is 15% (3÷20=0.15).

At this point, someone might ask, is this so-called extraction formula really reliable? What kind of coffee tastes good under this formula?

In fact, the answer to this question has long been known. In the 1950s, the American Coffee Brewing Research Institute verified that the most ideal extraction rate is between 18-22%. When the extraction rate is less than 18%, it is considered to be insufficiently extracted coffee, and the coffee tastes sour; when the extraction rate is greater than 22%, it is considered to be over-extracted, and the coffee tastes bitter and has a burnt taste. It can be seen that controlling the extraction rate of coffee can achieve the production of coffee with different flavors.

So how can we control the extraction of coffee? Scientists have derived a program model to adjust the extraction rate and help make delicious coffee.

Coffee Extraction

(Image source: pixabay.com)

Using mathematical models to help make delicious coffee

The research team, which included mathematicians, chemists, material scientists and baristas, created a mathematical model to simulate real coffee brewing conditions. They created a specific model of the ground coffee device, which contains thousands of coffee particles and the water used to brew the coffee.

Since there are many coffee particles and their arrangement is complex, the researchers repeated the simulation equation millions of times through mathematical calculations, and continuously poured water into the process to simulate the real conditions of brewing coffee. The mathematical model is used to predict how much solid coffee will eventually dissolve in water, that is, the extraction rate of coffee.

Diagram of the geometry of an espresso basket

(Image source: Reference 1)

By solving a series of equations, they found that the constructed model can accurately predict the extraction rate of coffee in real life. They imagined that when the coffee particles are large enough, water will flow through the coffee particles quickly; when the coffee is ground finer, the specific surface area of ​​the smaller particles will be larger, and the larger specific surface area means that there will be more contact area with water, so the substance can be extracted quickly. But in fact, when the coffee particles are ground too fine, contrary to the assumption, the too fine particles will block the gaps for water flow, thereby hindering the extraction instead of helping the extraction.

The goal of a barista is not only to make delicious coffee, but also to make delicious coffee reproducibly. Therefore, the researchers evaluated the reproducibility of the taste of prepared coffee by measuring the reproducibility of coffee extraction rate under different conditions. The results of mathematical simulation theory show that when the mass of coffee is less, water flows faster in a shallower coffee bed; at the same time, the particles formed when the coffee is coarsely ground are more uniform, the reproducibility of the extracted coffee is better, and it is easier to predict the coffee extraction rate in the constructed simulation equation.

It can be seen that contrary to expectations, in order to repeatedly brew delicious coffee, the barista should reduce the amount of coffee powder used in a single shot and grind the coffee a little coarser. Only in this way can we get highly reproducible delicious coffee.

However, not everyone likes the same coffee taste. Researchers have also designed a series of procedures for this situation. The principle is to mix over-extracted and under-extracted coffee in different proportions to finally prepare coffee with different flavors.

How can I control the degree of extraction at home?

(1) Grinding degree

To a certain extent, the finer the coffee is ground, the larger the surface area, which means better contact with water, more conducive to extraction, and a higher theoretical extraction rate.

Coffee Grinding

(Image source: pixabay.com)

(2) Brewing water volume

When making coffee, water will continue to flow through the coffee bed to complete the extraction. In theory, the more water flows through the coffee, the more ingredients are extracted, and the better the extraction.

(3) Brewing water temperature

The extraction of coffee requires the absorption of energy, and the most common energy source is the heat of water. The higher the temperature, the faster the extraction. It is recommended that the coffee extraction temperature be controlled between 90-92℃.

Coffee

(Image source: pixabay.com)

(4) Pressure when brewing coffee

Pressure also affects the extraction rate of coffee, with more pressure resulting in a higher degree of extraction.

(5) Turbulence of water on the coffee surface

Turbulence refers to the movement of water in the coffee bed when making coffee. When the water flow rate is very high, many small vortices will form in the system and the streamlines will not be clear. The more and larger the turbulence, the higher the degree of extraction.

After reading this article, do you feel that you have learned a lot about coffee? If you are also a coffee lover, use this 92℃ "hot" scientific knowledge to try to make a cup of delicious coffee at home!

Editor: Sun Chenyu

References:

1. Michael I. Cameron, Dechen Morisco, Daniel Hofstetter, et al. Systematically Improving Espresso: Insights from Mathematical Modeling and Experiment. Matter 2, 2020, 631–648.

2. Baggenstoss, J., Poisson, L., Kaegi, R., et al. Coffee roasting andaroma formation: application of different time-temperature conditions. J. Agric. Food Chem. 2008, 56, 5836–5846.

3. Uman, E., Colonna-Dashwood, M., Colonna Dashwood, L., et al. The effect of bean origin and temperature on grinding roasted coffee.2016, Sci. Rep. 6, 24483.4. Ross, CF, Pecka, K., and Weller, K. Effect of storage conditions on the sensory quality of ground Arabica coffee.2006, J. Food Qual. 29, 596–606.

5. Hu Rongsuo, Duan Qizhan, Dong Wenjiang, et al. Preparation and flavor quality characteristics of freeze-dried coffee powder. Journal of Tropical Crops, 2019, 40(8):8.

6. He Hongyan, Liu Guanghua, Wen Zhihua, et al. Preliminary study on factors affecting coffee extraction rate. Guangxi Agricultural Science, 2010, 41(3):2.