science of coffee extraction

In a drip filter machine the brewing process consists of three stages.

Initially in the filling stage, hot water is poured on the dry coffee grounds and begins to fill the filter, but doesn’t leave.

In the steady state stage the bed is saturated, water is still entering the filter, but also
leaving at the same rate.

Finally in the draining stage no more water enters the bed but still drains out. Only the steady state stage is considered in this study.

grind size:

"The really surprising thing to us is that there are really two processes by which coffee is extracted from grains.

“Initially, the concentration of coffee in the bed is determined by the balance between a rapid extraction from the surfaces of coffee grains and the rate at which coffee is removed from the coffee bed by the extracting water. Later in the process, the extraction is dominated by slow diffusion of coffee from the kernels of larger grains, which was initially negligible.”


It had previously been known that grinding beans too finely could result in coffee that is over-extracted and very bitter. On the other hand not grinding them enough can make the end result too watery.

"What our work has done is take that [observation] and made it quantitative," said Dr Lee.
"So now, rather than just saying: 'I need to make [the grains] a bit bigger', I can say: 'I want this much coffee coming out of the beans, this is exactly the size [of grain] I should aim for."

The researchers are now looking at the shape of the coffee bed in drip filter machines.
"The shape of the coffee bed is deformed as you brew the coffee. When it goes in first, it's sitting flat at the bottom of the filter, but at the end of [brewing] it's coating the walls of the filter. This also seems to play a role in how the coffee tastes," said Dr Lee.

"That would allow us to address another degree of freedom: how exactly you put the water in. Do you put it in as a single jet down the centre, like water pouring out of a tap? Or do you use something more like a shower head, where it's dripping down from lots of places. Those would have different effects in disturbing the coffee bed."


In a follow-up email, Lee told GeekWire that the findings suggest a French-style coffee press might result in a more refined brew, “in that you have more control over the length of time the coffee spends in contact with the water.”


1) Asymptotic Analysis of the Dominant Mechanisms in the Coffee Extraction Process.
 SIAM Journal on Applied Mathematics, 2016

2) Modelling Extraction and Transport of Coffee during Brewing
 Kevin M. Moroney, William T. Lee, Stephen B.G. O’Brien, Freek Suijver, Johan Marra
MACSI, Department of Mathematics and Statistics,
University of Limerick, Ireland.
kevin.moroney@ul.ie
Philips Research, Eindhoven, The Netherlands

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