☕ An equation for the perfect espresso

Brewing an espresso often relies on a succession of trials. Baristas adjust grind fineness and coffee quantity to obtain a precise flow rate. This flow determines the contact time between water and grounds, directly influencing the intensity and balance of flavors.


To move beyond this empirical approach, researchers examined the internal structure of the puck. Two coffees, from Rwanda and Colombia, were ground to eleven different particle sizes. Each sample was then analyzed using X-ray tomography, producing detailed three-dimensional maps.

These images reveal a network of pores, the tiny spaces between the particles. Some form continuous pathways allowing water to flow, while others remain isolated. The distribution of these passages determines how the liquid moves through the coffee.

The scientists quantified the proportion of these connected pores. This approach, from physics, describes fluid flow in fragmented media. Here, it makes it possible to identify areas where water flows freely or becomes trapped.


The resulting model links permeability to several factors: average grain size, total exposed surface area, and degree of compaction. The more connected pores there are, the easier the water flows, reducing extraction time and modifying the aromatic profile.

The authors indicate that their results closely match theoretical predictions. Their equation thus offers a practical way to anticipate the effect of a grinder setting or tamping pressure, without relying solely on empirical experience.

Some phenomena, however, remain to be explored. Coffee grounds swell upon contact with water, changing the puck's internal structure during extraction. This aspect could further refine the model's predictions.

Ultimately, this work could inspire machines capable of automatically adjusting their parameters. Without replacing human expertise, it paves the way for a more consistent and controlled espresso preparation.