A model for the permeability of coffee pucks validated using X-ray computed micro-tomography

Tuning the permeability of beds of ground coffee is central to making good espresso. Here, we develop a theoretical framework for such a permeability model, which depends principally on the pore volume fraction that is connected between the grains φ_p and the specific surface area of the interfaces between liquid and coffee grains, s. We test our theoretical predictions by using lattice-Boltzmann simulations of fluid flow through three-dimensional domains obtained via X-ray computed micro-tomography (XCT) of real packed ground coffee. Our tomography is performed on two different roasted coffees (‘Tumba’ from Rwanda and ‘Guayacán’ from Colombia) ground to one of 11 grind settings using a Mahlkönig grinder, ranging from very fine to coarse grinds. We find excellent agreement with our percolation theory, suggesting a practical way to relate grind size and packing fraction to the specific surface area to predict coffee permeability. We discuss this model in the context of optimal espresso recipe design and the effects of coffee dose to define a Forchheimer number that can be used to predict the onset of inertial flow in coffee.