About making coffee

by Tytus D. Suski

Apparently making coffee is quite simple a task. However, just as popular tea bags coexist with noble, refined tea infusions from China, India or Japan, there are several methods for giving a cup of coffee all the aroma that can satisfy even the most refined taste.

Most often a pressure expresso is used. The search for the fullest fragrance still going on and experimental research in this area having reached its limits, the need for a mathematical model of processes occurring during coffee percolation became quite clear. Due to such models it would be possible to search for optimal percolation parameters using computer simulations, without as much expense as real-life experiments require.

But then, the whole thing is not as simple as it seems. The quality of the coffee depends on the ratio between the amount of liquid and the amount of aromatic substances it contains. The latter in turn depends on the velocity of the flow, characterised by the pressure p and the permeability of the coffee layer. The pressure being constant in an expresso, permeability decreases very quickly, and eventually the flow q stabilises at some level q0 (lower than the initial one). Surprisingly, compression due to the pressure is not the only cause: more important is the fact that tiny particles detached from the structure settle on the filter, where they form a thin, very tightly packed layer. Therefore higher pressure does not necessarily make the filtration process quicker (see below):

To make the picture more complex, you should add to it the boiling water penetrating the still dry coffee powder, chemical reactions provoked by the temperature (of about 95oC or 200oF) that set aromatic substances free, and diffusion in a porous structure.

Each of these phenomena is difficult to describe by itself, and considered jointly they are indeed a serious (and basically still open) challenge, both in the choice of appropriate equations and in their solution. It may be interesting to add that the equation of porous media, so interesting for the Italians because of its relation to making coffee, is also useful for the Dutch in modelling water percolating through a dam.