Uneven extraction in coffee brewing

A recent experiment showed that, contrary to theoretical predictions, beyond a cutoff point, grinding coffee more finely results in lower extraction. One potential explanation for this is that fine grinding promotes non-uniform extraction in the coffee bed. We investigate the possibility that this could occur due the interaction between dissolution and flow promoting uneven extraction. A low dimensional model in which there are two possible pathways for flow is derived and analyzed. This model shows that, below a critical grind size, there is a decreasing extraction with decreasing grind size as is seen experimentally. This is due to a complicated interplay between an initial imbalance in the porosities and permeabilities of the two pathways in the model, which is increased by flow and extraction, leading to the complete extraction of all soluble coffee from one pathway.