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 analysed. This model shows that, below a critical grind size, there is a decreasing extraction with decreasing grind size as is seen experimentally. In the model this is due to a complicated interplay between an initial imbalance in the porosities and permeabilities of the two pathways which is increased by flow and extraction, leading to the complete extraction of all soluble coffee from one pathway.
Comment: 6 pages, 9 figures. Ancillary files: octave and wxMaxima code to derive and nondimensionalise model, solve it numerically and generate latex tables and figures. Accepted for publication in Physics of Fluids