Adding Up The Perfect Cup

Can understanding the math behind coffee brewing make for a better cup? A team of researchers at the University of Limerick believes it can. All brewing techniques involve some form of leaching via a solid-liquid extraction, but some methods might be able to produce better tasting coffee.

Espresso coffee is made by forcing hot water under high pressure through a compacted bed of finely ground coffee. (b) Drip filter brewing involves pouring hot water over a loose bed of coarser coffee in a filter. In either method, water flows through the bed, leaching soluble coffee components from the grains. Any undissolved solids in the fluid are filtered from the extract as the liquid leaves the filter. (Image courtesy of Kevin M. Moroney.)

By analyzing flow and extraction in a coffee bed and looking at the specifics of extraction mechanisms as they relate to coffee grain properties, the researchers hope to improve their understanding of the influence various parameters have on the final product.

Transfers included in the coffee extraction model (reproduced from Moroney et al, “Modelling of coffee extraction during brewing using multiscale methods: An experimentally validated model,” The diagram shows the transfers of water and coffee which are described by the coffee extraction model presented in the published research. (Image courtesy of Kevin M. Moroney.)

In previous models, the researchers considered factors such as coffee bed dimensions, flow rates, grind size distribution and pressure drop, while assuming a constant temperature and homogeneous coffee bed properties, regardless of water saturation. Although they determined this model to be mathematically complete, it might have been unnecessarily complicated.

That’s why the new research focuses on simplified equations to capture the essence of the process, while still considering brew ratio, brewing time, water quality and temperature, grind size and distribution, and extraction uniformity.

Location of coffee in the bed: The coffee bed consists of (intergranular) pores and grains. (Image courtesy of Kevin M. Moroney.)

This allows the researchers to recognize the most important parts of the equations that predict coffee quality for specific brewing configurations. By incorporating the changing shape of the coffee bed which occurs through the cone-shaped filter of most drip machines, the researchers can determine how position impacts the extraction and flow rate of the brew.

The authors recently published their findings in the SIAM Journal on Applied Mathematics, with the goal of inspiring further research on extraction processes, and aiding coffee lovers the world over in their quest for the perfect cup.

To learn about some coffee that’s truly out of this world, find out how Italy sent an espresso machine into space.