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Fresh ground

Fabian Wadsworth and Jamie Farquharson muse on finding Earth science in a coffee cup

Words by Fabian Wadsworth
31 May 2021
Jamie Farquharson

The moka pot can be thought of as a Darcy engine, after Darcy’s Law for fluid flow through porous media.

For Earth and environmental scientists worldwide, COVID-19 has isolated us from the university laboratories and field sites where we would have been working, and lockdowns or post-lockdown restrictions have variably confined us to our homes. These difficult times challenge our ability to deliver both our research and teaching goals.

In work-from-home mode, it has become important to us to find pedagogic opportunities with the materials available to us. Of all the physico-chemical dynamics that can be found in microcosm in a household, we posit that coffee preparation presents an opportunity for direct Earth science application. Coffee-making can be a daily mindful lesson in fluid- and thermodynamics. Could the preparation of coffee at home be a delicious access point for home-schooling and university teaching?

Fluid flow
Reactive fluid flow through porous media is a central theme across Earth, environmental and planetary sciences. The fundamentals can be taught and understood through percolative coffee preparation at home.

Whether you use a French press, a moka pot, pour-over techniques, or an espresso machine, most fresh coffee preparation involves moving hot liquid water through a pack of ground coffee particles, extracting on the way the stuff that makes coffee so potent and delicious. Therefore, fundamentally, coffee preparation techniques involve coupled advection-diffusion processes that are also commonplace throughout the Earth and environmental sciences. From gas exsolving and flowing through pore networks in stiffening magma, to the migration and extraction of oil, gas, water, and geothermal resources in crustal reservoir rocks, from fluid migration and lubrication along faults, to the formation and buoyant migration of melts during mantle melting or planet-scale differentiation. In all cases, coffee-making can be a pedagogic and conceptual access point to understanding these scientific processes.

Reactive fluid flow through porous media is a central theme across Earth, environmental and planetary sciences

The moka pot
We take the moka pot as a case study. After the bottom chamber – an aluminium autoclave not dissimilar to the steel alloy high-pressure autoclaves used in experimental petrology – is part-filled with water and once the metal coffee basket is loaded with loose fine-ground coffee (typically ~ 50 µm radius particles), the pot can be screwed together and sealed, placed onto the stove, and heat can be applied to the base. Some minutes later an over-flowing stream of thick black coffee emerges spilling into the upper collection chamber, ready to be poured.

The ‘magic’ of the moka pot is perhaps that the pressure gradient driving the flow of water is provided by self-pressurisation of the air pocket above the water. Heat from below causes the evaporation of some amount of the water, increasing the mass of gas in the air pocket, which causes the pressure in the fixed gas volume to rise. Once the gas pressure rises sufficiently, it forces the water to be displaced downward, up through the internal spout, and into contact with the base of the ground coffee at sub-boiling temperatures. Water percolates through the tiny spaces between the small coffee particles. The flow is restricted by having to make its way through coffee in what is a ‘permeability limited’ system, which gives it time to cool off slightly. During the time the water is in contact with the coffee, it leaches out caffeine, flavour-compounds, and some solids or colloids from the ground coffee, before emerging into the collection cup at the top.

At a fundamental level, the moka pot could be described as a Darcy engine—after Darcy’s law for viscous fluid flow in porous media. The interested user could vary the grind size of the coffee, the relative volumes of water and gas, and the heating rate, to tune the average contact time between water and coffee particles (being careful to have a working pressure-release valve). Beyond the science, moka pot users are a romantic people who will be fondly familiar with the clackety-clack of the aluminium-on-aluminium as you screw together the top and bottom components of the pot, and the burble and bubble of the so-called Strombolian phase at the end of the brew, signalling that it is ready. What better way to fuel an interest in the way physics and chemistry come together in geoscience, than by making coffee?

By Fabian Wadsworth
Fabian is in the Department of Earth Sciences, Durham University. Fabian is a volcanologist with a passion for coffee. He is excited by the variety and complexity of fluid flow phenomena – in Earth and the kitchen. 

By Jamie Farquharson
Jamie is an experimental and numerical geoscientist with a passion for volcanology. He investigates volcanic processes from the micro- to the macro-scale in order to understand the mechanisms responsible for complex eruptive phenomena observed in nature.

Further reading

• Caine, J.S. et al. (1996) Fault zone architecture and permeability structure. Geology 24, 1025-1028; https://doi.org/10.1130/0091-7613(1996)024<1025:FZAAPS>2.3.CO;2
• Connolly, J.A.D. et al. (2009) Permeability of asthenospheric mantle and melt extraction rates at mid-ocean ridges. Nature 462, 209-212; https://doi.org/10.1038/nature08517
• Gianino, C. (2007) Experimental analysis of the Italian coffee pot “moka”. Am. J. Phys. 75, 43-47; https://doi.org/10.1119/1.2358157
• Manning, C.E. & Ingebritsen, S.E. (1999) Permeability of the continental crust: Implications of geothermal data and metamorphic systems. Rev. Geophys. 37, 127-150; https://doi.org/10.1029/1998RG900002
• Michaut, C. et al. (2013) Eruption cyclicity at silicic volcanoes potentially caused by magmatic gas waves. Nat. Geosci. 6, 856-860; https://doi.org/10.1038/ngeo1928 
• Moroney, K.M. et al. (2015) Modelling of coffee extraction during brewing using multiscale methods: An experimentally validated model. Chem. Eng. Sci. 137, 216-234; https://doi.org/10.1016/j.ces.2015.06.003
• Navarini, L. et al. (2009) Experimental investigation of steam pressure coffee extraction in a stove-top coffee maker. Appl. Therm. Eng. 29, 998-1004; https://doi.org/10.1016/j.applthermaleng.2008.05.014
• Oostrom, M. et al. (2016) Comparison of relative permeability-saturation-capillary pressure models for simulation of reservoir CO2 injection. Int. J. Greenh. Gas Control 45, 70-85; https://doi.org/10.1016/j.ijggc.2015.12.013
• Vasseur, J. et al. (2020) Permeability of polydisperse magma foam. Geology 48, 536-540; https://doi.org/10.1130/G47094.1


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