Drinking coffee is a practice spread worldwide irrespective of race, age, and social extraction, and this makes coffee the leading commodity in the fair trade movement. For most people however, computational modelling, or coffee-in-silico is the furthest thing from their mind when sipping on their first coffee of the day. Dr Giacomini's research into mathematical modelling of extractions shows us that maths can be used to gain a better understanding of the coffee in our cups.
The power of coffee is that it can be functional, social, and healthy. For instance, it can resolve a headache, it usually aids concentration after a poor night’s sleep, and keeps you up when it is not time for sleeping. It is the deserved break during work that sometimes leads to new ideas or opportune meetings at the coffee machine. It is the best excuse to persuade a friend to meet. In addition, its daily consumption can yield scientifically proven health benefits (Preedy, 2015). For sure, the attractive and complex flavours of coffee are unmistakable and add to coffee’s in-filtration into our everyday lives.
In this relaxing and pleasant scenario, how can one imagine including Mathematics? By popular definition, mathematics is one of the most tortuous, unrestful and unsociable subjects one can think about (we appreciate there are individuals who might take exception to this!). The best quality of mathematics is to be curious and, consequently, ask how and why phenomena occur.
Scientific research into coffee’s health and social characteristics has been stimulated over the last few decades. In particular, a large variety of studies in Food Chemistry relating to coffee brewing. More recently, some studies focused on the mathematical modelling of coffee extraction have been developed (Moroney, 2016; Cameron, 2020; Giacomini, 2020). In fact, a key component of coffee research is an in-depth knowledge of the physical and chemical processes occurring during coffee preparation. Such knowledge comes from an in-depth analysis of the phenomenon under consideration. It starts from the observation of the real coffee extraction and the identification of some reasonable approximations in order to simplify the process by neglecting some minor details. Then, using the abstraction that is proper to mathematical investigations, a set of equations is obtained: this is called a model. The model represents the extraction equipment, e.g., the coffee machine and the grinder, as well as the barista skills, and recipe . It thus allows making an ‘in-silico’ coffee that virtually shows almost the same characteristics of the coffee in cup [an in silico experiment is one performed on computer or via computer simulation. The phrase is pseudo-Latin for "in silicon", referring to silicon in computer chips WIkipedia.] . Moreover, a model has the great advantage of being able to repeatedly make coffee for study purposes, under the same extraction conditions or new ones, without wasting materials from the real extractions.
Returning to our aim, we can describe in detail the extraction of the espresso coffee and start the construction of a proper model. Firstly, we should identify the main processes occurring during the extraction and, even before, what are the main elements involved. Water, roast and ground coffee are in the spotlight. Water is the carrier liquid that allows the whole extraction (Illy and Viani, 2005). As usual in traditional brewing, water is hot at about 93°C. In espresso extraction, water hits coffee with high pressure, at about 9 bar. Roast and ground coffee is the material that undergoes extraction and, for the espresso, it shows an essential feature: it must be tamped into the filter basket in order to be sufficiently compact and, at the same time, leave some void spaces among the coffee grains. The compactness is necessary to offer a sufficient resistance to the pressurised water impact; on the other hand, the void portion is unavoidable to create water flow into the ground coffee powder (Illy and Viani, 2005). Such void spaces are called pores and this feature conveys the technical name for the coffee in the filter basket: porous medium. Now, how do these elements interact during the extraction? Pressurised hot water enters the basket filled with the roast and ground coffee suitably tamped; the water flows through the void spaces among coffee grains and it dissolves various chemical substances from the wetted coffee grains; at the same time, the water also removes some amount of fine particles from the coffee powder, as shown in Figure 1.
Figure 1. Coffee in-silico physico-chemical processes
The previous phases are translated into these main physico-chemical processes:
• the fluid flow within the porous medium that mainly consists of water;
• the dynamics, namely the behaviour, of the dissolved chemical compounds and oily substances extracted by the warm fluid from the porous medium, which undergo dissolution and transport processes;
• the dynamics of the fine particles removed by the fluid from the porous medium, which undergo erosion and transport processes;
• the changing of the porous medium due to dissolution and erosion;
• the heat exchange between the fluid and the porous medium.
This rigorous description of the coffee extraction is referred to as the percolation of a fluid in a porous medium. The percolation also describes similar phenomena in other fields, like hydrogeology, where a widely studied phenomenon of percolation is the water infiltration in soils with transport of contaminants.
Finally, when dealing with a fluid flow, Fluid Dynamics deserves a mention. As suggested by the name itself, Fluid Dynamics is the discipline that studies fluids in movement. Mathematicians, physicists and engineers apply it in their studies, and we will use it to formulate a percolation model. Fluid Dynamics creates the thrust on the wings of an aircraft that permits it to fly, or allows a wind turbine to slow down and stop, or makes a football player score directly from the corner kick. Thus, among these surprising things, why not take advantage of Fluid Dynamics to prepare an equally astonishing in-silico coffee?
Dr. Giacomini has a PHD in Applied Mathematics and is a Post Doctoral Researcher at the University of Camerino. Her main research interests are Fluid Dynamics models for the study of real-life problems.
Preedy, V. R. (Ed.). (2015). Coffee in health and disease prevention. Academic Press.
Moroney, K. M., et al. (2016). Coffee extraction kinetics in a well mixed system. J. Math. Ind. 7.1. doi: 10.1186/s13362-016-0024-6.
Cameron, M. I., et al. (2020). Systematically Improving Espresso: Insights from Mathematical Modeling and Experiment. Matter 2.3: 631-648. https://doi.org/10.1016/j.matt.2019.12.019.
Giacomini, J., et al. (2020). Water flow and transport in porous media for in-silico espresso coffee. International Journal of Multiphase Flow, 126, 103252. https://doi.org/10.1016/j.ijmultiphaseflow.2020.103252
Illy, A., Viani, R. (2005). Espresso Coffee: The Science of Quality. Academic Press.
Complimenti! Ottima e rigorosa descrizione della perculazione del caffè Quindi, tra queste cose sorprendenti, perché non sfruttare la Fluid Dynamics per preparare un caffè in-silico altrettanto sorprendente?
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