Systematically Improving Espresso: Insights from Mathematical Modeling and Experiment

Abstract

Coffee extraction performed in an espresso machine is a process that depends on a delicate interplay between grind setting, coffee mass, water pressure and temperature, and beverage volume. Using a mathematical model based on the transport of solubles through a granular bed, paired with cafe-setting experiments, we elucidate the origin of inconsistencies in espresso production. Informed by the model, a protocol is proposed to systematically reduce coffee waste and beverage variation, resulting in highly reproducible shots.

An equilibrium desorption model for the strength and extraction yield of full immersion brewed coffee

“…(11) into Eq. ( 17) yields E = KE max , i.e., expressions (15) and (17) are self-consistent. Because the TDS is readily measured experimentally, Eq.…”

“…Melrose et al introduced a simpler “base model” for coffee brewing through a packed bed of coffee grains to generate TDS and extraction yields versus brew parameters 16 . Most recently, Cameron et al developed a detailed model for espresso extraction with the assumption of homogeneous flow through the coffee bed, yielding predictions for how to increase the extraction yield 17 .…”

An Equilibrium Desorption Model for the Strength and Extraction Yield of Full Immersion Brewed Coffee

“…4). These data points involved only mass measurements of the grounds before brewing and after oven-drying, as per equation (17). As expected, increased with the brew ratio, then plateaued around 20%, where it approached the values of the equilibrium .…”

“…The mass of the dried coffee grounds was obtained by subtracting the masses of the beaker and filter paper, each measured prior to coffee brewing. Then, was calculated using equation (17). The retention ratio was calculated as per equation 23from the measured TDS and the mass measurements of water, fresh coffee grounds before brewing, and liquid coffee beverage after filtration.…”

“…Melrose et al introduced a simpler "base model" for coffee brewing through a packed bed of coffee grains to generate TDS and extraction yields versus brew parameters 16 . Most recently, Cameron et al developed a detailed model for espresso extraction with the assumption of homogeneous flow through the coffee bed, yielding predictions for how to increase the extraction yield 17 .…”