Espresso Brewing
: Mathematical Modelling and Experiment

Student thesis: Doctoral Thesis


This work focuses on the development of a multi-scale model for the extraction and transport of coffee solubles in espresso. The motivation behind this research stems from the increasing demand for coffee, the desire to improve quality and flavours, and the need for sustainability in the face of potential supply deficiencies. The novelty of the model is in capturing liquid infiltration and flow through a packed bed of ground coffee, as well as coffee solubles transport (both in the grains and in the liquid) and solubles extraction. During infiltration, a sharp interface separates the dry and wet regions of the bed. A matched asymptotic analysis based on fast extraction rates, fast diffusion in the finer particles and slow diffusion in the liquid, reveals that the bed can be described by four time-varying asymptotic regions: a dry region yet to be infiltrated by the liquid, a region in which the liquid is saturated with solubles and very little extraction occurs, a slender region in which solubles are rapidly extracted from small grains, and a region in which slower ex- traction occurs from large grains. The analysis yields a reduced model that elucidates the rate-limiting physical processes. Numerical solutions of the reduced model are compared to those to the full model, demonstrating that the reduced model is both accurate and significantly cheaper to solve. Experimental data on time-resolved concentration is collected by measuring the amount of total dissolved solids (TDS) of an espresso shot split into multiple samples during brewing with the help of a rotating sampler. The data sup- ports the suggested formation of a saturation region in the bed and is used to validate the predictive capabilities of the reduced model. The work in this thesis improves the understanding of coffee extraction in espresso brewing through mathematical modelling and experiment which may ultimately aid to optimize extraction, reduce waste, and support baristas in producing consistently high-quality coffee.
Date of Award8 May 2024
Original languageEnglish
Awarding Institution
  • University of Portsmouth
SupervisorJamie Foster (Supervisor), Marianna Cerasuolo (Supervisor) & Andrew Osbaldestin (Supervisor)

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