Coffee extraction kinetics in a well mixed system
Open accessAbstract
The extraction of coffee solubles from roasted and ground coffee is a complex operation, the understanding of which is key to the brewing of high quality coffee. This complexity stems from the fact that brewing of coffee is achieved through a wide variety of techniques each of which depends on a large number of process variables. In this paper, we consider a recent, experimentally validated model of coffee extraction, which describes extraction from a coffee bed using a double porosity model. The model incorporates dissolution and transport of coffee in the coffee bed. The model was shown to accurately describe extraction of coffee solubles from grains in two situations: extraction from a dilute suspension of coffee grains and extraction from a packed coffee bed. The full model equations can only be solved numerically. In this work we consider asymptotic solutions, based on the dominant mechanisms, in the case of coffee extraction from a dilute suspension of coffee grains. Extraction in this well mixed system, can be described by a set of ordinary differential equations. This allows analysis of the extraction kinetics from the coffee grains independent of transport processes associated with flow through packed coffee beds. Coffee extraction for an individual grain is controlled by two processes: a rapid dissolution of coffee from the grain surfaces in conjunction with a much slower diffusion of coffee through the tortuous intragranular pore network to the grain surfaces. Utilising a small parameter resulting from the ratio of these two timescales, we construct asymptotic solutions using the method of matched asymptotic expansions. The asymptotic solutions are compared with numerical solutions and data from coffee extraction experiments. The asymptotic solutions depend on a small number of dimensionless parameters, so the solutions facilitate quick investigation of the influence of various process parameters on the coffee extraction curves.
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Recent studies have established that particle size, size distribution, and coffee packing bed are parameters that affect and determine diffusion of solids during coffee extraction.
“Recent studies have established that particle size, size distribution, and the coffee packing bed are parameters that affect and determine the diffusion of solids during the coffee extraction process48–50.”
From Effect of grinding, extraction time and type of coffee on the physicochemical and flavour characteristics of cold brew coffee (2019) · cites this paper as [49]
The General coffee extraction model section (page not provided) says grain-size distribution affects surface area, flow and extraction. The Introduction (page not provided) distinguishes diffusion from transport through a packed bed and says this paper analyzes a well-mixed suspension, not packed-bed extraction. It therefore does not establish that coffee-bed packing determines diffusion of solubles. (LLM, conf=0.84)
Experimental — accuracy not yet measuredThe results of this study validate earlier models proposed by Moroney et al. and Spiro and Seldwood and extend their findings into cold brew extraction over long time periods.
“The results of this study validate earlier models proposed by by Moroney et al.35,45 and Spiro and Seldwood52 and extend their findings into cold brew extraction over long time periods.”
From The Effect of Time, Roasting Temperature, and Grind Size on Caffeine and Chlorogenic Acid Concentrations in Cold Brew Coffee (2017) · cites this paper as [35]
Mathematical modeling of coffee extraction proposed by Moroney et al. suggested that the diffusion of coffee from the intragranular pores to the intergranular pores is the rate limiting process.
“Mathematical modeling of coffee extraction proposed by Moroney, et al.35,45 suggested that the diffusion of coffee from the intragranular pores to the intergranular pores is the rate limiting process.”
From The Effect of Time, Roasting Temperature, and Grind Size on Caffeine and Chlorogenic Acid Concentrations in Cold Brew Coffee (2017) · cites this paper as [35]
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- Authors
- Moroney, K. M., Lee, W. T., O’Brien, S. B., Suijver, F., & Marra, J.
- Affiliations
- University of Limerick (IE)
- Philips (Netherlands) (NL)
- Corresponding author
- Moroney, Kevin M
- Venue
- Journal of Mathematics in Industry
- Published
- 2016-06-30
- Volume
- 7
- Issue
- 1
- Pages
- 3-3
- ISSN
- 2190-5983 (ISSN-L)
- PMC
- PMC4986356
- OpenAlex
- W2473305965
- Cited by
- 44
- References
- 25
- Citations by year
- 2026: 1 · 2025: 3 · 2024: 6 · 2023: 5 · 2022: 6 · 2021: 10 · 2020: 2 · 2019: 5 · 2018: 2 · 2017: 3 · 2016: 1
- FWCI
- 2.97
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Locations
- Journal of Mathematics in Industry (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- University of Limerick Institutional Repository (University of Limerick) (acceptedVersion, cc-by-nc-sa)
- University of Limerick Institutional Repository (University of Limerick) (acceptedVersion, other-oa)
- Arrow@dit (Dublin Institute of Technology) (submittedVersion, cc-by-nc-sa)
- Figshare (submittedVersion, cc-by-nc-sa)
- University of Limerick Institutional Repository (University of Limerick)
- Funders
- Science Foundation Ireland (IE) (12/IA/1683)
- Topics
- Health Sciences › Medicine › Pharmacology › Coffee research and impacts
- Physical Sciences › Engineering › Computational Mechanics › Heat and Mass Transfer in Porous Media
- Physical Sciences › Mathematics › Numerical Analysis › Differential Equations and Numerical Methods
- Keywords
- coffee extraction, extraction kinetics, dual-porosity model, dissolution, matched asymptotic expansions, coffee brewing, time-scale separation
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