Asymptotic Analysis of the Dominant Mechanisms in the Coffee Extraction Process
Open accessAbstract
Extraction of coffee solubles from roast and ground coffee is a highly complex process, depending on a large number of brewing parameters. We consider a recent, experimentally validated, model of coffee extraction, describing extraction from a coffee bed using a double porosity model, which includes dissolution and transport of coffee. It was shown that this model can accurately describe coffee extraction in two situations: extraction from a dilute suspension of coffee grains and extraction from a packed coffee bed. Despite being based on some simplifying assumptions, this model can only be solved numerically. In this paper we consider asymptotic solutions of the model describing extraction from a packed coffee bed. Such solutions can explicitly relate coffee concentration to the process parameters. For an individual coffee grain, extraction is controlled by a rapid dissolution of coffee from the surface of the grain, in conjunction with a slower diffusion of coffee through the intragranular pore network to the grain surface. Extraction of coffee from the bed also depends on the speed of advection of coffee from the bed. We utilize the small parameter resulting from the ratio of the advection timescale to the grain diffusion timescale to construct asymptotic solutions using the method of matched asymptotic expansions. The asymptotic solutions are compared to numerical solutions and data from coffee extraction experiments. The asymptotic solutions depend on a small number of dimensionless parameters and so are useful to quickly fit extraction curves and investigate the influence of various process parameters on the extraction.
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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 [48]
Section 2.4 defines the grain-diffusion timescale using grain-size measures, supporting the particle-size and size-distribution aspects of the claim. It places bed porosity and bed height in the surface-dissolution or advection timescales, not the grain-diffusion timescale; the claim therefore overstates the packed bed’s role in diffusion specifically. Page numbers are unavailable in our copy. (LLM, conf=0.84)
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Cites
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Coffee extraction kinetics in a well mixed system
Moroney, K. M., Lee, W. T., O’Brien, S. B., Suijver, F., & Marra, J. (2016) · Journal of Mathematics in Industry · doi:10.1186/s13362-016-0024-6 · Cited by 44 · see citing works
Self-citation
- Authors
- Moroney, K. M., Lee, W. T., Brien, S. B. G. O., Suijver, F., & Marra, J.
- Affiliations
- University of Limerick (IE)
- Venue
- SIAM Journal on Applied Mathematics
- Published
- 2016-01
- Volume
- 76
- Issue
- 6
- Pages
- 2196-2217
- ISSN
- 0036-1399 (ISSN-L)
- 1095-712X
- OpenAlex
- W2551587219
- Cited by
- 24
- References
- 14
- Citations by year
- 2025: 2 · 2024: 2 · 2023: 2 · 2022: 2 · 2021: 2 · 2020: 2 · 2019: 8 · 2018: 1 · 2017: 2 · 2016: 1
- FWCI
- 4.27
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- SIAM Journal on Applied Mathematics (publishedVersion)
- Arrow@dit (Dublin Institute of Technology) (acceptedVersion)
- University of Limerick Institutional Repository (University of Limerick) (acceptedVersion, cc-by-nc-sa)
- Figshare (submittedVersion, cc-by-nc-sa)
- University of Limerick Institutional Repository (University of Limerick) (submittedVersion, cc-by-nc-sa)
- University of Limerick Institutional Repository (University of Limerick)
- Funders
- Science Foundation Ireland (12/IA/1683)
- Topics
- Physical Sciences › Mathematics › Numerical Analysis › Differential Equations and Numerical Methods
- Physical Sciences › Engineering › Computational Mechanics › Heat and Mass Transfer in Porous Media
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Advanced Mathematical Modeling in Engineering
- Keywords
- coffee extraction, dual-porosity model, asymptotic analysis, matched asymptotic expansions, surface dissolution, advection, extraction curves, coffee brewing
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