posted on 2023-03-03, 11:34authored byKevin M. Moroney, William T. Lee, STEPHEN O'BRIENSTEPHEN O'BRIEN, Freek Suijver, Johan Marra
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.
History
Publication
Siam Journal on Applied Mathematics;76 (6), pp. 2196-2217
Publisher
Society for Industrial and Applied Mathematics
Note
peer-reviewed
Other Funding information
SFI
Language
English
Also affiliated with
MACSI - Mathematics Application Consortium for Science & Industry